Fig 3 - uploaded by John Nagy
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Average population size at census time with respect to emigration rate for several values of (a) attack rate γ ˆ JA , (b) colonization rate β, (c) dispersal survival π and (d) catastrophe rate µ c , when the catastrophe rate is assumed not to depend on the local population size. Similarly, average population size for several values of (e) dispersal survival π and (f) catastrophe rate in full patches µ K , when the catastrophe rate is assumed to depend on the local population size according to (7). Other parameters have their default value (Table 2). Curves for different parameter values are drawn with different grey scale, as described in the corner of each panel. Attractors are drawn with a solid curve, and repellors with a dotted curve.
Source publication
Question: How might global climate change affect American pika (Ochotona princeps) metapopulation dynamics in the Great Basin, and how would such effects impact evolutionary dynamics of dispersal? Mathematical methods: A structured, semi-discrete, mechanistic metapopulation model in which patch age is the structuring variable. We apply adaptive dyn...
Citations
... Critically, while the context of each marsh dictates the emergent properties of the entire system, our modeling approach can indeed be synthetic and generalizable to other patchily-distributed endangered species. Our model and results thus have relevance to many species in metapopulations subject to climate stressors including American pikas (Ochotona princeps), Cabrera voles (Microtus cabrerae), Dupont's larks (Chersophilus duponti), and others [55][56][57][58][59]. A data-driven tool that can synthesize predictions and simulated interventions will be valuable to efficiently and effectively manage the numerous species and communities that depend on conservation intervention if they have any chance to survive. ...
While metapopulation theory offers tractable means to understand extinction risks for patchily-distributed endangered species, real systems often feature discrepant patch quality and accessibility, complex influences of environmental stochasticity, and regional and temporal autocorrelation. Spatially structured metapopulation models are flexible and can use real data but often at the cost of generality. Particularly as resources for management of such species are often critically limited, endangered species management guided by metapopulation modeling requires incorporation of biological realism. Here we developed a flexible, stochastic spatially structured metapopulation model of the profoundly endangered Amargosa vole, a microtine rodent with an extant population of only a few hundred individuals within 1km² of habitat in the Mojave Desert. Drought and water insecurity are increasing extinction risks considerably. We modelled subpopulation demographics using a Ricker-like model with migration implemented in an incidence function metapopulation model. A set of scenarios was used to assess the effect of anthropogenic stressors or management actions on expected time to extinction (Te) including: 1) wildland fire, 2) anthropogenically-mediated losses of hydrologic flows, 3) drought, 4) intentional expansion of existing patches into ‘megamarshes’ (i.e. via restoration/enhancement), and 5) additive impacts of multiple influences. In isolation, marshes could be sources or sinks, but spatial context within the full metapopulation including adjacency could alter relative impacts of subpopulations on all other subpopulations. The greatest reductions in persistence occurred in scenarios simulated with impacts from drought in combination with fire or anthropogenically-mediated losses of hydrologic flows. Optimal actions to improve persistence were to prevent distant and smaller marshes from acting as sinks through strategic creation of megamarshes that act as sources of voles and stepping-stones. This research reinforces that management resources expended without guidance from empirically-based modeling can actually harm species’ persistence. This metapopulation-PVA tool could easily be implemented for other patchily-distributed endangered species and allow managers to maximize scarce resources to improve the likelihood of endangered species persistence.
... Even though the Levins' classical model ignored the local population dynamics, it provided the important conceptual base on the future progress of metapopulation theory. Now, as anthropogenic alteration accelerate around the world and increasing number of species suffer from habitat fragmentation, the metapopulation setting is receiving ever more attention (e.g., Hanski and Gilpin 1997;Hanski 1999;Hanski and Gaggiotti 2004;Bulman et al. 2007;Wilson et al. 2009;Hanski et al. 2011;Schippers et al. 2011;Seppänen et al. 2012). ...
A proxy for the invasion fitness in structured metapopulation models has been defined as a metapopulation reproduction ratio, which is the expected number of surviving dispersers produced by a mutant immigrant and a colony of its descendants. When a size-structured metapopulation model involves also individual stages (such as juveniles and adults), there exists a generalized definition for the invasion fitness proxy. The idea is to calculate the expected numbers of dispersers of all different possible types produced by a mutant clan initiated with a single mutant, and to collect these values into a matrix. The metapopulation reproduction ratio is then the dominant eigenvalue of this matrix. The calculation method has been published in detail in the case of small local populations. However, in case of large patches the previously published numerical calculation method to obtain the expected number of dispersers does not generalize as such, which gives us one aim of this article. Here, we thus derive a generalized method to calculate the invasion fitness in a metapopulation, which consists of large local populations, and is both size- and stage-structured. We also prove that the metapopulation reproduction ratio is well-defined, i.e., it is equal to 1 for a mutant with a strategy equal to the strategy of a resident. Such a proof has not been previously published even for the case with only one type of individuals.
The American Pika (Ochotonaprinceps) is vulnerable to climate change as a result of its dependence on cool, moist conditions. Most research on climatic determinants of American Pika distribution has been done in the United States where conditions are different from those in the higher-latitude pika ranges of the Canadian Rockies. I examined recent (1980-2009) and future (2050s and 2080s) average and maximum mean summer temperatures for 114 current American Pika locations in Alberta to assess whether future conditions are likely to place these animals at risk. At all current sites, mean summer temperatures (MSTs) in the 2050s are expected to be below that chosen by the United States Fish and Wildlife Service as a threshold for at-risk status of 0. princeps. By the 2050s, most current American Pika locations have sufficient elevation within 5 km to allow individuals to migrate vertically to reach habitat with MST similar to that of their current location. Even in the 2080s, almost all current sites have sufficient elevation within 5 km to maintain extreme single-year and average MSTs lower than the highest values recorded at those sites in the recent past (13.9°C and 12.5°C respectively). However, by the 2080s under an extreme greenhouse gas emissions scenario, only 34% of current pika sites will allow for such migration. Although considerable uncertainty remains, particularly with respect to availability of habitat, these results suggest that American Pika populations in Alberta will likely be capable of persisting throughout this century, although their survival will depend increasingly on successful vertical migration.
