Class Note for ECOL 406R with Professor Bonine at UA
Class Note for ECOL 406R with Professor Bonine at UA
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Date Created: 02/06/15
What is Population Viability Analysis PVA One de nition a quantitative analysis of population dynamics with the goal of assessing extinction risk PVA is a process involving 1 demographic data for the species of interest and 2 some kind of mathematical analysis of those data The product of the analysis is at least 3 some quantitative prediction of extinction risk The development and use of PVA has been at least partially driven by certain policy legislation especially the National Forest Management Act 1976 What is meant by population dynamics Population sizes change over time Why Many things affect population size competition and other interactions population structure environmental variation disturbance and succession chance events habitat attributes habitat quantity quality con guration and connectivity Let s take a look at three simple models of population growth 1 Exponential growth In a closed population no immigration or emigration population growth can be modeled as a function of the per capita birth rate b and the per capita death rate d The intrinsic rate of increase r or more generically the population growth rate is the difference between the birth and death rates rbd We can use this model to predict population size at any desired point in time in the future if we know just two things 1 the population size at some point in time either the present or the past and 2 r the intrinsic rate of increase Question What does this model suggest about how many individuals are needed for a viable population Why don t populations follow the Jcurve predicted by the exponential model 2 Logistic growth In this model the population growth rate declines with increasing population size Birth rates go down andor death rates go up as the population gets bigger Why The result is that the population has a carrying capacity a stable population size that it tends towards Question What does this model suggest about how many individuals are needed for a viable population Alternatively it may be that the population growth rate increases with population size when the population is small That is birth rates go up and death rates go down as population size increases Allee effect Why might this happen Examples 3 Structured population growth What is meant by structure Individuals in a population often differ in their contribution to population growth or decline because they differ in their chances of survival or successful reproduction This may be because of differences in age developmental stage or size What does a structured population model look like It s a matrix More specifically it s referred to as a transition or projection matrix The matrix model allows you to project into the future how many individuals there will be in the different classes and the total population size Analysis of a matrix population model yields a number of useful things a The dominant eigenvalue 7 This is the growth rate to which the population eventually converges b Sensitivities These are the sensitivity of 7 the asymptotic population growth rate to an absolute change in each element in the projection matrix The sensitivities allow one to see what would happen to the population growth rate and hence extinction probability if we could improve survival and fecundity values in the projection matrix one at a time by a particular value In the loggerhead turtle example we can answer the question would it be better to focus conservation efforts on improving the survival of hatchlings or large juveniles or adults How much bang do you get for your management buck c Elasticities Elasticites tell us the proportional change in the population growth rate that will result from a proportional change in each matrix element How much percent change in the population growth rate will result from some given percent change in each life history transition survival or fecundity As above we can answer the question would it be better to focus conservation efforts on improving the survival of hatchlings or large juveniles or adults of loggerhead turtles So which do we use to guide management sensitivities or elasticites Generally elasticities are considered more useful for management considerations 4 Stochastic models a environmental stochasticity In reality the environment varies from one year to the next Some years may be good others bad for a population of an endangered species We want to be able to say what the trend is for that population On average is it growing or declining Some populations grow or decline with regular or somewhat predictable changes in their environment that is as a community recovers and changes after some sort of disturbance e g fire ood hurricanes or other storms This also can be modeled Especially with respect to fire which is now controlled in many natural communities we can ask questions like how often should we conduct controlled burns for an endangered species to persist in that community b demographic stochasticity Very small populations are vulnerable to extinction via demographic stochasticity The analogy is tossing a coin in the case of survival vs death or offspring being male vs female or rolling a die for example when the number of offspring can be a number between 1 and 6 c genetic stochasticity You learned about this in the lecture on conservation genetics Small populations tend to loose genetic diversity Via inbreeding genetic drift or combinations of the two Rule of thumb Demographic and genetic stochasticity can cause extinction in populations lt50 Environmental stochasticity can still cause extinction in populations gt50 5 Landscape scale or metapopulation models Four attributes of habitat affect population growth and Viability quantity quality con guration and connectivity Two general principles may be distilled from the theory of island biogeography MacArthur and Wilson 1967 and metapopulation theory Levins 1969 Populations in smaller habitat patches are more likely to go extinct and unoccupied habitat patches are less likely to be colonized the further they are from occupied habitat patches Places where populations are growing are referred to as sources and places where populations are shrinking are referred to as sinks Sink populations may be rescued by source populations the rescue effect Some last thoughts on PVA The answer to the question How big does a population need to be for there to be high certainty that it will not go extinct will depend on the organism The problem is quite complex PVA requires a lot of species and situationspecific data which takes time work and money whereas managers want answers predictions about extinction now Few species will get thorough PVA When should PVA be used and what type of PVA how complex Predictions from PVA can only be as good as the data that go into the analysis and we can only have degrees of confidence in the predictions from PVA Populations should not be managed to their minimum viable population size You should learn to be critical consumers of PVA literature One of the greatest strengths of PVA is the ability to play what if games with the model That is what if management were to increase patch sizes or connectivity What if adult survival could be improved Sources that I used for this lecture and sources of additional information Beissinger Steven R and Dale R McCullough 2002 Population Viability Analysis The University of Chicago Press Chicago Illinois Caswell Hal 2001 Matrix Population Models 2nd Edition Sinauer Associates Inc Sunderland Massachusetts Gotelli Nicholas J 1998 A Primer of Ecology 2nd Edition Sinauer Associates Inc Sunderland Massachusetts Levins R 1969 Some demographic and genetic consequences of environmental heterogeneity for biological control Bulletin of the Entomological Society ofAmerica 15 237240 MacArthur Robert H and Edward O Wilson 1967 The theory of island biogeography Princeton University Press Princeton New Jersey McCullough Dale R 1996 Metapopulations and wildlife conservation Island Press Washington D C Morris William F and Daniel F Doak 2002 Quantitative Conservation Biology theory and practice of population viability analysis Sinauer Associates Inc Sunderland Massachusetts