FW662 Lecture 15 – PVA 1Lecture 15. Minimum Viable Population Models, Estimating Population PersistenceProbabilities, Review. Reading: Beissinger, S. R., and M. I. Westphal. 1998. On the use of demographic models ofpopulation viability in endangered species management. Journal of WildlifeManagement 62:821-841.Optional:Boyce, M. S. 1992. Population viability analysis. Annual Review of Ecology andSystematics 23:481-506.A standard definition of a population is “a group of individuals of the same species occupying adefined area at the same time” (Hunter 1996). Two procedures are commonly used forevaluating the viability of a population, or the probability that the population will survive forsome specified time. Population viability analysis (PVA) is the methodology of estimating theprobability that a population of a specified size will persist for a specified length of time. Theminimum viable population (MVP) is the smallest population size that will persist somespecified length of time with a specified probability. In the first case, the probability ofextinction is estimated, whereas in the second, the number of animals is estimated that is neededin the population to meet a specified probability of persistence. For a population that is expectedto go extinct, the time to extinction is the expected time the population will persist. Both PVAand MVP require a time horizon, i.e., a specified, but arbitrary, time to which the probability ofextinction pertains.The topic of PVA has become very popular, with 2 recent books (Beissinger and McCullough2002, Morris and Doak 2002) providing extensive coverage of the topic.Definitions and criteria for viability, persistence, and extinction are arbitrary, e.g., a 95%probability of a population persisting for at least 100 years (Boyce 1992). Mace and Lande(1991) discuss criteria for extinction. Ginzburg et al. (1982) suggest the phrase “quasiextinctionrisk” as the probability of a population dropping below some critical threshold, a concept alsopromoted by Morris and Doak (2002), Ludwig (1996a) and Dennis et al. (1991). Schneider andYodzis (1994) use the term quasiextinction to mean the population dropped to only 20 femalesremaining.The usual approach for estimating persistence is to develop a probability distribution for thenumber of years before the model "goes extinct", or below a specified threshold. The percentageof the area under this distribution where the population persists beyond a specified time period istaken as an estimate of persistence. To obtain MVP, probabilities of extinction are needed forvarious initial population sizes. The expected time to extinction is a misleading indicator ofpopulation viability (Ludwig 1996b) because for small populations, the probability of extinctionin the immediate future is high, even though the expected time until extinction may be quiteFW662 Lecture 15 – PVA 2large. The skewness of the distribution of time until extinction thus makes the probability ofextinction for a specified time interval a more realistic measure of population viability. Simple stochastic models have yielded qualitative insights into population viability questions(Dennis et al. 1991). But because population growth is generally considered to be nonlinear,with nonlinear dynamics making most stochastic models intractable for analysis (Ludwig 1996b),and because catastrophes and their distribution pose even more difficult statistical problems(Ludwig 1996b), analytical methods are generally inadequate to compute these probabilities. Hence, computer simulation is commonly used to produce numerical estimates for persistence orMVP. Analytical models lead to greater incites given the simplifying assumptions used todevelop the model. However, the simplicity of analytical models precludes their use in realanalyses because of the omission of important processes governing population change such asage structure and periodic breeding. Lack of data suggests the use of simple models, but lack ofdata really means lack of information. Lack of information suggests that no valid estimates ofpopulation persistence are possible, since there is no reason to believe that unstudied populationsare inherently simpler (and thus justify simple analytical models) than well-studied populationswhere the inadequacy of simple analytical models is obvious. The focus of this paper is oncomputer simulation models to estimate population viability via numerical techniques, where thepopulation model includes the essential features of population change relevant to the species ofinterest.The most thorough, recent reviews of the PVA literature are provided by Beissinger andWestphal (1998) and Boyce (1992). Shaffer (1981, 1987), Soulé (1987), Nunney and Campbell(1993) and Remmert (1994) provide an historical perspective of how the field developed.Qualitatively, population biologists know a considerable amount about what allows populationsto persist. Some generalities about population persistence (Ruggiero et al. 1994) are:1. connected habitats are better than disjointed habitats;2. suitable habitats in close proximity to one another are better than widely separatedhabitats;3. late stages of forest development are often better than younger stages;4. larger habitat areas are better than smaller areas;5. populations with higher reproductive rates are more secure than those with lowerreproductive rates; and6. environmental conditions that reduce carrying capacity or increase variance in thegrowth rates of populations decrease persistence probabilities.This list should be taken as a general set of principles, but you should recognize that exceptionswill occur often. In the following section, I will discuss these generalities in more detail, and inparticular, suggest contradictions that occur.FW662 Lecture 15 – PVA 3Typically, recovery plans for an endangered species try to 1) create multiple populations of thespecies, so that a single catastrophe will not wipe out the entire species, and 2) increase the sizeof each population so that genetic, demographic, and normal environmental uncertainties are lessthreatening (Meffe and Carroll 1994:191-192). However, Hess (1993) argues that connectedpopulations can have lower viability over a narrow range in the presence of a fatal diseasetransmitted by contact. He demonstrates the possibilities with a model, but doesn't have data tosupport his case. However, the point he makes seems