Population and Community Ecology

Lecture Notes

Barnard College

Dr. James A. Danoff-Burg


Module 1: | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |

Module 2: | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |

Module 3: | 17 | 18 | 19 | 20 | 21 | 22 |




Lecture 1 –


  • Purpose of Ecology (Jonathan Krebs, 1972): To determine the factors that have produced the present distribution and abundance of organisms
  • Contrast popular conceptions of ecology versus scientific definition
  • Some "Ecological Taxonomies" :
    • Ecological Hierarchy
      • Individual
      • Population
      • Community
      • Ecosystem
      • Biome
      • Biosphere
    • Mode of Inquiry (know the goals and drawbacks of each)
      • Descriptive
      • Functional
      • Evolutionary
    • Types of Explanation
      • Proximate explanations
      • Ultimate explanations
    • Types of Data and Location of Study (in decreasing order of rigor, but increasing order of relevance to the natural world)
      • Theoretical
      • Laboratory
      • Field
  • Scientific Method
    • Science does not prove things
    • We can only support or disprove hypotheses
    • A sample scientific process (often called the Hypothetical-Deductive Method)
      • Observation
      • Explanatory idea
      • Creation of testable hypotheses
      • Creation of predictions
      • Design of experiment
      • Conduct experiment
      • Evaluate alternative hypotheses, leaving only one
      • Repeat this many times
      • If needed, modify best hypothesis and retest
      • If one hypothesis continues to not be rejected, then we consider the hypothesis a theory
      • Theory is the best supported idea to explain a natural phenomenon
    • Types of Hypotheses: Null (abbreviated Ho), Alternative Hypotheses (abbreviated H 1, H2, etc.)



Lecture 2 –

Diversity of Life & Natural Selection


James A. Danoff-Burg

Population & Community Ecology

Barnard College


Today’s Agenda

•Evolutionary ecology

•Power of evolutionary explanations

•Variation originates naturally

•Hardy-Weinberg equilibrium



Evolutionary Ecology


–using historical ecological, evolutionary, or systematic data to explain current ecological trends

Example: Penguins are only in the Southern Hemisphere - Why?
Functional explanation:

–food is not present elsewhere, constrains their location
Evolutionary explanation:

–phylogeny indicates that all related lineages have only existed in the Southern Hemisphere

–This is a more elegant explanation, explains more data

–also if it is supported, it obviates the need for the Functional explanation

Example II: Desert Pupfishes in Death Valley

•(also at this link and at this link)
Functional explanation:

–fish are specialists in the ponds in which they live
Evolutionary explanation:

–found there because of historical lake that became subsequently dried up,

–leaving isolated ponds that were all spring fed

•Again, Evolutionary is a simpler and more elegant explanation

Functional vs. Evolutionary explanations

•Many argue that if an evolutionary explanation is not disproven

–(speaking in double negatives, as is the norm in the scientific method),

•then it should be the first explanation adopted

–Before even exploring functional answers

Power of Evolutionary Explanations

•These explanations best explain the greatest amount of data in the most elegant manner

How variation originates in nature

•Point mutations


–leading to transcription errors


–leading to frameshift errors


–leading to frameshift errors

•Chromosomal rearrangements

–normal crossing over

–during Prophase I of meiosis


Most mutations are deleterious

•only 1 in 1,000 are beneficial
All of us have mutations in our body

–are continually created,

–something on the order of 1 in every 100,000 sex cells have some type of point mutation in them

Hardy-Weinberg Equilibrium
Explains why variation continues in a population
acts as a null hypothesis when testing for changes in the population


•two alternative alleles of a single trait

• P and Q

•p and q will substitute for the frequencies of each allele in the population

•p = 1 - q and q = 1 - p

Equation for diploid organisms

•1 = (p + q)2 = (p + q)(p + q) = p2 + 2pq + q2 = 1

•p2 determines the frequency of the PP genotype

•2pq determines the frequency of the PQ genotype

•q2 determines the frequency of the QQ genotype

Assumptions of H-W equilibrium

•huge populations
random mating
no immigration or emigration
no selection
no mutation

•these are violated when change is occurring in a population


An Exercise

•Determine the frequencies of each handedness allele for our in-class population

–assuming that individuals with either a PP or PQ will be right handed

–Lefties are only obtained by QQ


Selection and Speciation

•Violations of the Hardy-Weinberg Equilibrium can be produced by selection, drift, and/or other mechanisms

•These violations can produce longer-term evolutionary changes
Violations include:

•Breeding restrictions

–assortative mating, inbreeding)

•Population size

–(small populations, genetic bottlenecks [more on this later in term])

•Population demographics

–(what proportion of the population that remains can breed in the future?)


–(could introduce or remove novel alleles into a population)

Natural Selection

•First published by Charles Darwin and Alfred Russel Wallace in 1859

•Interesting historical story

–Darwin, the landed gentry

–Wallace, the lower-class striver


Darwin vs. Darwin (& Lamarck)

•incidentally, Darwin did NOT propose the idea of evolution

•do not confuse evolution with natural selection

–Evolution: as observed a scientific "fact", as we have

–Natural Selection: one of the mechanisms through which evolution can occur

•Darwin’s grandfather (Erasmus Darwin)

–was an early proponent of evolution

•Lamarck: Not the loser we paint him as


Proposed based on five observations

•variation exists in nature

•food and resources are limited

•organisms tend to out-reproduce their resources

•competition exists

•differential reproduction results

–leads to some lineages contributing more to the next generation than others

–Differential reproduction = natural selection

Nifty Darwinian Fact

•never in the Origin of Species did Darwin talk about the origin of species

–he was only interested in documenting the above five observations

–Never talked about the production of new species



#3 - The Beginning and the End of Species:
Selection, Speciation and Extinction


James A. Danoff-Burg

Population & Community Ecology

Barnard College


Types of Selection


–selection against one extreme or the other

•Stabilizing or Normative

–selection against both extremes


–selection against the mean

Selection Types




–the production of new species

•Two General Types of Speciation


•speciation that arises as a consequence of separation of a population


•speciation that arises within the normal cruising or home range of a species,

•usually through some sort of behavioral or ecological change,

•often as a consequence of symbiotic relationships

Speciation Types


Extinction and Speciation:
Intimately Related

•Produced from same events

–The same processes that could lead to a speciation event could lead to an extinction event

–Isolation, reduction in population sizes, strong selection pressures, etc.

•The latter is more common

–More populations go extinct than produce new species

–Similar to the number of favorable vs. disfavorable mutations

Thought experiment:

•How would each of the 5 H-W equilibrium assumptions be violated if a population were to go to extinction?

•Think this through


•We are in the throes of an extinction event that may be every bit as large as the very largest extinctions in the geological past,

–including the K-T extinction and the one at the Permian-

–Triassic boundaries


Individual Selection

•The individual is who lives and dies

–Not the species – they only disappear or explode locally

•Natural selection acts solely on the level of the organism

–Most commonly accepted explanation of how evolution works

•Not at the level of





–Other higher-level taxa

Individual Fitness

•Individual selection is the most commonly accepted mechanism of natural selection

•currency: individual fitness


–proportional contribution of that individual to the next generation

–only relative to other individuals in the population, not an absolute value


•Essence of our current understanding of natural selection

•Hasn’t always been such

–Historically, altruism and group selection were thought to also work differently from individual selection

•Altruism: reduce your fitness for another individual (usually relation)

•Group Selection: reduce your fitness for the good of the group

–Both were popular until the 70s

–Can they be explained using individual selection?

Individual explanations for Altruism

•Simple individual fitness would not predict altruism

–At least as how it was originally constructed

–Focused exclusively on the individual

•Individual selection modifications that WOULD explain altruism

–Inclusive fitness

•J.B.S. Haldane, the monks, and your drowning brothers

–Reciprocal altruism

•Most commonly found in long-lived groups


Individual Explanation for Group Selection

•Group Selection Definition:

–selection above the level of individuals

–Popular in the recent past as a way to explain why altruism occurs

•Currently thought of as an untenable idea

–At least as how it has been created and used

•Individualized Explanations:

–Inclusive fitness

–Reciprocal altruism


Resuscitating the Superorganism

•David Sloan Wilson, Eliot Sober, and others are trying to resuscitate the idea of group selection

•Using structured populations

•Definition of Structured populations

–A large group that is divided into smaller cohesive groups

–Each of which have a different selective values within and between the levels of group

–The groups compete against other groups at the same level of hierarchy

•Selection above the level of the individual


Examples of Superorganisms

•social insects

•cellular slime molds

•Common feature:

–relies on emergent properties that come about as a consequence of these groups

–Emergent properties are those that only exist above the individual – usually at the group level

–Example: Foraging patterns of army ants, fruiting body in cellular slime molds

•Both are produced only because of a collaboration between many individuals


Favored Ecological Settings

•Common environmental features that encourage species to act cooperatively

–Environment is divided into patches

–Patches are ephemeral (relative to the life cycle of the species undergoing group selection)

–Low migration

–Patches are colonized by a single or few individuals


–Decaying logs

–Dung pats


Favored Autoecological Properties

•The Higher-level group should have the following traits

–they have the ability to replicate themselves

–survival depends on the emergent property of the group (foraging, etc.)

–a mechanism exists for that attribute to be transmitted to the next generation

•Important – provides means for the trait to be heritable


A Theoretical Example

•John Maynard Smith's model of group selection

–“Trait groups”

–Individual fitness = fn(own genotype)(group genotypes)


•Wo = fitness of non-interacting individual

•c = cost of altruistic act

•b = benefit of altruistic act to others

•s = synergistic benefit accrued to both individuals if both are altruistic

•p = frequency of altruists in the population


Trait Group Evolution Equations

•Wa = W0 – c + pb

–Equation for cooperator / altruistic individual

•Wn = W0 + pb

–Equation for non-cooperator / selfish individual

•Initial Conclusions

–If altruism costs anything (and no synergisms exist), altruism will not evolve

–If only random mating / association exist, altruism will not evolve


When Will Trait Groups Evolve Altruism?


–Fitness combines additively θ synergistic benefits

–Altruists congregate into trait groups (particularly if they are related – common occurrence)



Group Selection –
Some Take-Home Messages

•May occur in some taxa living in appropriate ecosystems

•Requires many favorable confluences to occur

–Fitness combines additively θ synergistic benefits

–Altruists congregate into trait groups

–Particularly common if cooperators are related

•However ΰ Not a universal feature of life

–In contrast to how it had been historically discussed



#4 - Physiological Ecology

James A. Danoff-Burg

Population & Community Ecology

Barnard College


Our Emphasis Today

•The abiotic factors that influence the distribution and abundance of organisms

•This is what many researchers consider to be the main focus of ecology

–Again, the difference between our class and a traditional introductory ecology course

•Most of what an organism tries to do is to maintain internal homeostasis

–Today, we’ll be talking about how this is accomplished


Relation to Course

•How does this relate the rest of the course?

•My rationale

–Selection acts on the individual

–Individuals are the units that respond to the environment

–The environment is a key selective agent

–Physiological ecology is mostly coping with this aspect of natural selection


Regulating Homeostasis

•Organisms can try to do this by

–Regulating their internal body chemistry

–Changing behavior

•Example: butterflies in the Nearctic using sunning of their dark wing patches


•Most common in which types of organisms?

•Most organisms do this = Regulators


–Free-moving aquatic



•Which ones would not want to regulate their internal biochemistry to this level? = Conformers

–Why not?

•Common features of conformers

–those that are sessile


–In relatively stable environments


–They are unable to cope with rapidly changing environments


Ignoring Homeostasis

•Others don’t even try to differentiate between themselves and the environment

–These instead conform to their environment

•Example: tube worms at the bottom of the ocean in the hydrothermal vents 

–don’t regulate the concentration of salts in their blood

–if they are taken to another site that is more brackish

–they take on water until their cells burst and they die

–Constant environment, little variation

•Clearly this is not an option for those organisms that migrate great distances or are highly mobile

Important Abiotic Factors

•Those that would influence organismal distribution – which are they?

•Key components:




–Sunlight abundance (for photosynthetic organisms)

•-->these first four determine the climate<--

•Climate definition: prevailing weather conditions at a locality

Secondary Important
Abiotic Factors

•What are some other important abiotic factors?

•Including the following

–Soil type

–Water and/or soil pH

–Fire prevalence


–Space (plants and other sessile species mostly)


–Solubility of oxygen in water

–Pressure - atmospheric and water pressure

–Mineral abundance


Which Abiotic Factors are Important?

•How can we know which factors are key?

•Depends on the biology of the organism

–Differs between organisms

–Even neighboring organisms in a given locale

–Often common between closely related species

•ΰ the predictive power of phylogeny


Abiotic Features and Biotic Limits

•How could abiotic factors indirectly influence the presence and abundance of a species - or do so less obviously?

•Indirectly via

–Any of these factors influencing the organism’s host, prey, preferred food source, etc.

•Less directly via

–Multiple interacting factors

–Many of these are at work and simultaneously take effect

–Independently, they are not limiting – only collaboratively


Abiotic Factors and Species Ranges

•Typically, it is not that a species is absolutely excluded from an area

•They are usually less fit, more stressed, or less apt to mate and reproduce


Abiotics, Ranges, and Life Stages

•The resiliency or ability to live in marginal habitats varies based on the life stage of the organism

–Resiliency – ability to respond to change

•Immature stages of plants and animals are usually less hardy than are the adults



•Ranges of adaptation

–How much can the environment vary?

•in frequency and magnitude

–While still retaining the species

•Breadth of adaptation

–Can refer to any or all of the above abiotic factors simultaneously

–Are relative values

•Stenotopic - Able to live only at a very narrow range

•Eurytopic - Able to live across a wide environmental range


Adaptability and Multiple Abiotic Factors

•Not much relationship between how the organism copes with each variable

•Vary independently

–as to how much of any of the above conditions that are present in their preferred habitat

•Remember that the impact on the range will vary through the life span of the individual

–And also across the geographic range of the species

Diurnal Patterns of Adaptability

•Variation exists through the day

•Particularly true for ectothermic (or cold-blooded) organisms

–Their body temperature and thus sensitivity to a variety of stimuli vary in response to the environment

–Not exclusively

•Via sunning and a few other techniques

•Ectotherms can usually raise their body temperature quicker than does the environment and to a greater level

•E.g., lizards or butterflies and basking


Abiotic Extremes and Species Limits

•Not just the average, average high, or average low value that limits species

•Usually it is the extremes of the range that limit species distribution

–Even true if these are rare events

–Only occasionally lethal conditions will

            be catastrophic

•most extreme cold of the year

•the most saline part of the tidal cycle

–For example: the Saguaro cactus

•Temperature extreme lethal

•Freezing temp. longer than 40 hrs.

Interactions between factors

•Extremes may also weaken the individual / population

–Then other abiotic factors may have greater impact

–Also, biotic factors could be unleashed

•parasites, competitors, or predators can better have access or kill the organism

–Environmental extremes may slow or stop sexual maturity, or interest in propagation

•E.g., Cole Porter tune


Beneficial Abiotic Extremes

•Often needed for existence

–Not all abiotic extremes are bad

•If a desired extreme is not present, species propagation can be halted

•E.g., many insects use a heavy rainstorm as a cue to mate

–Rainstorm may have obliterated most of the other insect species’ populations

–if they are transported to areas that get the same amount of humidity, but not in heavy rainstorms, they will not mate

–Common among desert organisms

•Extremes often both determine the extent of and make possible species presence



•Clearly all of the above factors are important for the distribution of organisms. 

•These factors do not occur independently of each other

•There are characteristic Biomes within which organisms / populations / species / communities tend to be associated.

•Define Biome?

•One definition:

–A major regional or global biotic community, such as a grassland or desert, characterized chiefly by the dominant forms of plant life and the prevailing climate. (Dictionary.com)


Types of biomes



•Coniferous forest

•Deciduous forest



•High-altitude cloud forest



Biomes, Abiotic Factors, and Species Ranges

•Abiotic factors determine biomes

•Abiotic factors determine species presence

–Both limits and makes possible

•Species presence identifies the biome

•Circular relationship exists between these three variables



Lecture 5 –
 Population Growth

James A. Danoff-Burg

Population & Community Ecology

Barnard College


Actuarial tables

•Actuarial tables = Life Tables

•developed by life insurance companies

–introduced to ecologists by Raymond Pearl in 1921

•Life insurance companies have a very vested interest in knowing how long people are going to live

–Basis of your car insurance and life insurance policies


Humans vs. Other Species

•Lots of information on human life expectancy


•Little for other animals


•Less in plants or other organisms



–Little is known about basic biology of most species

–Even economically important species


Two types of life tables


–Stationary in time

–a snapshot of what is going on in the population at one time

–a population cross-section at a single time

–a.k.a. “time specific” life table


–reports the data observed from following a single generation from birth to death

–a.k.a. “age specific” life table


Differences in Life Tables

•If life expectation improves through time, the static would undershoot the cohort curve

–Improved life expectation can occur via:

•improved health care in humans

•improving environment for other organisms

•fewer predators

•whatever would improve the quality of life for the population

•Cohorts also tend to be more accurate than statics

–if a pop’s life expectancy is decreasing, then so will the cohort curve

•inverse of above


Deriving Life Table Data

•Most derived from

–Survivorship directly observed

•follows cohorts through time

•Observe age of death

–Age structure directly observed

•Most useful for static life table

•One type of data can be used to derive the others


Types of data

•All of these columns can be derived from each other

•Usually based on the information in x and nx columns

–These are usually the observed data

•Factors measured / recorded

–x = age interval

•often implicitly an interval

•this can be determined to be whatever (month, yr)

–Nx = survivors beginning at age interval x

–lx = proportion of orgs surviving to start of x

–Dx = number of orgs dying between x and x+1

–qx = mortality rate between x and x+1 (dx)

–ex = mean life expectancy of orgs alive at x

•this is the main interest of Life insurance Co.


How to Derive These Factors?

•Derive subsequent columns from the data of x and Nx

Dx = Nx - Nx+1

lx = Nx / No

qx = Dx / Nx

ex = the sum of all of capital Lx from age x to the last age / N of age x

Lx = (Nx + Nx+1) / 2

used only for calculations of ex


Survivorship curves

•Derived from graphing Nx against x

–usually with a log normal converted Nx

•Three main types of survivorship curves

Type I

•A low death rate through most of life, until right at the end of life

•Typical of humans and many other vertebrates

Type II

•Constant death rate throughout all age classes  

•Typical of many bird populations & some extremely less developed human countries

–Many other species will have a curve that is intermediate between Types I and II

Type III – Most Common

•Staggeringly high initial death rate, followed by a leveling off and a constant death rate

•Typical of those with mass spawning

–sea urchins, many marine fish, most trees, parasites


Population Changes

•Due to both intrinsic factors of growth as well as extrinsic factors


–only looking at factors at work within the species, and not those that operate on the population

–e.g. reproductive capability, physical growth

–Models that include this as well are usually more realistic than those models that do not


–Resource abundance, climate, competition, etc.

–this can be an idealized way of looking at population growth

•If only this factor is considered


Causes for Population Change

•What is a general term for the internal mechanisms that can be used to cope with changes in some of the extrinsic factors?

•Hint: we studied them during last lecture

•Answer: Physiological Ecology

–Mechanisms for maintaining internal homeostasis



Lecture 6
Exponential Population Growth

James A. Danoff-Burg

Population & Community Ecology

Barnard College


Populations Change

•Derivation of the growth rate of a population

–Growth rate is equal to r

•A term we’ll get to shortly

•What are the general factors that change a population’s size?

•They are:

•birth (B)

•death (D)

•immigration (I)

•emigration (E)


Relation Between Change Variables

•How could we put this into a simple equation?

–B and I increase the population

–D and E decrease the population

•Beginning equation:

–N(t+1) = N(t) + B – D + I - E

•N(t+1) = size of the population at t+1 in the future

•N(t) = size of population now

Simplification in Equation

•Close our population

•No E or I

–This is assumption 1 in our model

–We’ll change this later when we discuss metapopulations

•New equation: N(t+1) = N(t) + B – D


Rates of Change

•Thus far

–Absolute number of individuals born in the time unit

•B = # born

•D = # died

•If we desire a per capita RATE of change

•b = B / N

•d = D / N

–b & d are often called the instantaneous birth and death rate

•Happening continually and instantaneously


Growth rate

•Rate for a closed population is equal to r = b - d

•r has many equivalent names

–the intrinsic rate of increase

–the instantaneous rate of increase

Exponential Assumptions

•Closed population

•No Immigration or emigration


•individuals in the populations are assumed to be capable of reproduction the moment they are born

•Constant b & d

•having more individuals in a population does not matter

•There is no interindividual difference in reproductive or death potentiality

•Can get a partial individual increase or decrease

•No time lag

r = The Malthusian parameter

•Thomas Malthus = predicted human overpopulation

•exponential growth = growth of populations when there are no external limiting forces

–E.g., abiotic or biotic like predators, parasites, competition for resources, etc.

•This is an idealized situation

–Necessary to provide a null hypothesis

–Violations allow us to better understand population


Natural Occurrences of Exponential Growth

•Does occur in nature

•Usually only briefly


–introductions of species into unnatural habitats

–ecological release

•Could also occur because of human alterations of the environment

•Elimination of natural predators


Differential Growth Equation

•The differential exponential growth equation

dN / dt = rN

•Can also represent this as DN / Dt = rN

•This is the base of all subsequent growth equations that we’ll explore

Integrating Differential Equation

•If this is integrated, we get the Nt =No(e)rt

•Symbols mean

–e is the base of the natural logarithm (approx 2.717)

–r and t are multiplied together to get a power to which to raise e

•You can also derive r from the slope of the straight line obtained by plotting the ln of the abundance data

Doubling time

•A special case of the exponential growth equation

–when Nt = 2 (No)


–t double = ln(2) / r

–divide through by No to eliminate it

–then take natural log of equation to get the bolded equation

•r tends to be related to body size

–smaller body size θ larger r (generally)

–Smaller body size θ shorter doubling time


Continuous Versus Discrete Population Growth

•Species do not reproduce continuously

•Thus far we’ve assuming that has been the case

–Assumptions # 2 & 5

•Continuous vs Discrete Graphs look different

–continuous is smooth,

–discrete has serrations like the teeth on a saw

•Reproduction often occurs later in life (assumption 2)

•Jumps up when an individual is born and decreases when an individual dies (assumption 5)


Discrete Growth Curve

Difference in Equations?

•Continuous & Discrete equations are identical

•Use a different growth rate term in Discrete growth

–lambda (l) is used rather than r

–Clear difference in equations

–You will always know it is a discrete growth

•Has a finite rate of increase

•Limited by discrete individuals and temporal clumping


Properties of Lambda

•l always positive

–It is a ratio

–May be small, but never negative

•l is the ratio of population size during the next time period to the current time period

–Similar to N(t+1) / N(t)


A Key Difference

•Continuous and discrete models are very similar when resources are unlimited

•Differ tremendously when they are limited

–Discrete growth will be highly erratic

–Continuous growth will scale itself to the resources



•Stochasticity definition:

–A force that produces non-deterministic models

•models that will not necessarily produce the same result when run repeatedly

•All we’ve done thus far have been deterministic

•Two types of stochasticity

–Demographic – sequence of births and abundance of different groups in the population

–Environmental – external changes


Deterministic vs. Non-Deterministic

•Deterministic models

–all that we’ve discussed thus far

–will produce the same curve irrespective of how many times we run the model

•Non-deterministic models

–Incorporates the environmental stochasticity

•variability associated with good and bad years due to resource availability

–Incorporates demographic stochasticity

•that there is not an even distribution of ages in a population


Variability in Non-Deterministic Models

•Incorporated in a population in non-deterministic models using variance

•Use mean population values for r (r with line over it)

•Use mean population sizes (Nt with line over the N)

•Substitute these into Nt = No (e) r   t

•Mean Values are Key in Non-Deterministic Models


Non-Deterministic Curves

•we get an increasingly erratic curve

–Similar to FIGURE 1.3 in Gotelli

•From this we determine that

–population variance increases with time

–the variance of N at time t (Nt) depends on the mean size and variance of r

–high r size and variance --> high variance

–if no variance in r, we have the deterministic model



•High variance θ instability

–variance in r is greater than 2r (average r) θ the pop will likely crash to zero & go extinct

•E.g., Demographic stochasticity

–probability of a birth or death occuring next in the sequence depends on the relative magnitudes of b and d

–variance increases with time, particularly important at small pop sizes

High Rate Magnitudes θ Instability

•High b and d θ greater variance and elevated probability of extinction

–particularly if both are high


–A population will have much greater turnover of individuals

–Increase the probability of chance runs of one sex



Lecture 7 –

Logistic Population Growth

James A. Danoff-Burg

Population & Community Ecology

Barnard College


Logistic growth

•Also incorporates density dependent factors in population growth

–Definition: factors that increase in intensity with increasing population sizes

–Density independent growth = main change in assumptions from exponential growth equation

•How would density dependent factors affect growth?

Logistic Growth Assumptions

•Inconstant b and d

–Exponential growth assumes constant b and d

–Logistic: slowing b and increasing d with increasing N

•K is constant

–Does not change with increased crowding

•Linear and incremental relationship

–Increasing N θ decreasing b and increasing d

Logistic Model

•Exponential growth is a special case scenario of the logistic growth model

–When there are no crowding effects

–No density dependence

•Most density dependence impacts are negative


Logistic Growth Curve

•sigmoidal if starting below K

•exponential decline if above K

–both settling on K, given enough time

•What would be the effect of increasing or decreasing each of the values in the logistic equation?

–N, K, r (more later)


Logistic from Exponential Model

•Exponential model: DN / Dt = rN

–DN / Dt = (b-d)N

•Need to modify b and d

–Using density dependence constants to account for the differential effect of crowding

•How to do so?


Modify b

•b = bo - aN

•a = a constant that reflects the population’s response to crowding in terms of the birth rate

–The impact of crowding increases with N

–aN will increase with increasing N

•If a = 0 then it becomes the same as the density independent growth birth rate

–b = bo - aN

–b = bo – (0)N

–b = bo


Modify d

•d = do + cN

•c = a constant that reflects the population’s response to crowding in terms of the death rate

•If c = 0 then it becomes the same as the density independent growth death rate

–d = do + cN

–d = do + (0)N

–d = do


Defining K

•Incorporate these modified b and d into the exponential model

•the Karrying Kapacity is derived from this substitution

K = N – ((bo - do) / (a + c))


Facts on K

•K = the summary term for all the forces at work on the population

–a and c reflect the effects of density dependent growth

•K = the relationship between unfettered growth and the effects of crowding

–Relating intrinsic b and d to a and c


Deriving the logistic equation

•Logistic growth equation derived from this substitution

DN / Dt = rN

•After some simplification:

DN / Dt = rN(1-(N/K))

•Which part of this is novel relative to the exponential growth equation?



•Everything on the right side in the parentheses is new

DN / Dt = rN(1-(N/K))

•(1-(N/K)) can be referred to as the unused portion of K

–When N < K there is still unoccupied portions of K

–Population growth will therefore occur


Equilibrium and stability

•Equilibrium is achieved when:

–r = 0

–N = 0

–N = K

–at the intersection of a declining bo and increasing do is K and stability

–Also some trivial situations

•K = 0

•t=0 (or no time for population change to occur)


How to Attain Equilibrium

•The population will return to equilibrium if it is disturbed from it

–by decreasing bo (when?)

–By increasing do (when?)

•Also can be achieved in an unstable system

–where N continuously vacillates

–incorporates a different definition of equilibrium

–not constant, but rather consistent ΰ dynamic equilibrium

•If the time lag between an action and its effects on the population are greatly delayed (more later)


Allee Effect

•Not all density dependent effects are negative

•Benefits of Crowding = Allee Effect

–b continues to increase with increased density and/or d continues to decrease

–generally are very species and ecologically-dependent

•Usually only true up to a certain density

–above a critical value, the regular effects of density dependence will take hold


Examples of Allee Effect

•Can you think of some? 

•the evolution of altruism

–social facilitation of feeding

–predator defense

–nest preparation

–formation of zebra herds or musk oxen, etc against predators



Time lags

•Originate because there are delays in births deaths, etc in response to environmental change

•Closer to reality: cannot immediately compensate for environmental changes

•This is usually represented by tau (T)

–Most relevant population size is that of the population at a time in the past (T) - the time lag

Time Lags θ Oscillations


Effects of T

•The response time (1/r) will be inversely related to r

–Larger r, smaller T θ logically

–With large rT values, get dynamic equilibrium – always vacillating

–With intermediate rT, get convergence to K

–With small rT, get RAPID convergence to K (essentially get base logistic growth curve)

•Oscillations reduce with time (dampened oscillations) until K is reached or approximated

–Then population vacillates about the mean K

•Variation in carrying capacity

–With decreasingly stable K, we get instability in the population

Read the three Model variations in Gotelli

•Discrete population growth

–Curves that are closer to reality

–Recognize that individuals do not reproduce partial individuals

–Births and deaths often occur clumped in time

•Differences between discrete and continuous growth in Logistic relative to the more minor differences in exponential growth

•Stochastic logistic population growth




Lecture 8 –
Age-Structured Population Growth

James A. Danoff-Burg

Population & Community Ecology

Barnard College


Temporal Changes in Age Structuring in Populations

Cultural Changes in Age Structuring in Populations

Contextualizing Today

•Most of this section we have already done

–when we covered how to construct life tables and the different types of curves that could be derived from different types of survival curves

•Our goal today is to be able to at least approximate r

–we’ve been assuming this is provided

–Will approximate r using the data that we are normally given


Deviations from previous models

•Using exponential growth curve

•Changes in assumptions of exponential growth

–No instantaneousity

–Uneven age distribution in the population

•Another way to say this is that the birth and death rates depend on the age of the individual

•Young do not reproduce

•Elderly are more prone to death

•Also are continuing to assume that there are equal sex ratios


Changes from the earlier life table discussion

•A few minor terms are different between Life tables and those in Gotelli

–Age classes are defined as the uppermost age that an individual has in a class range (e.g., a 1-4 class would be referred to as the 4 year age class

–Sx = Nx as we’ve been using

•New term

–gx = probability of surviving to age class x+1, given that we made it to age class x – this may increase or decrease through time

•in contrast to lx, which can only decrease


A few new terms that we’ll need today

•Bx = #births (raw data) in that age class

–the per class birth rate = bx

–a value that is usually given and differs from the birth rate (b) that we’ve been using

–Generally only use the number of females and assume that the proportion of males to females is equal

•if it is unequal, then we have skewed estimates of the POPULATION birth rate

•but accurate estimates of the per female rate irrespectively

•If bx = 0 then that age class is incapable of reproducing


Repetitiveness of Birthing

•Parity - births per female through their lifetime

•Big bang reproduction or one-time

–Semelparous in animals (-parous = Latin for giving birth from parere)

–Monocarpic in plants

•Continual reproduction or ability to continually reproduce through life

–Iteroparous in animals

–Polycarpic in plants


Relating this to Life Tables

•How would each of these reproductive trends be mirrored in the tables of b values?

•An answer:

–Semel- only a b value at one age class

–Itero - b values in more than one


Net reproductive rate (Ro)


–the mean number of female offspring produced per female over her lifetime, in units of number of offspring

•Assumes that the Ro is the mean number of female offspring per female over lifetime

–or by assuming that Ro is the mean number of offspring per pair of monogamously reproducing species

–however the latter is only a special case

•normally we refer only to the number of female offspring per female


Calculating Ro

•Ro = sum lx times bx for all life stages

–if Ro is > 1, then r is likely to be positive

–if Ro is = 1, then r is likely to be zero

–if Ro is < 1, then r is likely to be negative


Ro and r

•Ro does not differ from r if there is instantaneousity

–with generation time and thus a lack of instanteousity, they do differ

–there is a gross relationship between the two

•Ro, lambda, and r are related

–Ro measures population increase as a function of generation time

–If no age structuring of population, Ro ~ lambda (the finite rate of increase)

•however, lambda is a function of absolute time, whereas Ro is a function of generation time

–r = ln(lambda)


Calculating Generation Time

•Need to calculate the generation time to get a more accurate estimate of r

•Generation time (G) = sum of lx times bx times age divided by sum of lx times bx

•r (estimated) = ln Ro / G

–accurate to within 10% of r

–the more specific r is determined by the Euler (pronounced ‘oiler’) equation

–We won’t get into here

–Discussed in Gotelli



Lecture 9: Mutualism and Commensalism


James A. Danoff-Burg

Population & Community Ecology

Barnard College


Introduction to communities

•What is a community and how do they interact?

•Definition of communities:

–A group of organisms belonging to a number of different species that co-occur in the same habitat or area and interact with each other

–Same time, same place, multiple species


•along the shore of the Hudson river along Riverside park

•those living in one of our sites at the BRF

•those organisms that are living on each of our faces


How can two species interact?









+ positive impact, - negative impact, 0 no impact

the active participant or initiator is the first consideration


Types of Interspecific Interactions

More Later on Other Relationships






•Today: Mutualism & Commensalism




–When one organism (secretes a chemical that) prevents another from living near it

–Trees, Barnacles, other sessile organisms

•Commensalism as a special case of mutualism

–the relative benefits to one party are so negligible as to be zero




–Two (or more) species live in close association on, in, or with each other

–e.g.: mutualists, commensalists, parasites, and parasitoids



•Mutualism - tremendously understudied field within ecology

–Much of the work that has been done has lapsed into frequent story-telling

•all is as it should be

•the world is a warm fuzzy place

–Equally plausible:

•most mutualisms originate by the capture, slavery, and exploitation of one species by another

–Both parties benefit by the current relationship

•one may just barely be benefited by the relationship

•the other party may benefit colossally by the relationship


Dominance of Mutualisms

•The majority of the world’s biomass is composed of mutualistic species

–trees and their nitrogen fixing Rhizobium fungi in the roots

–most corals and unicellular algae in them

–flowering plants and their pollinators

–the huge number of microorganisms in the digestive systems of many animals

•Commensalism as a special case of mutualism

–the relative benefits to one party are so negligible as to be zero


Extreme Mutualism?

•Could say that all Eukaryotes are the result of a mutualistic relationship

–Endosymbiotic origin hypothesis for Eukaryotes

•Pressures of parasitism, parasitoids, and predators have produced more biodiversity

–more on this during the next few lectures

–Huge diversity of environments and types of interactions


Mutualistic Generalities

•Generalities of mutualists

•More applicable as we go along a gradient from occasional mutualists to facultative to obligate mutualists

–Form an evolutionary gradient

–Less frequent θ More frequent θ Necessary relationship


Eight Features of Mutualists

•Simple life histories, relative to parasites

•Sexuality is suppressed

–in favor of asexual budding - e.g. corals

•No conspicuous dispersal phase

–e.g. mycorrhyzal fungi

•Evolution of simultaneous dispersal events

–e.g. Sceptobiini beetles and their host ants


Eight Features of Mutualists

•Stable population cycles

•fewer outbreaks, fewer crashes

•Relative to parasites or predators/prey

•Stable proportions of each individual in the relationship

•e.g., ants and aphids

•diminishing benefits of ant tending to the aphids at high aphid densities


Eight Features of Mutualists

•Niche breadth is greater

•Best viewed in facultatively mutualistic relationships, when they are and are not living together

•e.g. mycorrhyzal fungi and their host legumes

•legumes can exist w/o them but they can only live in very few types of habitats

•Multiple host relationships are common

•not many are species specific

•not as true for obligately host specific relationships

•e.g. lichens and algae are very host specific


Modeling Mutualism

•Use the logistic growth model

•What are three ways in which the mutualism could be summarized? 


–increase in b

–decrease in d

–increase in K


Modeling Mutualism

•How could we summarize this in the logistic growth equation? 

–Use the original equation

–Add a term at the end that summarizes the beneficial effects of the presence of the second species on the first


Modeling Mutualism

•Logistic Equation as basis

•DN / Dt = rN(1-(N/K)) + AM M) 

•Explanation of terms

• A(alpha) = the beneficial conversion of the presence of M individuals into N individuals

• (X) = time with which mutualistic relationships are formed between the species

•M = density of the second mutualist in the population


Extending the Model

•For the second species

–Put equation in terms of benefits to species 2 with increasing population size of species 1

–Use Alpha () for impact of species 1 on species 2

•Increasing any of the values above θ mutualism

•We’ll get to another way to model this growth at the end of the competition discussion next time




Lecture 10: Models IV - Competition

James A. Danoff-Burg

Population & Community Ecology

Barnard College



•Two types of competition:

–Resource (or exploitative as Gotelli calls it)

•directly takes away some of the limited resource

•also includes pre-emptive competition


•an individual or population directly reduces the competitive ability of a competitor


Competing Competitions

•Another way to split up competition:


•resource or exploitative and pre-emptive



•competitive exclusion

–when one species outcompetes and excludes another from their habitat


Lotka and Volterra

•The creators of the “Lotka-Volterra Competition Model”

•Independently derived the competition model in 1925 and 1926 respectively


The Model

•Similar to the brief model that we composed for the mutualism relationships

–Based on the logistic model

•Competition Equation

 DN / Dt = rNN (1 - (N + αM) / KN)

 DM / Dt = rMM (1 - (M + βN) / KM)


Symbol Explanations

• α (alpha)

–per capita effect of species 2 on the population growth of species 1

–relative to the impact of intraspecific competition within species 1

• β (beta)

–the per capita effect of species 1 on the population growth of species 2

–relative to the impact of intraspecific competition within species 2


Model Novelties

•Intraspecific vs. Interspecific Competition

–Low α (or β) value (< 1)

•θ Greater Intraspecific competition than interspecific competition

–Large α (or β) (>1)

•θ Greater Interspecific competition than intraspecific competition

– α (or β) = 1

•each individual added of the same or different species would have equal effects on the population growth

Intraspecific Competition

•Usually relationship is asymmetrical

•Reflected by unequal β and α


–If α = 4 and β = 1, how else could you state this? 


Equilibrium in the competition model


–set DN / Dt = 0, then simplify.

Result: Nt = Kn – αM


Kn is diminished by presence of M individuals

αM represents the amount of the environment that is consumed by M individs, in terms of N individs

•If α = 0, then it reduces to N = K - 0, as in the logistic equation


Graphical representations of the model

•These equations allow us to determine the equilibrium for a given community

–they don’t allow us to tell how stable is that equilibrium

–nor do they tell us much about the dynamics of the relationship between the species


State-Space Graph

•Y axis is sp. N

•X axis is sp. M

•the combination of abundances of sp. N and M are graphed out

•This graph shows all the possible joint abundances between the species

•Still doesn’t show any stable points


Time and Stability and the Graph

•Now let's incorporate time and stabilty to get a linear isocline for an individual species, which shows the stable point for all communities

•This shows the set of abundances for which the growth rate (DN / Dt) of one species is zero



•The isocline ONLY shows the stability for species N

•The point at which N has a zero value (directly on the X axis) is Kn/ α

–roughly equivalent to the maximum number of M individuals that Kn could contain



•If we move off the isocline, we must return to it

–only by moving vertically, as we are only noting change in numbers of sp. N

•If we move the species off the isocline and then move back to the isocline

–single species movement vector

•If we plot another line that shows the isocline for sp. M, we have two lines plotted on the graph


Joint Species Competition Outcomes

•We get four joint species competition outcomes

•after plotting onto the state-space graphs the individual movement vectors

•the resultant summed community vector for all unique quadrants in the graph


Four Outcomes

•Competitive exclusion of N

•Competitive exclusion of M

•Stable coexistence

•Unstable coexistence


Competitive Exclusion

•Competitive exclusion of sp. N by M (M is a higher and parallel line to N)

•Competitive exclusion of sp. M by N (N is a higher and parallel line to M)


Stable Coexistence

•Coexistence and stable equilibrium (crossing lines, with Kn / > Km and Km /  > Kn)

–Results in lower equilibrium values for both species


Unstable Equilibrium

•Outcome depends on initial conditions

–Produces an unstable equil

•Crossing lines with the Km value above the Kn/ value


Unstable Equilibrium cont.

–If the combination of the two species are in either the right top most or left bottom most quadrants then the two spp. would both go toward the equilibrium point

•If not, then the community goes to exclusion of the other sp.

–Perturbation θ Movement off Isocline θ exclusion of one or either of the species

–Stability is uncommon

•environmental or demographic perturbations




Lecture 11 –

Predation I


James A. Danoff-Burg

Population & Community Ecology

Barnard College


Overview on Predation

•Broadly interpretation:

–Herbivory - predation on plants

–Carnivory - predation on animals

•also normally thought of as predation in a less refined sense

–Parasitoids - predation on animals whereby one animal kills the other and lives on or inside of it

–Parasitism - similar to parasitoids, but do not kill the host

–Cannibalism – intraspecific predation on animals


Predation and Selection

•Predation (in a broad sense) pressure

–How to detect?

–Exclude the predator

–Observe the growth rate of the prey population

•e.g., rabbits into Australia -- no predators from the beginning

•e.g., Herbivore exclosure fences

•e.g., Parasitism -the sea Lampreys in the Great Lakes - only introduced from 1921-1945 in each of the five lakes,

•Predation (in large sense) forces θ huge effect on prey population sizes


Prey Responses to Predation

•How could prey respond to predation?

•Some possibilities

–Chemical defenses

–Fighting back


–Escape (better fleeing)

–Mimicry (Batesian and Mullerian)

•a. Batesian- mimic is not dangerous, but model is

•b. Mullerian - model and mimic are dangerous and often are aposematic

–Aposematism (warning color)

–Posturing (pretending to be something you are not)

–Dilution effect (schooling or masting)

•a. Predator satiation effect

–Mutualism with another org for protection

–Physical Defenses

–Acoustic startle response

–Feigning death


Prey Responses to Predation

•Categories not mutually exclusive

–Multiple responses can and do simultaneously occur in the same species

•Majority of predation is focused on non-random sample of prey population

–Usually the weakest, most ill, youngest, and oldest


•(or maybe not, from the perspective of natural selection)

•Least able to contribute to the future reproductive ability

•Most defenseless of the prey population

–θ “benefit” of predation for species


Prey Responses to Predation

•Strong predatory influence

–Effect the population structure of prey

–e.g., Dingoes in Australia

•When present θ many fewer prey juveniles than adults

–Juveniles are 5% of pop

•in comparison to when dingoes are absent

•When dingoes are absent

–Juveniles are 55% of pop

–How would this influence prey population?


Life-dinner principle

•Why are prey usually one step ahead of their predators?

–Coevolutionary arms race

•Between predators and prey

•Repeated compensatory change between the two species

•Changes occur in response to changes in the other species


–Canadian snow hare and Canada lynx


Co-Evolutionary Arms Race

•Three assumptions of the relationship between the two species

–Species must be closely tied together

–Prey driven

–Prey changes precede the predatory response


Predator-Prey Cycles


Strength of Predation Pressure

–Impact on prey population cycles


–Occur when there is a lag time between the activities and course of the prey and those of the predators

–High predation pressure θ permanently oscillating or at least dampening oscillations

–Consequently, predators may occasionally peak above sustainable prey levels

–intermediate predation levels lead to cycles that damp out quicker

–predators always are below the levels of the prey

–Low levels of predation pressure

–Possibly due to broad predation preferences

–Lead to no oscilations and steady Ks

–Predators are always well below the levels of prey



Lecture 12 –
Predation II


James A. Danoff-Burg

Population & Community Ecology

Barnard College


Predation Model – Applicability

•Easily generalizes to all the remaining two-species community interactions


•closest to predation

•need to allow for multiple “predators” consuming a single prey and having a long-term association


•non-lethal, multiple predators on the prey


•would be most similar to herbivory, given these modifications


Predation Population Growth – Assumptions

•Prey (V) is limited largely by predation

•Prey and Predators (P) encounter each other randomly

•Predators are prey specialists and depend on them for their food

•Predators can continue to expand their prey consumption rate without limit


Predation Population Growth – Assumption 1

•The prey is limited only by predation

–In the absence of predation

•the equation for prey population growth would be the exponential growth equation (dV / dt = rV)

–If predators were present

•need to incorporate a term to summarize the detrimental effects of the predator species being present 

•dV / dt = rV - αVP


α * V * P

•Losses due to predation are proportional to the product of predator and victim numbers

• α is the encounter rate of prey by predators

– α is not the same alpha as in the competition model

•Solve for equilibrium (dV / dt = 0)

–simplified, we find that the equation for the Prey would simplify to P = r / α

–Only in terms of the PREDATORs


–the equilibrium solution is set by the number of predator species nearby

–A logical consequence of assumption 1


Predation Population Growth -  Assumption 2

•Predators and prey encounter each other randomly in a uniform environment

–There are no hiding places for prey

–Prey are dispersed randomly

–Prey are not clumped together into refugia


Predation Population Growth – Assumption 3

•The predators are extreme specialists

–Feed on nothing else other than the prey

•Predator growth equation

–The inverse of the above prey population growth equation (at equilibrium) would be dP / dt = -qP

q = per capita death rate of predators

•What would happen if we eliminated the prey population?

dP / dt = 0

•Therefore: the predator pop declines exponentially as the prey population declines


Expanding the Predator Equation

•Include both the positive and negative effects of the influence of prey abundance

dP / dt = βVP - qP

• β is the conversion efficiency with which predators can convert prey into more predators


Predator Growth Equation
dP / dt = βVP - qP

•Positive growth only occurs when the prey is present

–as the first term on the right side of the equation would be zero if not, and the predator population would decline to extinct

•Equilibrium situation (dP/dt = 0)

–Simplified, we would find that the equation for the Predators would simplify to V = q / β


–the equilibrium solution is set by the number of prey species nearby

•Logical consequence of assumption 3


Responses of the predator population to the prey pop

•The functional response of the predators to the prey pop can be summarized by αV

–More encounters θ more predators

•The numerical or growth response of the predator population to prey abundance is βV

–More efficient conversion of V θ P, more predators


Prey Population Growth – Assumption 4

•Predators can continue to expand their prey consumption rate without limit

–Unrealistic, but necessary

–It is a consequence of the mathematics and graphs

–More on this in a moment


Prey Isoclines

•Prey isocline - flat horizontal line with Y intercept = r / α

–Prey abundance is determined only by predator abundance


Prey Isocline

•At the Y intercept, there are no prey

–if we look at this value on the Y axis, how could we explain this situation?

–The growth rate of the prey is equal to or less than the handling time of the prey by the predators

–r / α = the number of predators that control the growth rate of the prey population


K for the Prey?

•There is no K value

–Assuming exponential growth

•Isocline equation:  dV / dt = 0

–Draw the movement vectors only horizontally

–If we were to disturb the prey pop away from the isocline

•Isocline = negative sloped line that has been elevated to unlimited K

K = infinity


Prey Movement Vectors

•Above isocline

–prey moves to the left

•more predator individuals than the prey population can sustain

•so it decreases toward zero

–Consequence of Assumption 4

•Below isocline

–prey moves to right

•fewer predators present than can control the prey population

•the prey population increases without bound

–Consequence of Assumption 1


Predator Isocline

•Vertical line with X intercept equal to q / β


Predator Isocline

•A logical consequence of equilibrium

–the predator population: determined by the number of prey

–Equilibrium = critical number of prey necessary for the predator population to exist

•A suggestion

–Think of this line as a sloped line

–a positive line with K at the end of it at infinity

–predator population increases with the prey population


Predator Movement Vectors

•Draw only vertical arrows for the predator population

–Displace the predator population off the predator isocline

•Possibly by augmenting or decreasing the number of predators present locally

•Movement is up to the right of the line

•Movement is down to the left of the isocline

•The equation of the isocline

dP / dt = 0

–same as all other isoclines


Graphing the Two-Species State-Space Graph

•Sum community movement vectors differ in each quadrant

•Result: a smooth continual ellipse that flows around counter clockwise


Summary Community Movements

•Summary ellipse

–adheres most closely to the prey isocline

–prey drive the system

–if we have no prey, we have no predators

•The predator population peaks when the prey is at its midpoint and vice versa

•Peaks of the predator and prey pops are off by a quarter cycle

–victim numbers are usually well above predator numbers

–because of the reduction in biomass as you go up the food chain


Extinction Probability

•High initial population sizes θ Increased probability of extinction

–Use a high initial value of any of the populations

–Closer to the axes

–Increase the probability that one or the other of the species would go extinct

•As long as the isoclines do not change

–Paradox of enrichment


Amplitude of the cycle

•Amplitude is determined by the starting points of the ellipse

–Consequence of initial population sizes of V and P

–Constant ellipse shape

•merely expanded outward accordingly so that each point would be on a similar shaped ellipse


Period of the Cycle

•Period is the speed with which the populations cycle from peak to peak

–Increase r and q

•these determine the speed of population cycling

–Equation of the period is roughly = C ~ 2π / (Φ(rq))


Approximating reality with the model

•Incorporating a victim carrying capacity

–Prey do not generally grow exponentially

–Usually the isocline has a negative slope and a K

–Rather than using the (1-(N/K))

•Substitute a constant (c)

•density of the prey population = cV2

–New equation:

•dV/dt = rV - αVP – cV2

–intersection point of the X axis = r/c

•r/c ~ carrying capacity of the prey population


c (or unused portion of K) = Stability

•c stabilizes the interaction to static equilibrium

•Missing now:

–Dramatic oscillations



Making the predators “satiatable”

•One of our 4 initial assumptions

•Modification: predators have also an upper limit

•A novel plot: n / p / t on Y, V on the x axis

–Lotka-Volterra predation = Type I response

•Unrealistic: predators do not eat without end

•predators are limited by handling time


Predator Satiation

–Modify the response to reflect these realities

–Type II response

•Need handling time (h) incorporated

•Need satiation point = maximum consumption ability

–Satiation point = 1/h

–A.k.a., the maximum predation rate

–How predators respond

•Functional response

•Differing prey abundance consumption


Search Image and Handling Efficiency

•When a predator first begins to feed on a new prey item

–They are slow in recognizing the new prey

–They are clumsy in handling them

–Eventually improve with experience

•Type III response

–Prey switching is common


Impacts of Functional Responses

•Reduced predation selective force on the prey at higher prey densities

•Implications of masting or prey aggregations

•Implications for controlling prey population cycles

–important for  biological control


Predator Functional Response Curves and Biological Control

•Species with Type I predator responses are best

•Low to intermediate densities, the Type II would be useful 

–To a lesser degree Type III also at intermediate levels


Additional Readings

•Focus on the last few sections in Chapter 6

–The Paradox of Enrichment

–Incorporating Other Factors in the Victim Isocline

–Modifying the Predator Isocline

•Won’t discuss these in class




Lecture 13:

Predation III - Parasitism and Herbivory

James A. Danoff-Burg

Population & Community Ecology

Barnard College


Changing Various Factors

•What factors can change in the predator-prey cycling?

dP / dt = βVP – qP

dV / dt = rV - αVP


–r, α, β,  q, V, P, etc.

•We briefly talked about this earlier

–Review and expand upon this now


Increasing r

•Example: annual grass is suddenly able to reproduce at twice the rate it was previously

–increase r θ increase of prey replacement rate

–number of herbivore species that the patch can produce in any given time span is increased

•Effect of this on the K of V? 

–Handling time and ability of P to consume limitlessly has not changed

–K of V would not increase

•predators can consume the same proportion of prey

•Type I predator response to prey


Increasing α

•What would be the effect of predator search efficiency

–You would decrease the number of V throughout cycling

•Prey would be found and killed quicker

•Leads to a fewer P throughout cycling


Increasing β

•Make the predators better at converting prey resources into other predators

–Increasing predator efficiency

–Making the predators better predators

•More efficient θ greater β

–more instability and greater vacillations in the populations and lower K of V


Increasing q

•What would be the effect of increasing the q of the predators?

–Predators die quicker

–Maintain same overall consumptive rate

–Predators get more food per individual


Situations unique to Herbivory or Parasitism (Parasitoidism)

•Beneficial herbivory

–Can herbivory actually be good for the plant?

•Supporting data: plant growth tends to increase following herbivory


•Often get overcompensation for the damage

•The plant grows more vigorously or reproduces with greater fervor than it would without the damage


Other Support for Beneficial Herbivory

•Increased seed production from additional terminal branches being added to the tree

–Usually only the terminal branches of a plant flower & produce seed

•Mangrove trees

–more aerial roots form when the main branches were infested with herbivores

–θ greater stability in the shifting soils of the estuary in which they live

•Modeling beneficial herbivory

–increase r

–Leads to above changes with increasing r


Evidence Against Beneficial Herbivory

•Lack of statistical power

–Not really been demonstrated that it is because of herbivory

–Could be because of mere removal of tissue (by wind, etc.)

•Sampling bias?

–Possibly plants that are chosen by herbivores do this independently of herbivory

•Comparing Azaleas and Grasses

–Reduced production of plant secondary compounds

–Comparing two different groups of plants

•1- slower growth because of increased secondary compounds

•2 - faster growth, higher herbivory, and decreased secondary compounds


Parasite-Induced Behavioral Changes

•How do parasites differ from the other examples we’ve been discussing thus far?

–many many individuals jointly can feed on the victim (similar to herbivory)

–host doesn’t (usually) die (similar to herbivory)

–parasite lives inside its food source (unique from all earlier interactions)


Parasite alteration of host behavior


–snails infected with a worm, climb aquatic vegetation, apparent to avian predators, snail can’t retract body because eye stalks are swollen

–A question for thought: What impact would this change have if the parasitic worm had no detrimental impact on the avian predators?


Lecture 14 –
Causes of Population Change


James A. Danoff-Burg

Population & Community Ecology

Barnard College


Key factor analysis

•How would you determine the most important factor regulating a population? 

–What would regulate the population?

•The biotic and abiotic factors that we have discussed thus far



–density dependent effects

–fungal infection

–thermal gradients



A Possible Way to Answer the Question

•Before and after a force

–We can measure the impact of a force by measuring the population before the presence of the force and also then after it has been present

•This is usually summarized as lower case k for each force

•The difference is usually expressed in terms of log Nt - log N(t+1)

–Nt = number of individuals in the population before the force was introduced

–N(t+1) is the number after the force

•once you have factored out all the other forces


An Overall K Value

•Summarize all the effects into the overall ktotal value

ktotal = k1 + k2 + k3...

•The key factor

–The force that most strongly affects the survival

•In reality

–there will usually be multiple factors that together determine the population size

–ecologists usually refer to the most important one. 

•Key factor calculation

k = Log10 Nt - Log10 Nt+1


Example: Colorado potato beetle


Example: Colorado potato beetle

•Strongest factor is by far emigration during the female x 2 stage

–sex ratio was female biased

–females left the population?

•Larger k values = greater impact

–k ~ 0 θ chance?

–k > 1 θ important factor


k Values


–Do not tell us the relative importance of each factor as determinants of the year-to-year fluctuations in mortality

•only that a factor is important in determining population size in the current year

•not in determining CHANGES in population size from year to year

•Longer-term calculations

–Use average k values

–Example using 10 years’ data in the case of the Colorado Potato Beetle in BHT

•In sum:

–K values θ quantifying relative strength of influences on population growth & mortality


Populations Control

•Definition of terms

•Top-down control

–limitations on population growth imposed by those higher up in the food chain

–e.g. predators on prey, herbivores on plants, parasites on host, etc.

•Bottom-up control

–controlled by biotic resources

–e.g., prey on predators, etc.

–Just the inverse of the above


Population Control and Models

•Previous models

–Both competition and predation models have included both top-down and bottom up controls

–We were simultaneously looking at the reciprocal effects of both on the other


•Progressively increase numbers of trophic levels in a food chain





•Top levels of the system

–controlled only by their supporting resources and intraspecific competition

•Lower levels of the food web

–change depending on the number of trophic levels in the food web

–Cascade downwards from top consumer

–Alternating impacts


Simple Trophic Systems

•Few trophic levels are rare

•Found mostly in island ecosystems

–e.g., tropical island of Aldabra

•plants (many species)

•giant tortises are found

•no predators on the tortise


More Complex Trophic Systems

•More common

•Food web

–many trophic levels

–more relationships among the species in the web than a food chain


A Quick Summary

•Stiling has an excellent review of the conceptual models testing these ideas for natural environments that are very complex

–most of them try to explain how ALL communities function across the entire planet

•Probably unrealistic

–More likely: have multiple models that are applicable to different communities

–Determine the conditions under each model will be most applicable



Lecture 15 –
Metapopulations I


James A. Danoff-Burg

Population & Community Ecology

Barnard College




–a group of populations that are linked by migration

•A species = sum of all its metapopulations

•Limited migration between the populations

–thus far we’ve been ignoring the influences of neighboring populations by assuming that migration was non-existent)


Metapopulations in Context

•Individual population changes = the best indicator for the entire species?

–the assumption of no migration & closed populations is not that far off

•Determinants of migration rate


–Size of home range

–Prevailing environmental conditions

•do they have to move

–Density of the local population

•do they have to move?


Migration Rates

•Migration is often on the scale of very few individuals per generation moving between populations

•Would this be sufficient to affect the genetic composition of a population?

–Depends in part on the population size

–Small pops θ very important


Uniformity in Population Growth Models

•Uniformity in distribution in models

–Assume that all individuals are equally distributed across space

–Assume equal probability of survival in a diversity of

•How can we now introduce heterogeneity into the environment?


Patchiness of Metapopulations

•Introducing Patchiness

–The world is hardly a salad bar for herbivores

•most species have only a few host species they can feed on

–A parasite would look at each of the hosts as they wander around the landscape as mobile patches

•Other animals (non-hosts) are inhospitable territory




–smaller organisms view the world more fine grained

–larger organisms view the world as being more coarse grained

–Example: the leaves on a tree

•Each is a novel unexplored territory for aphids

–when one individual invades a new territory, it could grow exponentially

•For an herbivorous mammal

–each tree would only be a small portion of the resources that it would need to exist

–Organisms interact with the world differently

•And differently in different habitats


Novelties in the Metapopulation Model


–In past, no migration was a viable assumption

•True for huge population sizes and isolated populations

–In reality

•Most animal species migrate, and nearly all plant species disperse either their seeds and/or their pollen

–thus you do have to account for metapopulation dynamics


–We do not consider the population size, only its persistence

•Don’t distinguish between size of the component populations OR cycling OR constant populations


Building the Model

•We have only two possible states of the pop

–local extinction - 0

–local persistence - 1

•Seque also up in scale

–No longer concerned about the fate of individuals

–Also geographically, we are looking at a larger area


Building the model

•Scale of Regional vs. Local extinction

–Local extinction much more likely than extinction of the metapopulation

•An analogy: a single individual dying and the entire population going extinct

•Probability of extinction of a population

pn = 1 - pe

•pn = probability of local persistence

•pe = probability of local extinction

•Example: 1 - 0.8 = 0.2 = pn


Multiple years



–could also be (1- pe)(1- pe)(1- pe)(1- pe)...

–repeated n times

•where n is the number of years

•Probability of regional extinction increases tremendously across years, with high persistent local extinction probability

–Example: if pe = 0.8 for 4 years

–pn = 0.04%, almost no chance of survival


Probability of Extinction of a Metapopulation

•If we have two pops, we have two independent probabilities of extinction

•We multiply the probabilities together and then subtract that resultant value from 1

1 - (pe1)(pe2) = Px (1 - 0.8*0.8 = 36% Px)

•Px = probability of regional persistence

–This equation could be expanded indefinitely for whatever number of pop probs you have


Expanding the Concept

•Special case

–when all the pe are equivalent

–you could simplify the above equation as 1 – pe2 = Px

•Figure 4.1 in Gotelli

–calculate all possible Px values for all component populations

–assume that all have the same extinction probabilities

–Px increases logistically as the number of n increases

•With multiple populations

–e.g., pe = 0.8, Px goes from 20% (1 pop) to 36% (2 pops) to 41% (4 pops) to 83% (8 pops) to 97% (16 pops)

–Compare with pn = 0.04% for 4 years for a single population

•Metapopulations spread the risk of extinction around


An Aside on Empty Niches

•Can there be unoccupied niches? 

–Avered by G. Evelyn Hutchinson

•niches do exist independently of whether the animals exist to occupy them

–Others would say that in fact the niches do not exist until there are animals to occupy them.

•A lack of herbivory at the tops of trees Ή empty giraffe niche

–Only means that large leaf herbivory does not occur.

•As an extreme example

–Think of the niche as existing in extreme environment

–Define that same “niche” in the Arctic, where giraffes do not occur

–the giraffe niche is still unoccupied, and will likely stay that way


Building the Model Parameters

•f = fraction of pop sites that are actually occupied

f = 1 when all sites are occupied

•I = immigration rate or colonization rate of novel patches by the organism

–analogous to B (number of births)

•E = extinction (or emigration) rate

–I and E are not exactly the same as true immigration and emigration, but comparable

pi = probability of local colonization

•This probability can be empirically derived in part from Key Factor analysis

•we would also need information at each life stage as to the organism’s vagility

•pi also depends on f

–high f values θ increase the probability of colonization


Simple Metapopulation Model

•Equation: df / dt = I - E

–Comparable to the initial exponential growth rate model (dN / dt = B - D)


–there is no influence of regional occupation of other patches on pe or pi

–changing f does not change pe or pi

Metapopulation Equilibrium

•When would the metapopulation be at equilibrium according to this model? 

•ANS: when I = E


Complicating the Model

•Let I = pi(1-f)

–same thing as saying that the colonization rate = the probability of local colonization multiplied by the unoccupied portion of the available populations.

•Let E = pe(f)

–extinction rate is a product of the probability of local extinction multiplied by the fraction of the patches that are occupied


A More Complicated Model

•Incorporating more realistic assumptions

df / dt = pi(1-f) - pe(f)


–homogenous patches

–no spatial structure

–no time lags

–constant pe and pi

–regional occurrence (f) affects pe and pi

•when the more complicated portions are incorporated

–large number of patches

•we can get a small f and still have some patches occupied


Complicated vs. Simple Models

•Differences in heterogeneity

–Simple model assumes constancy across range

–Complicated allows for differences in pe and pi across range


Island-Mainland model

•This is essentially what we have described above

•assume huge and constant propagule rain from either a separate mainland or by residual local propagules

–as in the seed bank for plants

–Propagules = new dispersers that could form new colonies

•An example of Source-Sink Dynamics




Lecture 16 –
Metapopulations II


James A. Danoff-Burg

Population & Community Ecology

Barnard College


Island-Mainland model

•This is essentially what we have described above

–Basis of the Metapopulation model

•assume huge and constant propagule rain from either a separate mainland or by residual local propagules

–as in the seed bank for plants

–Propagules = new dispersers that could form new colonies


Sophisticating the Metapopulation Model

•Internal colonization

–this takes into account that most of the recolonization events occur

–because of colonization by other patches

•not included in the base island-mainland model

Internal Colonization


–need to modify pi = (i)(f)

•i is a scalable constant

•increases as f increases

•reflecting the enhanced probability that a patch will become colonized when more of the surrounding patches are occupied


Sophisticating the Metapopulation Model

•Rescue Effect

–when we have more patches occupied θ usually have more individuals in the metapopulation

–Consequently θ an increased rate of migrating individuals arriving at patches

–Therefore: "rescued" from extinction


Rescue Effect

•Particularly important with populations that are declining in size

–Consequently θ extinction is less likely


–Modify pe = e(1-f)

–e is another scalable constant that decreases as f increases

•summarizes the strength of the rescue effect


More Sophistication of Metapopulation Model

•Incorporating even more reality

–Using the island-mainland model

–Incorporate Internal Colonization AND Rescue Effects


A More Sophisticated Equilibrium

•Substitute the above two modified equations for pi and pe

–slightly more complicated model Equation

df/dt = (i)(f)(1-f) - (e)(f)(1-f)

df/dt = 0 = i – e


–At equilibrium (meaning?)

•the equation simplifies back to an analog of the first metapopulation model

df/dt = i – e


Observations on a Sophisticated Equilibrium


–when i = e θ df/dt = 0

•no change in f

–when i < e θ negative and declining df/dt

•f dwindles

•until extinction, if these values do not change

–when i > e θ positive and increasing df/dt

•f will continue to increase in occupancy until f = 1

•When f = 1, all patches are occupied

•df/dt goes towards zero


Reading in Gotelli Chapter 4

•Be certain to have read through

–the checkerspot butterfly

–heathland carabid beetle



Lecture 17 –
Island Biogeography


James A. Danoff-Burg

Population & Community Ecology

Barnard College


Island Biogeography

•Which situation would you expect to have the greatest community species diversity?

•A. Island close to mainland OR B. Island far from mainland

Island Biogeography

•Which situation would you expect to have the greatest community species diversity?

•A. Larger island   OR B. Smaller island


Island Biogeography

•Which situation would you expect to have the greatest community species diversity?

–A. Larger island 

–A. Island close to mainland

•Most of the basis of Island Biogeography

–Simple model

–Generally accepted


Equilibrium Model of Island Biogeography (EIB)

•Builds on

–island biogeography, metapopulation models, the climax community, and succession

•More on these in a few lectures


–Changes in community species composition through time

•Climax community

–Climax community a.k.a. = fully mature community


•No change in the mean number of taxa at climax through successional time

•Turnover rate can be high, with many species becoming extirpated or colonizing the area


Equilibrial Model of Island Biogeography

•Simberloff and Wilson (early 1970s)

–Original proponents

–Built on the idea of Island Biogeography with equilibrial addition

–First study fumigated mangrove islands of different sizes & distances from shore

–Looked at the species & trophic types that were present on the islands initially and at climax community


Equilibrial Theory of Island Biogeography - Results


Size of Island (long-horn beetles)


Species-Area Relationship


Equilibrial Theory of Island Biogeography


–there was a balance between extinction and colonization on these islands θ equilibrium number of taxa

•Upon arrival at the climax community, There was a constant number of species in the plots from one observed time unit to the next

–The same species were not found in the fumigated islands, but similar guilds were present


Island Biogeography Conclusions

•Supported main assertions

•Assertions re: # species:

–Near > Far

–Bigger > Smaller

–There is an equilibrial number of species

•Spawned a great deal of additional research by many others

–One of two main proponents (Simberloff) no longer agrees with equilibrial assertion


An Historical Note

•The ideas as we have presented them were produced in reverse order

–Island biogeography was first suggested in 1963 by E.O. Wilson and Robert MacArthur

–Equilibrium between extinction and colonization was not formally tested until 1967 by Simberloff and Wilson

–Metapopulations did not come until much later in the 1980s


Formal Statement of the EIB model

•Principles of EIB

–The number of species on an island tended towards an equilibrium value  Ŝ

–Steep curve of colonizers initially

•gradually levelling out at  Ŝ

– Ŝ is determined by the equilibrium values of E and I

•balance between E and I


Ŝ is Determined by the Equilibrium Values of E and I

•I is determined by the proximity to the dispersal source AND by size of the island

–higher for closer to the site

–larger islands provide bigger targets for dispersing organisms = The target effect

•E is determined by island size AND by competition AND by distance to the source population

–smaller islands will have larger E values

–those species that are already present will influence the extinction of the successive ones

–smaller distance θ lower E and increasing persistence


Island Size and Extinction Rate

•Why would smaller island size increase E values?

–Smaller islands may restrict the population sizes of the species present

•Smaller pops are much more strongly affected

            by population fluctuations

–think back to the population growth models

–Those species that require larger home ranges or patches for existence would be unable to continue to live

–Those species requiring a certain type of habitat may go extinct because the habitat is not on the island

•islands tend to have fewer types of habitats and niches than do mainlands


Species Presence and Extinction Rate

•Why would those species that are already present influence E & I?

–If no species of a comparable guild or niche is present, even a weak competitor will be able to thrive

•Not so if there is already a better competitor for the resources already present

–Colonization rate decreases with increasing number of species present on the island

•the island approaches maximum number of species that could colonize it

•decreasing probability of any single species invading

–Species extinction rate increases with increasing number of species present

•better competitors win out


Distance from Source and Extinction Rate

•Why would decreasing distance to the source area decrease E?

–Rescue effect

•those populations that are too small could still continue to live if there is a constant influx of novel colonizers or immigrants


I and E & Ŝ and Ť

•Equilibrial Values

• Ŝ = Equilibrial number of species on the island

•Ť = Equilibrial turnover rate


Area Effect & I and E & Ŝ and Ť

•Area effect comes about as a consequence of the Target Effect

–Larger islands are better targets for dispersal propagules

–Larger islands have lower extinction rates & higher  Ŝ


Distance Effect & I and E & Ŝ and Ť

•Distance effect

–Far islands are rarely encountered by dispersal propagules

–Near islands have higher immigration rates &  Ŝ


Making the Model More Realistic

•Linear I & E is unlikely

•Usually nonlinear I and E

–Differential dispersal ability θ Nonlinear I

•Most species have a short dispersal distance

–Increasing species interactions θ Nonlinear E


Species Area Relationships

•Thomas Lovejoy's experiment in Brazil


•in late 1970’s Brazil’s government required owners of tracts of rainforest to set aside at least 50% of their land as undisturbed areas

•Brazil also allowed Lovejoy to ask farmers to set aside the tracts in regular sized patches (islands)

•From 1 hectare to 1000 hectares in size

•Recorded the numbers of animals and plants that were found after the patches had time to stabilize


Species-Area Relationships of Lovejoy’s Experiments


–Smaller patches had many less species after a while

–Huge edge effects

•drying and light penetration

–Patches that had 90% less area had the species diversity reduced by 50%

–Those species in smaller patches differed from those deeper in the forest

•mostly those found in the edges are those that favor disturbed environments


Implications of Lovejoy’s Work

•Support the independently proposed idea of MacArthur and Wilson

–The equation  Ŝ =cAz holds for the relationship between number of species and area,

• Ŝ = # of species maintained by an island at equilibrium

•c = constant that summarizes the number of species that are usually found in a unit area in a specific ecosystem

–c is larger in tropics, and much smaller in deserts

•A = area of the island

•Z = constant that is determined by the dispersal ability of the species and the proximity of the island to other sources

–it changes as you go from one set of islands to another the same species


Implications of the Species-Area Relationship


–a 90% reduction in area size θ have a 50% decrease in species abundance

–It is in large part on these data and models that conservationists try to estimate the minimum sizes of land that they need to protect to preserve the local biodiversity

•Other supporting data

–Species counts of reptiles and amphibians in the Caribbean islands

•If the log of the number of species is plotted on the Y axis and the log of the island area on the X axis

•We find that there is a staggeringly perfect straight regression line that can be fitted to the data points using 7 islands in the Caribbean

•This is one of the most often repeated sets of data to support the ideas of IB



Lecture 18
Communities, Species Diversity, and Community Stability


James A. Danoff-Burg

Population & Community Ecology

Barnard College



•Defining Communities

–How would you define communities?

•from earlier in the semester


–“An association of interacting populations, usually defined by the nature of their interactions or the place in which they live” (Rickliefs)


Properties of communities

•How can we characterize communities?

•Some possibilities:


•number of species that are found in an area


•Number of individuals


•An interaction between richness and abundance

–Number of trophic levels

–Number of guilds

•method or location of foraging

–Relative abundance of different species




–a large scale community of organisms that are usually found together

–Defined by their predominant vegetation

•e.g., the Tiaga is defined by being all evergreens and is at a Northern latitude

•what is the dominant vegetation in a desert?

•the tundra?


Biomes and Communities

•Relationship between these two?

–It is possible to think of communities as being formed because of two forces that may or may not simultaneously be at work

•An analogy

–community to a body

–each species in the community has a role to play

–in other words the species come together because they “need” each other to exist


Biomes and Communities

•Advocates of the community as body

–often have very sharp distinctions between biomes (called ecotones)

–Distinctions come about because some of the key species were missing

•the divisions between prairie and deciduous forests are usually really distinct

•Critics of community as body

–communities are not at all akin to an organism

–the species are often found together merely because they have the same physiological requirements


Open vs. Closed Communities

–Two theories about the origin and maintenance of communities

–Open communities

•do not have clearcut boundaries between biomes

•there is no ecotone present in these types of communities

•advocated by those who view the physiological requirements as the reason for species being distributed

–Closed communities

•have strong ecotones and have very tightly overlapping species distributions

•advocates of the communites as a body view the world as being full of closed communities


General Types of Communities


–sharp boundaries

–abrupt ecotones

–distinct associations between species


–boundaries are vague, gradual

–little or no association between species




–Transition zones between biomes

•Additional interpretation / theory

–Sites of generative forces for speciation and origin of community diversity

–using the paper by Smith et al.

•In Science magazine 1997, June 20 (276:1855-1857)

–usually been thought of as merely being the edges of most species ranges

•more stressed regions with less fit organisms occupying it.

•ecotones have much lower species diversity than the surrounding biomes

•shouldn’t be such important areas to conserve

•However, these regions may be key in generating new species


Smith et al. 1997 – Ecotones as Biodiversity Generators

•Summary of main points

–Explored genetic diversity within a bird species called the little greenbul (Andropadus virens) in Cameroon

–Had an ecotone between Savanna/Sahel and Equatorial Rainfores

•each of which should present different selective forces on the birds

•rainfall and other variables differ tremendously

–Measured and compared the rates of migrations of birds

•using allele frequencies on the basis of 8 microsatellite loci

•measured morphological divergence in 5 morphological characters that have a close correllation with feeding ecology, flight, and fitness

–winglength, weight, tarsus length, upper mandible length, bill depth


Experimental Sampling Design





•all but upper mandible length significantly differed between the poplations in the ecotone versus the forest

–generally ecotone had larger values

•but not at all between ecotone-ecotone and forest-forest comparisons

•Gene flow between populations differed and was quantified using the microsatellite data

•Main Result: despite varying Nm values (effective migration rates), the ecotone-forest morphological divergence still existed

–when Nm got to be huge the difference was swamped out





•Morphological divergence: due to selection for those species that had the optimal values for each trait

•The magnitude of the difference between ecotone and forest greenbul populations

–similar to that observed when many different species were compared

•Divergent selection as observed here will often lead to the production of new species

–ecotones may be integral to the production and maintenance of biodiversity in tropical rainforests


Conservation implications

•For the long-term good, ecotones should be preserved as well

–Even though they may have fewer species in them

–Even though there may be lower abundance values in them

–Even though the individuals in them are usually more stressed

–Even though the individuals in them are usually less fit

•Should be retained because they are such important generative forces for biodiversity


Species Diversity and Community Stability


–diversity = stability

•Stability Defined

–often defined as unchanging communities

•E.g., the same plant species are found in a certain patch from year to year to year without change

–Alternatively: dynamic equilibrium

•the host and parasites fluctuate continually

•without either of them being exactly at equilibrium


Stability Terms


–Lack of change in response to perturbations

–perturb a system & measure whether the community actually changes at all

–measure any aspect of community before and after the perturbation


–How much of a disturbance can be absorbed and still rebound

–Two features

•Elasticity - how quickly the community returns to the stable equilibrium point

•Amplitude of the resilience - how large of a disturnbance that the community can take and still bounce back


Stability Example

•Dan Simberloff and Edward O. Wilson’s work on Florida Mangroves

–Surveyed all the arthropods on each of the mangrove islands

–Tented entire mangrove islands

–Fogged the tree with a biodegradable insecticide that killed ALL animal living on the tree

–Noted the arthropods that returned to the tree islands over few months


Results of Mangrove Experiment


–Species richness had stabilized after 200 days

•elasticity = 200 days on average

•even for total devastation

–The actual species that recolonized differed from those that were there before the fogging

–Same trophic structure was present in the islands following recolonization

•suggesting that the proper way to define the stability of these island communities was by trophic or guild structure

•NOT by the actual species present

–Rate of turnover of the species on the islands continues

•at a natural rate of 1.5 species going extinct and recolonizing the islands at a background rate

•--> therefore the communities on the islands are always changing


Some Questions

•Do the same species have to be present after a disturbance as were there before for a community to be stable?

–Can the same community ever exist?

–Are there multiple stable states of a community?

–Can you ever dip your toe into the same river twice?

–Merely semantic?

•What is a community? 

•Is it defined only on the basis of the species that are present or on the trophic guilds present or general animal lineages present? 

•More later…


Stability and diversity

•Traditional view

–diverse ecosystems are more stable

–Called the equilibrium hypothesis

–Bases of this conclusion? 

–Mostly data on pest species outbreaks


Data for Stability & Diversity Hypothetical Relationship

•Naturally simple ecosystems => much more susceptible to invasions

–have huge outbreaks of the pest species when they invade

•Outbreaks on an unnatural and simple ecosystem tend to be colossal

–particularly in agricultural ecosystems

•If these ecosystems are reduced even further by the application of pesticides, outbreaks are even more common among pest species

–Likely due to extermination of the predator species

•Diverse tropical ecosystems seem to not have the huge outbreaks of temperate ecosystems

•Metaanalysis of more than 40 food webs

•more stable food webs tended to have a higher species diversity than frequently disturbed areas

Conclusion θ Diversity = Stability


Data Against Diversity = Stability

•Generally: reevaluations of the above data

–May be a dynamic interrelationship between diversity and stability


–Fluctuations of small mammals in tropical regions

•tend to be as large as are those found in northern temperate regions

–Agricultural systems are not good model systems

•The plants in them are totally artificial

•Have never had time to evolve resistences to the pests

•Actually many of the responses were bred out so that the plants would be more palatable

•These are not at all valid comparisons

–Diverse tropical ecosystems DO have huge fluctuations in some pest species

•at least in the one system under study

–Tropical ecosystems are tremendously susceptible to human disturbance

•Moreso than are northern forests

•Not such a strong point given that the tropical forests’ soil is notoriously poor

–Not a seed bank in the soil for things to regenerate from

–Confound soil type with diversity effects here

–Data still have yet to be collected to adequately address this issue


Non-Equilibrium Hypothesis

•Researchers opposed to Equilibrium Hypothesis

–Dynamic relationship between Diversity & Stability

•Species composition is constantly changing through time

–Intermediate levels of disturbance tend to produce the highest levels of diversity

–High levels of disturbance

•select strongly for those species that have high growth rates and are r-selected

–Low levels of disturbance

•Competitively dominant species will rule the roost and chase out all others

•Outcome: Intermediate Disturbance Hypothesis

Intermediate Disturbance Hypothesis

–figure 14.9 in Stiling

•middle values produce the greatest diversity values




Lecture 19 –
Amazon Biodiversity and Community Change


James A. Danoff-Burg

Population & Community Ecology

Barnard College


Why Are the Tropics So Diverse?

•Tropics are more diverse than similar temperate zones

–More species are found only there than in any other ecosystem

•Approximately 50-80% of all species that are found in the world are found ONLY or predominantly in the rainforests


Global Distribution of Biodiversity

•Greatest in areas where NPP is greatest

–Terrestrial: toward Equator  - Why?

–Aquatic: near shore, marine upwellings – Why?

•With many regional exceptions!



•focus of what we are talking today

•More than 65% of all tropical ecosystems are in Central and South America!

•The number of species present are much more than in other geographic locales

•Amazon is home to more endemic biodiversity than any other single location on Earth


Reasons for Amazonian Biodiversity

•Three main categories of explanations

–Abiotic Proximate

–Ecological Proximate

–Evolutionarily Ultimate


Abiotic Proximate
Explanations 1, 2

–Lack of freezing temperatures

•extreme values are most important

•The area with the extreme values usually defines the extent of most species

–Abundant rainfall

•even in the dry season, there is abundant rainfall

•Remove one of the main impediments to plant growth

–some plant lineages CANNOT cope with such extreme rainfall

–die if moved there

•Constant rainfall θ more plant species occupy a given area

–leads to our next two mechanisms


Ecological Proximate
Explanation 1

•Increased species packing (= "spatial heterogeneity theory")

–Many plant species in the tropics θ greater number packed into an area of identical size

•Supported by data

–More plants θ more niches of a greater diversity θ greater species packing

–Also θ increase in the number of canopy layers in the forest

•sometimes up to five canopy layers!

•increase # niches even farther


Ecological Proximate
Explanation 2

•Increased productivity

–Increased productivity θ greater species packing

–each species is able to accumulate more resources in a unit time

•More important in very productive areas than in less productive areas

•the niches can be much more fine-grained in high-productivity sites than in low productivity sites


Ecological Proximate Explanations 3, 4

•Increased interactions

–this is a consequence of reasons 3 and 4

–more species θ more intereactions θ more opportunities for specialization


•Predation and herbivory

•Mutualisms and coevolutionary relationships

•Larger area

–θ many potential habitats

–Many niches to occupy and therefore for many species to evolve


Ultimate (or Evolutionary) Explanation 1

•Glacial Refugia hypothesis

–traditional view: the tropics have been frequently fragmented into refugia due to glaciation

•Jurgen Haffer 1969, a petrochemist and birdwatcher

•“during the ice ages the temperature stayed the same, but the precipitation levels plummeted, θ shrinking of the tropical forest and isolation of the tropics into those areas that were able to maintain relatively high rainfall

•Much work has been inspired by this suggestion, most of which has of late contradicted it


Glacial Refugia Tested

•Cracraft and Prum 1988

–looked at the geographic distribution and phylogenies among four groups of closely related species of parrots and toucans

•found that barriers were present and that all four of the groups had similar biogeographic history

•However, spots that the barriers isolated predated those postulated by the refugia hypothesis

•were likely due to geological events that well preceded glaciation


Ultimate Explanations 2, 3

•Stability through time

–contrary to what the refugia hypothesis suggests

–intermediate levels of disturbance produces highest diversity levels

–the idea that the tropics have been stable for a long time period is not borne out by the geological data

•There have indeed been many changes in the tropics

•as was emphasized by the refugia hypothesis

•Lower extinction rates

–May come about as a result of stability

–those sites that are longer lasting (stable) will accumulate more species

–will become more diverse


Community change


–Definition: the nonseasonal, directional, and continuous pattern of colonization and extinction on a site by populations

•A species cannot occur locally without the following

–It can reach the site and is within the roaming distance

–The appropriate resources exist in the site

–It is not outcompeted, over preyed upon, over parasitized


–the appearance and disappearance of a species requires that conditions, resources, and/or the influence of enemies varies through time as well

–if they were constantly good, the organism would not disperse


Succession Definition

•Chronological distribution of organisms within an area

•The directional sequence of species within a habitat or community through time



–Single area


Successional Role Players

•Early successional species, pioneers, or colonizers

•Later successional species

•Changes in diversity

–Through time


Pioneer Species

•Hallmarks of a pioneer species


–Fast growing (high photosynthetic rate for plants)

–Good dispersers

–r-selected species

–Poor competitors


•These don’t put energy into secondary chemicals

•Can’t fend off the herbivores as later arrival will be able to

–Early successional trees have leaves that continue all the way into their canopy, not just at the crowns


Later Successional Species

•Hallmarks of Later Successional species

–Good competitors

–Shade tolerant (plants)

–Larger species

–K-selected species

–Later successional species trees have their leaves at the extremes of their branches


Modeling Succession

•Can we predict the future if…?

–knew the species that were initially present

–the likelihood that one species would replace another

•How do you know when a community is at the climax community for a site? 

–Production = respiration (input equals output)

–organic materials cease to accumulate

•Simple models assume the climax community will always be the same

–Not that viable or naturally accurate


Succession Across Biomes

•Differs depending on the native biodiversity present

•Succession in more complex communities

–Will take longer

–Have more intermediate stages

–Have different community members throughout

•Succession in simpler communities

–will of course be simpler

–e.g., in desert flora, the first plants to invade will often be those that compose the climax community


Succession Types – by Process


–Consumption of a finite resource


–Requires ongoing extrinsic environmental changes


–Intrinsic factors within the community


Degradative succession


–successsion that occurs as a finite resource is decomposed

–e.g., log decomposing, garbage dumps and discarded trash, dead animal in the forest

•Usually occurs over a short time scale of months or years

•The process has a termination point in that the resource will be completely used up

–metabolized and mineralized

•Usually the process entails each species changing the environment enough so that it no longer suits the abilities of that species and it will have to leave

–this is one of the hallmarks of succesion in general and is called facilitation


Degradative Succession - Example

•Medical and forensic entomology

–Able to date the time of death of an individual by the insects that are present on the corpse at the time of discovery

–Changes from locale to locale, and insect profile must be analyzed and determined specific to each site


Allogenic succession


–succession that occupies a new resource that does not become degraded or disappear

•the new resource forms as a result of changing external geophysicochemical forces (allo- external, genic - originated)

–e.g., siltation

•Generally happens on a very long time scale (many years)

•Siltation by the Mississippi River is an example of this - creating novel land that stretches into the Gulf of Mexico

•As the land becomes more firm, plants that require a firmer soil (grasses and other herbaceous plants) can invade and displace the pioneer species (sedges and rushes)


Autogenic Succession

•Autogenic Definition:

–succession that occurs as a result of biological processes driven by ecological forces of species within the community

–generally take place over many many years

•e.g., accumulation of litter in a forest, or peat in a bog, or increase in shading by the canopy

•when a newly exposed patch of land is colonized


Allogenic vs. Autogenic Succession

•How to distinguish between these two?

•take a soil core of the site

–the pollen from the resident plants that would be present would differ as you went from the bottom up in autogenic

–In allogenic, the plant community would stay relatively consistent

–The distinction between allogenic and autogenic becomes less clear when biological processes can accellerate the process with their roots holding the silt in place


Autogenic Succession Types
– by Habitat


–New habitat from barren ground


Mechanisms of Succession







–Early occupants change the abiotic environment in a way that makes it comparatively less suitable for themselves but more suitable for the recruitment of others

•Particularly important in sites where primary succession is occuring

–in that the ground usually has not been able to harbor ANY species at first

–e.g., glaciation, new sand dunes, new lava flows, pumice plains from volcanic eruptions, sudden deposition of massive amounts of sediment due to tsunamis

•Usually takes the form of the early pioneers changing the soil type

–pH, drainage, decomposition of organic carbon, nitrogen content

•Most important of the three mechanisms of succession & Oldest in the literature


Facilitation Example

•Lichens on a boulder

–accumulate wind-blown soil around themselves

–the soil eventually covers them up and buries the lichens

–making the lichens unable to compete

–the plants start to grow in the area now covering the lichens since there is sufficient soil to allow root growth




–the early pioneers actually PREVENT later arrivals from gaining a toehold

–A mechanism for this in plants? 


–Later species will only gain admission if the early succession species die off

•due usually to extrinsic forces

–Otherwise, the early successional species stay on forever (if no external disturbances)



–Pioneer species do not change the environment to make it easier for later arrivals to take hold

–Later species may still eventually displace the pioneer species

•they may eventually outcompete the earlier species




Lecture 20
Trophic Structure


James A. Danoff-Burg

Population & Community Ecology

Barnard College


Community Structuring

•Building on previous information

–Food webs / chains

–Top-Down, Bottom-Up control

–Community Diversity and Stability


Food web participants


–Primary producers (Autotrophs)

•the generation of plant material by converting energy into matter

–or protists or bacteria by photosynthetic protists/bacteria

•chemosynthetic bacteria

–light or energy released by the cleaving of chemical bonds for chemoautotrophs

–Secondary Producers



–Primary consumers - herbivores or planktivores

–Secondary consumers - primary carnivores

–Tertiary consumers - secondary carnivores


Types of Interspecific Interactions

•Direct interactions

–Simplest types of interactions

–predator eating the prey, herbivore eating the plant, parasite parasitizing the host...

–most readily apparent

•Indirect interactions

–Interactions that do not have the species directly encountering each other

–E.g., effects of forest fragmentation size in Brazil (Lovejoy’s Experiment)

•Small sized patches and trophic cascades

–All species were affected, even those that could have lived there

–Peccaries and poison dart frogs


Indirect Interactions

•Unexpected consequences

–Peccaries and poison dart frogs

•Both herbivores

•Could be competitors

–Decreasing one herbivore leads to a dramatic decrease in another species

•Other species is at least partially a competitor

•normally get an increase in one competitor when the other competitor is excluded


Strength of Interactions

•Weak interactors

–often ignored from the analysis of food webs

•would greatly complicated the web analysis

•Strong interactors

–tightly woven into the fabric of the food web

–Strongest interactor = keystone species

•That species that, when removed, lead to a total breakdown of the food web


Keystone Species


–The strongest interactor

–That species that, when removed, leads to a total breakdown of the food web

•Originally = terminal predators


–keystone species can be at nearly any trophic level

•Relevancy of top-down or bottom-up control of communities?

•A question

–can detritivores be Keystone species?


Determining Keystone Species


–Numerical abundance?





A Special Case

•Biomass of the English Channel species