Dispersal in heterogeneous habitats: thresholds, spatial scales, and approximate rates of spread

Abstract

What is the effect of landscape heterogeneity on the spread rate of populations? Several spatially-explicit simulation models address this question for particular cases and find qualitative insights (e.g., extinction thresholds) but no quantitative relationships. We use a time-discrete analytic model and find general quantitative relationships for the invasion threshold, i.e., the minimal percentage of suitable habitat required for population spread. We investigate how, on the relevant spatial scales, this threshold depends on the relationship between dispersal ability and fragmentation level. The invasion threshold increases with fragmentation level when there is no Allee effect, but it decreases with fragmentation in the presence of an Allee effect. We obtain simple formulas for the approximate spread rate of a population in heterogeneous landscapes from averaging techniques. Comparison with spatially explicit simulations shows an excellent agreement between approximate and true values. We apply our results to the spread of trees and give some implications for the control of invasive species.

Integrodifference equations in patchy landscapes

“…As noted by several authors (VanKirk, 1995;Fahrig, 2002;Dewhirst and Lutscher, 2009), the scale of landscape heterogeneity can have significant effects on population spread rates. Following the procedure outlined in Section 4.5, we scale the spatial variable by the period of the landscape and introduce the dimensionless parameterp = l 1 l , the percentage of good habitat.…”

“…Numerous studies have also found that population persistence in patchy landscapes is highly sensitive to the scale of dispersal relative to landscape heterogeneity (VanKirk, 1995;Fahrig, 2002;Dewhirst and Lutscher, 2009). Most importantly, we wish to consider the effect of individual movement behavior at the interface of two 4.…”

“…Several studies suggested that population persistence is highly sensitive to the ratio of these scales (VanKirk, 1995;Fahrig, 2002;Dewhirst and Lutscher, 2009). …”

“…Low values ofp correspond to high fragmentation levels and large loss of suitable habitat whereas large values correspond to low fragmentation levels and low loss of suitable habitat. Dewhirst and Lutscher (2009) ) showing (a) spread of EAB into a periodic landscape of host trees with uniform initial density in good patches after t = 10 generations (black), t = 12 generations (red) and t = 14 generations (blue) and (b) remaining phloem densities after t = 9 generations (black), t = 11 generations (red) and t = 13 generations (blue). Parameter values are given by the point estimates listed in Table 6.1 with l 1 = l 2 = 1 and mean dispersal distance 1 a = 0.22 km.…”

“…For wind-dispersed seeds, such a choice seems entirely reasonable, but when the dispersal process is affected by landscape features, new effects can occur. Dewhirst and Lutscher (2009) included heterogeneity phenomenologically by allowing the variance of a kernel to depend on initial location. More mechanistically, VanKirk and Lewis (1999) derived kernels on a single patch with a semi-permeable boundary from a random walk.…”