Genetic estimation of dispersal in metapopulation viability analysis

Abstract

For geographically closed populations, it has long been known that the dynamics of rare populations are affected by demographic stochasticity, and that a short string of ‘bad luck’ (of the random variable demographic outcomes in a finite population) can easily drive rare populations to extinction. The commonly taught approximation for calculating this extinction risk, PðextinctionÞ 1⁄4 ð b Þ0 (where d, b and N0 are the respective death rate, birth rate, and initial abundance), clearly shows how sensitive population fate can be to initial abundance (Gotelli, 2008). However, when populations are geographically connected to others, immigration can ‘rescue’ rare populations from becoming extinct, and the connectivity of multiple populations created by dispersal greatly bolsters the persistence probability of the overall population. As dispersal amongst fragmented habitats increases a population becomes panmictic; overall abundance is enhanced through connectivity and the impact of demographic stochasticity on extinction risk decreases. Conversely, if dispersal is completely impeded by the loss of connectivity among habitat patches, the dynamics in each local population will be more greatly affected by local abundance, birth and death (Clobert et al., 2001). Between the realms of zero and panmictic dispersal resides the concept of a metapopulation (Levins, 1969, 1970). Theoretical studies have demonstrated the positive nonlinear relationship between metapopulation viability and the rate of dispersal among the component sub-populations (Hanski, 1999). Thus, it is not surprising that Greenwald (2010) found metapopulation viability in ambystomatid salamanders to be affected by methodological approaches to estimating dispersal that produce disparate results. The genetically based approach to estimating contemporary (as opposed to historical) rates of dispersal in a metapopulation viability framework will nevertheless be of use to many. The unique viability issues that a rare or declining population faces often requires development of original population models that match the available data and knowledge. For future users of Greenwald’s approach, I suggest using a programming language to develop a population model that matches the situation (Caswell, 2001; Bolker, 2008). Use of canned software packages can produce biased predictions when the user is forced to make complex modeling assumptions about levels of density dependence, environmental stochasticity, probability density functions describing stochastic processes, mutation rates and more (Morris & Doak, 2002). Moreover, it is not universally true that population viability is insensitive to initial abundance (Greenwald, 2010). Because of demographic stochasticity, Allee effects, inbreeding depression and other factors, a small population’s risk of extinction can be highly sensitive to abundance (e.g. see the simple equation above). Thus, careful attention should be paid to both the actual and genetically effective levels of abundance that viability projections are initiated at. Nevertheless, the assumptions made in Greenwald’s (2010) models should not take away from the novel use of genetically based estimates of dispersal in a metapopulation viability analysis. In the past, many have used dispersal– distance functions to parameterize dispersal in population models. Underlying these functions is the biological assumption that a landscape is homogeneous; a single probability density function describes an individual’s random chance of moving a given distance, regardless of where it is coming from, where it is going to, and the habitat it must cross to get there (i.e. akin to the dispersion of gas molecules in a room). Dispersal–distance functions might adequately describe wind dispersal of seeds, movement of invertebrate larvae in oceans and other passive forms of dispersal. However, a single homogeneous function cannot capture the complex processes involved in the movement of a vagile animal from one location to another across a heterogeneous landscape that is reap with both costs and benefits to dispersal and philopatry. Greenwald’s (2010) use of genetic-assignment tests for estimating contemporary dispersal in and out of specific