FACTS AND FIGURES ABOUT INVASIVES FROM COX
Lecture 1 – Introduction to Invasion Biology
Lecture 2 – Terms and Language
Lecture 3 - Accidental species introduction
Lecture 4 – Intentional introductions
Lecture 5 – Introduced parasites
Lecture 6 – Characteristics of invasive species
Lecture 7 - Community and ecosystem - structure and function
Lecture 8 - Diffusion models
Lecture 9 – Traveling Waves in Heterogeneous environments
Lecture 10 – Stratified Diffusion
Lecture 11 - Application and testing of models: Types of data needed to construct models
Lecture 12 - Application and testing of models: Choosing between models
Lecture 13 – Exotics and Evolution
STATISTICS ABOUT INTRODUCED SPECIES
1)More have been introduced into North America than any other continent - approximately 6,600 species of terrestrial, freshwater, and marine organisms have been introduced into NA (VERY conservative estimate - doesn't account for those brought before European immigration, doesn't really account for many insects, freshwater orgs, or plant pathogens in Canada; also underestimates those organisms that are not pests and does not include those that are of uncertain origin "cryptogenic" species - "hidden origin")
2)aa. This trend is continuing in that between 1980 and 1993, more than 205 new species were discovered in the US - again probably an underestimate
3)aaa. This process of introductions began early on during human evolution, post domestication of commensal and agricultural species, but only really picked up after World War II. After the second war to end all wars ended, the world began to become much more of a global marketplace and international trade increased -- international trade is one of the main reasons why we have the problem with introduced species we have currently
4)In the US, introduced species have either caused or contributed to the decline of approximately 49% of all species on the threatened or endangered species lists - from Wilcove et al. 1998, Bioscience article
5)Of those listed approximately 15.8% were due to introduced predators or herbivores, 7.1% competitors, 0.8 diseases are the primary threat (total of 23.7% with exotics as primary threat) from Simberloff 1996, Consequences vol. 2 online journal
6)The distribution of invasive species in N.A. is of course not uniform - any guesses as to what would be the most likely locations? Why do you think there? -- Hawaii is first (4,598 spp established! - approx another at least 3,300 spp in cultivation, but not established!) -- Florida & Gulf coast next most heavily invaded (over 2,000 spp established, with another 25,000 plants in cultivation but not established! incl. 8% of all insects) -- Calif & pacific coast states with at least 674 spp of exotic plants (11% of the flora)
a)cc. also, Coastal marine areas and inland freshwater lakes are also strongly affected by exotics
7)The groups of organisms that are of the most interest to the public are disproportionately impacted by exotics -- of the listed species above, fish are most severely impacted (57% of listings are due at least in part to exotics), mammals next (36%), and plants least (22%)
8)Among plants, not all species are equally likely to invade (DON'T TELL WHY I THINK THAT THE TAXA ARE LIKELY TO INVADE) -- those that are most likely to invade are grasses (r-selected, disturbed habitat specialists - account for 11.2% of grass species in US), composites (r-selected, disturbed habitat specialists), legumes (able to grow in poor soil conditions, disturbed habitat specialists), and crucifers (no idea?) -- why do you think that these species are the most prone to invade?
a)ee. similarly, the geographic origin of the terrestrial invader species is not uniformly distributed around the world (WHY DO YOU THINK THAT THIS IS THE CASE? WHAT PATTERNS WOULD YOU PREDICT?) - primarily Eurasia for Northern North America - primarily tropicalCentral & South America for Florida - primarily Asia for Hawaii -- likely because of combination of recent human traffic (hence paucity from Australia and Africa) and climatological similarity to place of origin (hence the similarities in latitude)
9)N.A. is not the only location for exotic spp. wars - in terms of the ratio of native to exotics, Australia and New Zealand have a worse problem than N.A. (even though they have a smaller total number of species introduced) -- Australia has around 1,700 exotic plants (approx 21-43% of flora o S. Australia) and New Zealand has around 1,570 plants (about 47% of total flora!). -- it is particularly a problem there, as the biota of these regions are disproportionately comprised of exotic species, given the essentially island characteristic of both countries.
FACTS ABOUT SPECIFIC INTRODUCED SPECIES:
a. Pigeons (Columba livia), a.k.a. rock doves, introduced into New France, present day New Foundland in 1605, used as food, for keeping as pets, as navigation, and deliveries - for a long time, there was debate as to whether the pigeons were native or introduced
b. Honeybees (Apis mellifera)
c. Sea Lamprey (Petromyzon marinus), introduced into the Great Lakes with the formation of the Welland Canal near Niagara Falls, Canada in 1920s, bridging the gap in height
Notes from Board:
Deliberate Introductions – why introduce?
Accidental introductions – how are they introduced?
Native Invasives – how can this occur? Primarily through human action
Agenda for day:
(take home: were not able or willing to make a go of it using the native biota, were only able to last, for as little as they did before investors withdrew support, based on the assistance of introduced species, particularly bees,
- idea of America's political system being reflected by both the ethnicities & the Biota
- read off the percentage of native vs. Nonnative people in the US & their ethnicities
- people grow homesick, want to bring some of the old country over with them
- people prefer to work with the plants & animals that you know in the ways in which you know than to learn anew how work with new spp.
- this lack of familiarity w/the local biotawas the main reason that the first few colonists in New France (1604) and Jamestown (1620-1624) (the so called “lost colony”) either failed or had such difficulties
- reasons for introductions are diverse : list off
1. Intentional for agriculture,
2. Intentional for sport,
3. Intentional for decorative,
4. Intentional for land stability
5. Accidental - fellow travelers
6. Accidental - as a consequence of land changes
-also have pest species that are not introduced, that are in fact native to the area, but who have expanded their ranges because of human activities – particularly because of fire suppression, grazing, fragmentation, or other alterations of the habitat.
oExamples of this include red maples (due to fire suppression – leading to a decline in the germination success of many oaks)
oMesquite in the desert southwest (due to fire suppression and increased grazing – leading to a loss in many species of desert grassland plants and their animal associates
1. No class on 27 September (Yom Kippur), 6 Nov (Election Day), 22 Nov (Thanksgiving)
2. Be thinking about which species that you would like to begin working on for the class – it should not be one with which you are already familiar or have worked on already
GENERAL IDEAS ABOUT INVASIVES
1)Current attitude towards introduced species: WAR! INVASION!
a)Think of some of the dire quotations about the current view of introduced species, akin to war and terminology of conflict
2)current attitude about invasives is fueled by threats to biodiversity and estimations about the roles that invasives play in species loss
3)role of language in science structures our look at the subject - think about the facts of the case and try to recouch them in terms that are the opposite of Invasion Biology as we talk about matters in the course -could these facts be interpreted so that they are not as bombastic and negative?
4)Some Invasion Language definitions:
a)-introduced: species that come from one location and are brought to a new location
b)-exotic: usually ditto a, but also a species from another location
c)–alien: ditto a
d)– nonnative: ditto a
e)-invasive: a species that becomes abundant and influential invaders of a community of native species
f)adventive: Located outside habitat, though a reproductive population may not be established
g)-tramp: An widespread ant species spread by human commerce with a specific syndrome of life history characteristics: extreme polygyny, unicolonial or highly polydomous nest structure, and colony reproduction by budding (sensu Passera 1994)
h)-commensal: a species that lives with another
i)-pest: any species that is not wanted by humans – exclusively a human construct
j)-domesticate: any species that we have domesticated and have around us by choice – sometimes used as a counterpoint to commensal or tramp
k)Native: not introduced into that area by humans (the delineator that we could use to determine a native vs. non-native plant.
9. Notes about presentations:
a)Sign up for two presentations, all of which will be done in pairs
b)Write up a sheet that has the following format – fill in the blanks
i)Hypothesis Tested / General Goal / Theme(s) of Paper:
ii)Structure of Paper:
iv)Questions for Discussion:
c)Make up a total of at least 5 questions for discussion that can be used to trigger discussion, if it is flagging
d)You should plan on giving a quick review of the paper (10-15 minutes or so) and hopefully the discussion will either begin during your review or will begin and grow after your presentation – don’t be upset if we start talking about the paper before you finish all you had to present.You can work it into the discussion as we go along, or as the discussion slows.
1.three main phases of the invasion process: Dispersal and introduction, Establishment, Integration
l)the current most likely modes of dispersal for exotic species occurs in a number of ways, nearly all of which involve or occur because of humans, particularly for long-distance dispersal (WHAT ARE THEY?)
m)not all species that are introduced are successful - have two perspectives about this: 1. the Tens Rule: 3 10% relationships, only 10% of the species will make each of the steps to become a pest: only 10% of those dispersed will appear in the wild, only 10% of those will become established, only 10% of those will become problem species - therefore only 0.1% of the species that arrive on the shore will become a pest species -- this is a gross generalization from the observed statistics -- ex: Hawaii Plants (11.2% of established plant species have become pests)
n)OR 2. approximately only 1 in 7 (14.3%) are successful enough to cause problems to human endeavors - Simberloff 1996, Consequences vol. 2 online journal
5)the spread of species often does not happen in an orderly and progressive way, with the range gradually expanding each year like ripples on a pond - there are several models that have been advanced to account for this. Often there will be an incubation period or a long lag time between the time when a species has been introduced until it explodes in population size (akin to a logistic growth curve)
6)successful integration of species into a community leads to long term impacts on the evolution of the species that live in that area - they impose new patterns of selection on the native species - the natives also evolve in response to the introduced species of course, if and once they survive the initial onslaught of the exotics, a process called counteradaptation
-Recap the ideas for modes of accidental dispersal that the class came up with in lecture –
ospecies often escape from cultivation (Kudzu - Pueraria lobata) or from labs (African Clawed Frog, Xenopus sp.)
-Add to them that the movement of species (both intentionally and accidentally) is not a novel phenomenon.
ospecies have moved around since humans began migrating and dispersing around the globe
oa variety of seeds, vermin, and other human associates have accompanied them continually - most of the early movements did not move around large quantities of species, typically only a few individuals.
-Shipping and exploration have greatly accelerated the pace of movement.
oThe large-scale movement of species via ships even predates the use of ballast (originally dry ballast consisting of rocks, soil, or other stones, now essentially unfiltered seawater) for shipping.
oEncrusting species (barnacles, etc.) and boring species (isopods, barnacles, etc.) have moved around even with the earliest of European explorers.
oBefore 1820, over 90% of the insect introductions were beetles - attesting to the importance of dry ballast in the movement. These can also be traced to ports in Southwest England and to their arrival points in Nova Scotia, PEI, and St. Lawrence area. (later 1840-1860 leps became most common invaders, with the increase in commerce in living plants)
-Between travel, shipment, and war (large scale movement of huge machines and the organisms inadvertently contained within them), we are accelerating the arrival of the Homogocene (from Rosenzweig).
-many species were introduced so early into the northeast that their names seemingly reflect nativeness (Kentucky bluegrass [Poa pratensis], Canada bluegrass [Poa compressa], Canada thistle [Cirsium arvense], common dandelion [Taraxacum officinale]
-Given that Ecology, even in its earliest of modern Naturalistic roots, did not begin until well after the earliest of these movements, and even is the case currently if we work with organisms about which little is known, we have a problem.
oWhat is the true distribution of species?
oPotentially, many of the species that we currently think of as having a Holarctic distribution may have originally been very limitedin their distribution (say to the northern European seas).
oAn impact of this realization is that many of us rely upon the distribution of species to conduct biogeographic studies. as a consequence, many of these studies may be flawed, possibly leading to erroneous conclusions about phylogeny, if these characters are used in analyses.
oThese errors could in turn lead to errors in studies of evolutionary or conservation biology. If the latter is the case, we may make errors of judgment in the design of conservation preserves or some similar applied question.
Notes on Prep readings for Hudson valley article (by Will and Erin) – from Cox
- many of the introductions into the Northeast have been ecological time bombs, with long lag times before becoming invasive (our fourth stage of the invasion process, after integration), great example is Purple loosestrife.
- Purple loosestrife (Lythrum salicaria) was introduced into North America before 1814 (when Asa Gray and John Torrey surveyed Northeastern NA. plants first noticed it). It did not become an invasive until 130 years later, with the advent of the US highway system in the 1940s and irrigated farming - both of which disturbed and created wetlands. Now it is essentially continent-wide in distribution.
Much of the disturbances (nationwide as well as in the NE) are due to land alterations. in the NE, this began in earnest in the 1600s. Clearing forests, farms established, wetlands drained, etc. Facilitated the establishment and integration of species that were introduced with the movement of property and ballast and livestock feed and bedding and in and on the colonists and domesticates
- Carp, although intentionally introduced for sport and food, have been of major importance in the Hudson Valley.they were first intentionally introduced into the Hudson in 1831. Propagated on a small scale until 1870s. federal, state, and private hatcheries began in the 1870s and led to the widespread cultivation of this species and dissemination of the species across NA. Now they are viewed as less desirable because they destroy aquatic vegetation and lead to increased turbidity, which leads to increased egg and larval mortality of various native species. control of them depends on killing the entire water body / watershed with rotenone or other piscicides and then restocking native species (since all are killed).
Cox’s chapters 14 – 16 form Part III, which details intentional introductions for game purposes, native invasives (Cox’s “homegrown exotics”), and human domesticates (respectively)
A. Game introductions -
i)Main threats: competition and ecological replacement, land degradation, genetic hybridization, importation of exotic illnesses (which we’ll talk about next week) – also beneficial aspects: could replace species that have been extirpated by human activity (eg. Gemsbok and horses)
1.From 1948 – 1977, the US F&WS encouraged the introduction of exotic species into N.A. for the purposes of game – The federal program was stopped in 1970 and in 1977 Carter stopped the use of federal funds and resources for exotic introductions (but what about fish stocking…?)
a.African Gemsbok (Oryx gazella) was introduced into New Mexico and have successfully competed with pronghorn (Antilocapra americana) and feral horses (which are themselves reintroduced)
b.Reindeer into Alaska competing with Caribou and destroying native tundra
c.Game Ranching is popular in west, particularly Texas of axis, sika, and fallow deer, blackbuck and nilgai antelope, Barbary sheep, Ostriches, emus, Eurasian wild boar – were all introduced into Texas in 1930’s to 1950’s because of the extreme depletion of native game species by hunters
2.Fur bearing animals have been introduced in many areas, particularly nutrias – these southern South American rodents devastate the local salt-marsh vegetation through over reproduction and then over grazing and in the process, competing with the native wintering waterfowl – also serious predators on bald cypress seedlings, and could lead to the elimination of this type of vegetation in coastal Louisiana
3.Game birds – ring necked pheasant into NW US – nest cuckolder in the endangered prairie chicken nests
4.Sport fish – carp (huge despoiler of native vegetation and the local shore ecology), brown trout outcompeting the native golden trout (Onchorhynchus aquabonita) in California’s Kern River
B. Homegrown exotics (local invasives)
(diseases – epidemics and epizootics – viruses, bacteria, endosymbiotic organisms) or Emerging Infectious Diseases (EIDs from Daszak et al. 2000, Science)
1. Unique features to these phenomena:
a)Biological modes are a bit different – quick review of life history of many species
i)Often infect more than one species and as a consequence need normal host as well as intermediate host(s)
ii)Often spread by the intervention of one or more vectors
iii)Obligately symbiotic (parasitic, parasitoidal, etc.)
iv)Often have diseases go between humans and other animals in both directions – these are called Zoonotic illnesses (from Latin for “animal” “disease” “alteration” –[otic])
b)Similar modes of spread and introduction are necessary (hurdle #1)
c)In addition, before the parasite causing the epidemic or epizootic can become established, and certainly before it can become integrated into the population (following the scenario that we discussed at the beginning of the class), the following are needed:
i)Vector (if any)
ii)the intermediate hosts (if any) are needed
iii)Proper environmental conditions needed for all of the host(s) and vector(s)
d)Consequently, the deck is stacked against parasites becoming established, much more so than for free-living species
e)Have several ecological types of parasites (decreasing ease of establishment in novel areas)
f)However, the spread of these diseases is being increased with increasing shipping and travel rates, particularly between areas that were not previously exposed to shipping and travel
i)Of particular importance for the spread of epidemics is adventure travel to novel areas
2. Examples of introduced epidemics (Read Guns, Germs and Steel, by Jared Diamond, which talks about this quite a bit):
a)Smallpox, which is believed to have been introduced into the Roman Empire from Asia, which wiped out ¼ of the Roman Empire’s population, and is hypothesized to have been one of the factors which ended the Roman Empire
b)Bubonic plague in the 1300s in Asia, which decimated the population in central Asia, spread by the invading Mongols, who picked up the illness from Europe (where it wiped out 1/3 of Europe)
d)Malaria - which is introduced into many areas where it was not previously.
e)Cholera – a disease introduced into and from many areas around the world – e.g., Vibrio cholerae which was introduced into Peru in 1991 from Asia – introduced in ballast water of ship, coincided with an algal bloom and then a red tide out break (dinoflagellates, which are the intermediate hosts) as a consequence of an El nino year – sickened over 300,000 people and led to the temporary ban on the selling of seafood exports from Peru, which is a major component of their economy
3. Examples of introduced epizootics of interest to humans.
a)Shrimp viruses among the shrimp ranchers (or farmers)
b)American Foul Brood disease (a spore forming bacterium, Bacillus larvae) that may have been introduced into the US from elsewhere, probably Europe, incubated here and then reintroduced into Europe and elsewhere
1)It is of great interest to determine what species may become invasive
a)If there are characteristics that can be used to predict the species that may become established, we can predict better which species should receive the majority of effort in control, when they are discovered in novel locations
b)Great and obvious applied value and utility
c)The characteristics that make a species an invader in one ecosystem may be different from those that make or predispose a species to become an invader in another ecosystem – there may be a case-dependency on the species that can be expected to be invasives
2)What are the characteristics that may predispose species to become invasives?
a)Abundance in native land (Williamson & Fitter 1996: likely to become invasive, probably single most important factor when comparing established invasives and native species)
b)Widespread distribution (often conflated with abundance)
c)Great dispersal ability or migratory tendencies
d)Seed production – or great reproductive capability (often thought of as being key – Williamson & Fitter 96 disagree) – being r-selected in general
f)Large body size (height, leaf size, and taller than wide)
g)Small body size
h)When an essential symbiont or key interactor is present elsewhere
j)Affinity with humans (anthropophilic)
k)Capacity for asexual reproduction
l)Number of individuals being dispersed or released and the number of release events
m)Species has a history of invading elsewhere
n)Close relative has a history of invading similar habitat or just capable of invading anywhere
3)The above characteristics can be broken down into three general categories:
a)Those that maximize or enable high reproduction
b)Those that enable great ecological dispersal
c)Those that enable species to be greatly ecologically flexible
1)As we’ve been discussing the papers thus far and the general phenomena that underlie them, we’ve been assuming that all locations are susceptible to invasion and that that susceptibility is uniform and high
a.this is not universally the case, there are entire ecosystems that are relatively immune to invasion – such as the vernal pond flora in central California, which seem to be free of exotics
b.Similarly, not all species have been equally successful in invading all areas and that not all species are capable of invading a single given area – despite the fact that they have been introduced into those areas
c.given that there are ecosystems that are differentially susceptible, species that are differentially successful, and that the ranges in which those species are able to invade are not limitless – we should be able to create some rules within which we should be able to predict which ecosystems may be invaded, where species can disperse, and where they will be successful
d.We can look at these questions in at least two ways: Empirically what have their impacts been? And Theoretically, what would we expect from the introduction of a novel player? – The papers that we’ll be looking at today generally talk about the first question (empirical impacts of exotics), so let’s talk now about the theory end – what can we expect?
2)Four general phenomena can be described and modeled that could bear on the above points
a)Characteristics of invaders (discussed last week) – we went through and came up with many characteristics of invaders in different ecosystems and why they were thought to be so important.Remember that we concluded that most of them could be lumped into three general categories – 1) those that enhanced the population growth rate, 2) those that ensure that they will be dispersed, and 3) those that allowed them to take advantage of the new place
b)Do characteristics of invaders predict their impact?
i)Well, numerically we have an ability to predict that very few of the species introduced will have a major, ecosystem function-altering impact, because of the tens rule
ii)However, the tens rule is only an empirical observation, not a theoretical derivation – we don’t really know why it is that only around 10% of the introduced will become established and why only 10% will become integrated (invading) into the community
iii)Can get keystone exotics that dramatically restructure the ecosystem into which they have been introduced – what are the characteristics of those that do dramatically alter the ecosystem functioning where they have been introduced? (from Cox, ch 17, p. 240s)
(1)Ecological distinctiveness of the exotic, relative to the preexisting natives appears to be a key factor in the impact expressed
(2)Animals of higher trophic levels often have a disproportionately large impact (such as the piscivorous Nile Perch in Lake Victoria)
(3)Detritivores tend to have minimal impact on the ecosystem
c)Are there characteristics of resistant ecosystems? – where would we expect to be immune to introduced species?
i)Related questions: are communities tightly constructed and related to each other homeostatically (as Cox says – meaning that there is some sort of a feedback loop tying together the population sizes of each species in the community) or are they loose assemblages of individual species that have similar ecological requirements? In other words, are they open or closed?
ii)The first view is the equilibrial hypothesis of community structure – there are clear assembly rules that bind together the construction of communities, most of which lie in the environmental conditions in which they occur.If we know the ecosystem ahead of time, we could elegantly predict what species will arise there.
(1)Species are tied together based on their interactions (mutualisms, competitions, predation, etc.)
(2)Based on the intricate relationships among the species, we should expect that these types of communities are closed to invaders and should have lower invasion rates
(3)Therefore, the main time in which these communities would become invaded would be when they are disturbed or the environmental conditions are made to change for some reason
(4)This viewpoint also believes that changes in community structure are unnatural and usually a consequence of those changes – the land-use managers who attempt to espouse consistency in preserving a given community implicitly adhere to this view of communities
iii)Second view is the nonequilibrial hypothesis for open communities
(1)consequently, the communities are easily invaded and those species that find the appropriate environmental conditions (including the absence of predators and prey) will be able to invade
(2)under this viewpoint, the “constancy that we sometimes witness is merely because the species do not accurately track the environment which is actually continually changing”
(3)this viewpoint views that change is inevitable and a natural part of the ecosystem
iv)experimentally choosing between these two viewpoints is not easy, as all communities are invasible to some degree – similarly, it seems that disturbing all ecosystems will lead to an increase in the number of invasive species arriving and taking over
v)A similar debate about the relationship between community characteristics and invisibility is the role of enhanced biodiversity in preventing invasion.
(1)This will be the focus of the Wiser et al. paper that we’ll discuss today.
(2)Won’t talk longer about this
d)When will these invasions happen and at what rate?
i)Frequently, exotics have a time lag between their introduction and their explosion WHY?
(1)often this is correlated with the occurrence of a disturbance or perturbation or the introduction of an exotic species
(2)Possibly this is essential for the building up of the species to a population size that is large enough to be explosive
(3)Could be happening because of some ecological limitation (need to adapt to the local ecosystem?) or because of some genetic limitation slowing them (bottlenecks and hybridization with local species)
Goal of animal movement models is to reduce the movement of species to the fewest possible variables that can nonetheless still account for most of the observed data.
Implied in this discussion is that we are not going to be able to model the movement exactly. Also,there is therefore no universally agreed upon final point at which a model is finished or is even adequate - they are mostly heuristic devices for elucidating the essence of why and how species move.
We'll be talking about three general categories of models in the next three weeks.
1. The base diffusion model - this is the simplest model, generally assuming that the environment is homogenous and that there are no interindividual differences in the population.
·recognizes that there are temporal fluctuations in population growth rates due to clumping of birth and death events (discrete growth) or due to density dependence within our population (logistic growth)
2. The Traveling wave model in heterogeneous environments
·essentially only a modification of the diffusion model, with the assumption of uniformity in the environment being change
3. Stratified Diffusion models
·Recognize both short and long-distance dispersal modes available to the animals
·Changes the assumption of uniform and random walks
We'll talk today about the base version of these movement models - the Diffusion model.
What would be the features of both the simplest environment and the simplest species that could disperse within that environment?
1. Uniformity of resources (food, shelter, mates, hosts)
2. No predators or parasites or other factors limiting or affecting their growth and movement
3. no abiotic environmental factors (wind, storms, etc.)
4. no density dependent factors are at work either (population is growing exponentially)
5. random walk - no directionality in movement - no obstructions hindering reverse movement – no influence of the movement of one species on another
6. equal survival probabilities and equal death probabilities
7. No difference in the Diffusion rate (rate of individual movement)
8. (For MRR studies we also include: that the recapture rate is constant and representational of the population as a whole
Base equation of the model:
Time lags leading to pulses in the distribution of species (more later in the traveling wave model discussion.)
Jump dispersal - when sudden long-distance (amount depends on scale) dispersal occurs -- possibly due to the movement of propagules (seeds, spores, planktonic forms, presence in ballast water, other human movement, etc.)
1.Background: thus far we’ve been talking about spreads of species in homogenous environments, which has thus far created a single spread of animals across an environment
·Need to correct something that I said incorrectly last time about waves of spread
·I had erroneously said that you could get a series of waves under the base diffusion model – you would not, you would only get a single wave front that increases behind the wave front and then stabilizes at the carrying capacity (since we are using the logistic growth model)
·The phenomenon that I mentioned last time (with the species consuming all the resources behind the wave front and then making the environment uninhabitable will be relevant to our discussion today. More on that in a bit.
2.Our wrinkles of the day: change the environment to be non-uniform
·The Environment will be thought of as a linear environment, with some patches being favorable, and others disfavorable
·Individuals will try to get out of the bad patches quicker than the good patches and will do better in the good patches than the bad
·This could also be true in a 2-D environment, where the patches change regularly outward in the form of a bulls-eye
·Because the environment is non-uniform, we have to have two sets of constants that will be included into the base Fisherian diffusion model (1 will be for the favorable environment and 2 for the disfavorable environment)
·l1 and l2 are the lengths of each patch == l1 and l2 are different but unchanging
·epsilon1 and epsilon2 are the intrinsic instanteous growth rate of the population in each patch == epsilon1 is > epsilon2; epsilon 2 may be negative, which will be relevant below
·d1 and d2 are the diffusion coefficients in each patch == d1 < d2
3.Regular environments, with l1 and l2 unchanging and uniform, produces two main outcomes, based on the relative sizes of l1 and l2
·If favorable patches are greatly separated from each other (l1<<l2), then the population will decline locally until it goes locally extinct (fig. 4.2a)
·If favorable patches are relatively clumped together (l1>>l2), then we get our traveling wave, with a steady increase of the size of the general area that is occupied. (fig 4.2b)
·When would the traveling periodic wave be obtained? When will the invasion be successful? (section 4.3) (see Fig. 4.3)
·E2 (the proportion of the intrinsic growth rate of the unfavorable to favorable patch; epsilon2/epsilon1)
·D2 (the proportion of the diffusion coefficient [dispersal speed] of the unfavorable to favorable patches; d2 / d1)
·When the threshold E*2 value is exceeded (E2 > E*2), the traveling periodic wave will be obtained
·E*2 = -(tan L1 / 2)squared / D2
·When the threshold D*2 value is not exceeded (D2 < D*2), the traveling periodic wave will be obtained
·L*2 = 2(tan L1 / 2) / -E2
·When the threshold L*2 value is not exceeded (L2 < L*2), the traveling periodic wave will be obtained
·D*2 = 2(tan L1 / 2)squared / -E2
·What speed will this wave be spread, on average? (assuming constant D and d1=d2)
·If there is no heterogeneity, it spreads only as a consequence of epsilon and D; v= 0 in fig 4.4c
·If the environment is exactly half and half (good vs. bad habitat), the wave spread is roughly one half the rate if there were no heterogeneity (v = 1 in fig 4.4c)
·If the environment is largely unfavorable, there will be times that the population will not become established, let alone spread (v is large, = 4 in fig. 4.4c)
·Patch size is of utmost importance – not just an absolute patch size, but the relative sizes of the good versus bad patches is key – as is the relative sizes of the bad patches relative to the dispersal abilities of the organism (not stated by S&K, but should be emphasized)
·This is also the point at which we introduce the idea that I had prematurely introduced last week about the patches behind the front expanding into optimal, all l1 habitat initially, being overexploited, and made to be incapable of supporting the species
·This would also produce the traveling wave front, but would do so only by slowing down the waves behind the frontal one with the disfavorable habitat
·The front wave would expand as though there was not unfavorable habitat
·The secondary waves would be slowed by the recovery time (epsilon) of the resources
4.Irregular environments, with inconsistent l1 and l2 sizes leads to Traveling Irregular Waves
·We could do one of two things with this mixed bag of patch sizes
·A. we could calculate the spread of the species in each patch and then add them all together
·B. we could calculate the mean values of l1 and l2 and incorporate the sample variance into the equation – this latter one is the preferred route and is akin to incorporating environmental stochasticity into the base exponential and logistic population growth models.
·We again have two possible outcomes in this model
·A. local extinction (like fig 4.2a in periodic traveling waves)
·B. irregular expansion of the propagating wavefront (like fig 4.5)
·Here the wavefront expands irregularly and as a consequence of the relative widths of the good and bad patch widths
·Also it seems that the degree of sample variance does not play a huge role, based on simulations – the average spread of the population through time seems to remain very constant, irrespective of the degree of spread irregularity – the average spread is very similar to that of the traveling periodic wave
·Therefore: the spread of the irregular traveling wave can be pretty accurately approximated with the simple periodic traveling wave
5.S&K then talk about the implications of these outcomes relative to:
·habitat fragmentation and the movement of species through that environment
·A reflecting versus absorbing barrier
·Edge effects and their impact on the spread of species
·The SLOSS debate
1.How Stratified Diffusion differs from the previous models of diffusion
2.Discussion of movement types – range-versus-time curves
3.Scattered colony expansion model
4.Coalescing Colony Model
Premise: review the types of models that have been used to model the spread of invasive species
In class we covered three general models
1. Diffusion with random walk
2. Diffusion in a heterogeneous environment
3. Stratified Diffusion
·these are really only the very start of the types of models that are used to model the spread of species
·some have said that the difficulty in modeling and the inability to generalize any local model to more global uses may be the reason why people think that invasions cannot be easily predicted using mathematical models
·similarly the question of which model to use is relatively opaque - how to solve this?
Let's first talk about the features of the species that would need to be modeled in order for the model to be constructed
1. autecological attributes -
·the ecological or natural history characteristics of species that may lead them to become invasives (e.g., nitrogen-fixing, short juvenile periods, large dispersal phases, and others from Kolar & Lodge)
2. Environmental resource fluctuations
·this is applicable to both the novel and the original habitats in which the alien originated –
·primarily boiled down to the resource availability and disturbance regime –
·many scientists say (as we've heard already) that no invasion happens without a disturbance, since humans have accelerated the disturbance regime so appreciably, we are responsible for much of the current invasion rate
3. Organismal-environment interactions
·environmental quality influences so strongly the reproductive rates of the invasive species,
·often these come about synergistically, such that the reproductive success of the invasive is not solely determined by additive processes
4. Demographic processes -
·age or sex-specific mortality patterns,
Go through their model on p. 251
Predictive models of plant spread - Three general types:
Those that are used can be broken up into three categories, based on the model data input and the output (taken from Higgins and Richardson 96 - available online in the readings section)
1. Simple demographic models (involves ecologically meaningful data that influence birth and death rates) - predict the number of individuals in a single population - usually these are incorporated into what are thought of as the usual invasion models (what we've been discussing) -- useful for predicting the likelihood of establishment, extinction, and population density
a. Exponential growth model
b. Logistic growth model
c. Discrete models (a.k.a, Logistic -difference models) - analogous to the logistic growth model, but time and population sizes are used as discrete variables, e.g., not continuous individuals as in the exponential and logistic base models - continuous models are more realistic and better developed than discrete models
2. Spatial - phenomenological models are most interested in predicting the area of the environment that is occupied by the invasive species, based not on the ecological mechanisms that may be used to predict the spread.Instead they assume that the organism-environment interactions are relatively homogenous and determined by empirically derived constants
a. Regression models -use historical spread data to quantify the relationship between area invaded and time - attempts to fit the area occupied already to logistic curves using a regression - recognize that the spread of species progressively slows as more of the environment is occupied - often used to infer backwards where and when a species was introduced into the local environment
b. Geometrical models - assumes that there are multiple introduction foci - uses simple exponential growth and ignores demographic stochasticity
c. Markov models- similar to above but use matrix algebra to capture more of the space and time variables - commonly used in forecasting landscape change impacts - a summed variable at some time t+1 in the future that is occupied by the invasive - incorporates differential birth, death, and population change rates in each landscape form - assumes that history has no effect and that only the current ecology is important and that transition probabilities are constant through time - have been used in the past to predict the spread of root disease epidemics - involve no ecological mechanism, so it may be useful if it is impossible to predict the future but cannot muster much background information on the species, but have a great history of the land use and changes
3. Spatial-mechanistic models - based on independent estimates o ecological parameters, usually at a lower ecological level (say individual behavior) and then extrapolated to higher levels (say the level of populations) - they therefore enrich our ecological understanding
a. Reaction-diffusion models (what we have spent the last three weeks studying)
§assumes that the population size increases and spreads out evenly locally and according to a normal distribution (greatest in the center and follows a normal distribution curve
§these models are pretty robust to violations of many assumptions and have successfullypredicted the spread of a great many animal species
§this is often because of the strongly erratic and leptokurtotic dispersal distances in plants due to wind and animal dispersal mechanisms
§predict that the square root of the area should be a linear increase
b. Metapopulation models
§metapopulations are systems of local populations that are connected by dispersing individuals
§can be modeled as a system o population growth models
§if we make an analogy between the local focus of the invasion with the local population and model the population growth explicitly in the local environment, we can very accurately predict the spread of species
§have the problem of introducing a scaling artifact into the model when the local patches are sufficiently dissimilar to not allow us to make homogenizing assumptions.
c. Individual-based cellular automata models
§used then metapopulation assumptions of habitat homogeneity and clean separation between the component patches does not apply, say when the species do not have local patches or flow evenly one "population" into another
§here, the local environmental conditions experienced by each individual are important and we therefore need to model the spread of a species on an individual by individual basis
§assumes that there are a discrete array of cells that can each take on a number of states that will impact on the spread of the species
§incorporates the environmental stochasticity and heterogeneity into them
§not commonly used, even though they have obvious utility, most likely because of the huge amount of background initial ecological assumptions necessary to create the model
How to select a model?
1. Demographic models are of most use locally, when the spread of the species is from a single introduction point
2. Spatial-phenomenological models are of most use when we are only interested in the area covered by the spread of the species AND the area is relatively even and homogenous, at least at the level of the analysis OR when the ecological mechanistic understanding is limited
3. Spatial - mechanistic models - of use when we know more about the base ecological situation than in the spatial-phenomenological models- these models require that a great deal of effort go into determining the parameters behind the models (parameterizing the models)