Abstract
Dispersal and fecundity are two fundamental traits underlying the spread of populations. Using integral difference equation models, we examine how individual variation in these fundamental traits and the heritability of these traits influence rates of spatial spread of populations along a one-dimensional transect. Using a mixture of analytic and numerical methods, we show that individual variation in dispersal rates increases spread rates and the more heritable this variation, the greater the increase. In contrast, individual variation in lifetime fecundity only increases spread rates when some of this variation is heritable. The highest increases in spread rates occur when variation in dispersal positively co-varies with fecundity. Our results highlight the importance of estimating individual variation in dispersal rates, dispersal syndromes in which fecundity and dispersal co-vary positively and heritability of these traits to predict population rates of spatial spread.
Highlights
Predicting the spatial spread of species over time is a central question in ecology (Hastings et al 2005; Jongejans et al 2008)
Using analytical approximations for small individual variation in dispersal rates, Appendix A demonstrates that randomly transmitted variation in dispersal rates increases the rate of spatial spread by a term proportional to the squared coefficient of variation in the mean dispersal distances
Predictions of spread tend to rely on mean estimates of population parameters for dispersal and life-history traits, but these may vary within a population and evolve through time
Summary
Predicting the spatial spread of species over time is a central question in ecology (Hastings et al 2005; Jongejans et al 2008). Mathematical models combining demography and dispersal have a long history of providing insights about the ecology and evolution of spatial spread (Skellam 1951; Kot et al 1996; Hastings et al 2005; Beckman et al 2020). These models have guided conservation and management decisions to control the spread of invasive species These models relied on mean estimates of dispersal and demographic rates These rates, often exhibit substantial individual variation within populations (reviewed in Schupp et al 2019). As this individual variation is known to have important consequences for many ecological and evolutionary processes (Bolnick et al 2011; Moran et al 2016; Snell et al 2019), it is natural to ask what effect do they have on rates of spatial spread
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