Evolution of dispersal by memory and learning in integrodifference equation models

In this paper, we develop an integrodifference equation model that incorporates spatial memory and learning so that each year, a fraction of the population use the same dispersal kernel as the previous year, and the remaining individuals return to where they bred or were born. In temporally static environments, the equilibrium of the system corresponds to an ideal free dispersal strategy, which is evolutionarily stable. We prove local stability of this equilibrium in a special case, and we observe convergence towards this equilibrium in numerical computations. When there are periodic or stochastic temporal changes in the environment, the population is less able to match the environment, but is able to do so to some extent depending on the parameters. Overall, the mechanism proposed in this model shows a possible way for the dispersal kernel of a population to evolve towards an ideal free dispersal kernel.</p

Shapefile of county-level bagworm occupancy

Shapefile of county-level bagworm occupancy constructed from Wollerman, E. H. 1971. Bagworm. United States Department of Agriculture Forest Pest Leaflet 97

Bagworm pupal survival

Bagworm pupal survivorship as a function of latitud

Bagworm larval survival

Bagworm larval survivorship as a function of latitud

Populations of infected livestock and mosquitoes.

<p>(a), (b) and (c) represent the populations of infectious livestock (solid line) and vectors (dashed line) in patches 1, 2 and 3, respectively. Same values of parameters are adopted in <a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0003388#pntd-0003388-g003" target="_blank">Fig. 3</a>. Populations of both infected livestock and mosquitoes alter their patterns during the festival time. Due to the effect of increased movement rates during the festival, the peak of infected livestock population is not necessary to be the same as that of the infected mosquito population, i.e. patch 2.</p

Basic reproduction number.

<p>(a), (b) and (c) represent the populations of infectious livestock (solid line), the instantaneously local basic reproduction number (dashed line) and the instantaneously global basic reproduction number (dotted line) in patches 1, 2 and 3, respectively. Values of other parameters are identical with those in <a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0003388#pntd-0003388-g003" target="_blank">Fig. 3</a>. The instantaneously global basic reproduction number is computed by considering the three patches as an entirety, while the instantaneously local basic reproduction number is measured only within the local patch based on the current disease dynamics.</p

Appendix A. Eleven additional figures showing the fit of each element of the model to the empirical data available (e.g., bagworm dispersal, male and female emergence phenology, life span, and fecundity).

Eleven additional figures showing the fit of each element of the model to the empirical data available (e.g., bagworm dispersal, male and female emergence phenology, life span, and fecundity)

Adult bagworm longevity

Data on adult bagworm longevity (in hours) by se

Interaction between the daily increment in movement speeds and the daily imported number on the size of cumulative infected livestock population.

<p>(a)-(i), simulations of the cumulative numbers of infected livestock at year 4, 29, and 62 (by row) in patches 1, 2, and 3 (by column). Same values of parameters used in <a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0003388#pntd-0003388-g003" target="_blank">Fig. 3</a>.</p

How daily increment in movement speed impacts basic reproduction numbers.

<p>(a) Instantaneously global reproduction number; (b)-(d) Instantaneously local reproduction numbers in patches 1, 2 and 3. In (b)-(d), km per day, described by solid, dashed and dotted lines, respectively. (e) Local reproduction number in patches 1, 2 and 3 are simulated by solid, dashed and dotted lines when km per day. Values of other parameters are identical with those used in <a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0003388#pntd-0003388-g003" target="_blank">Fig. 3</a>.</p