Shaw Allison K.

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Shaw
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Allison K.
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  • Article
    Sex-biased dispersal and the speed of two-sex invasions
    (University of Chicago, 2011-04-07) Miller, Tom E. X. ; Shaw, Allison K. ; Inouye, Brian D. ; Neubert, Michael G.
    Population models that combine demography and dispersal are important tools for forecasting the spatial spread of biological invasions. Current models describe the dynamics of only one sex (typically females). Such models cannot account for the sex-related biases in dispersal and mating behavior that are typical of many animal species. In this article, we construct a two-sex integrodifference equation model that overcomes these limitations. We derive an explicit formula for the invasion speed from the model and use it to show that sex-biased dispersal may significantly increase or decrease the invasion speed by skewing the operational sex ratio at the invasion’s low-density leading edge. Which of these possible outcomes occurs depends sensitively on complex interactions among the direction of dispersal bias, the magnitude of bias, and the relative contributions of females and males to local population growth.
  • Preprint
    Sex differences and Allee effects shape the dynamics of sex-structured invasions
    ( 2017-02) Shaw, Allison K. ; Kokko, Hanna ; Neubert, Michael G.
    The rate at which a population grows and spreads can depend on individual behaviour and interactions with others. In many species with two sexes, males and females differ in key life history traits (e.g. growth, survival, dispersal), which can scale up to affect population rates of growth and spread. In sexually reproducing species, the mechanics of locating mates and reproducing successfully introduce further complications for predicting the invasion speed (spread rate), as both can change nonlinearly with density. Most models of population spread are based on one sex, or include limited aspects of sex differences. Here we ask whether and how the dynamics of finding mates interact with sex-specific life history traits to influence the rate of population spread. We present a hybrid approach for modelling invasions of populations with two sexes that links individual-level mating behaviour (in an individual based model) to population-level dynamics (in an integrodifference equation model). We find that limiting the amount of time during which individuals can search for mates causes a demographic Allee effect which can slow, delay or even prevent an invasion. Furthermore, any sex-based asymmetries in life history or behaviour (skewed sex ratio, sex-biased dispersal, sex-specific mating behaviours) amplify these effects. In contrast, allowing individuals to mate more than once ameliorates these effects, enabling polygynandrous populations to invade under conditions where monogamously mating populations would fail to establish. We show that details of individuals' mating behaviour can impact the rate of population spread. Based on our results, we propose a stricter definition of a mate-finding Allee effect, which is not met by the commonly used minimum mating function. Our modelling approach, which links individual and population-level dynamics in a single model, may be useful for exploring other aspects of individual behaviour that are thought to impact the rate of population spread.
  • Article
    The evolution of marine larval dispersal kernels in spatially structured habitats: Analytical models, individual-based simulations, and comparisons with empirical estimates.
    (University of Chicago Press, 2019-01-17) Shaw, Allison K. ; D'Aloia, Cassidy C. ; Buston, Peter M.
    Understanding the causes of larval dispersal is a major goal of marine ecology, yet most research focuses on proximate causes. Here we ask how ultimate, evolutionary causes affect dispersal. Building on Hamilton and May’s classic 1977 article “Dispersal in Stable Habitats,” we develop analytic and simulation models for the evolution of dispersal kernels in spatially structured habitats. First, we investigate dispersal in a world without edges and find that most offspring disperse as far as possible, opposite the pattern of empirical data. Adding edges to our model world leads to nearly all offspring dispersing short distances, again a mismatch with empirical data. Adding resource heterogeneity improves our results: most offspring disperse short distances with some dispersing longer distances. Finally, we simulate dispersal evolution in a real seascape in Belize and find that the simulated dispersal kernel and an empirical dispersal kernel from that seascape both have the same shape, with a high level of short-distance dispersal and a low level of long-distance dispersal. The novel contributions of this work are to provide a spatially explicit analytic extension of Hamilton and May’s 1977 work, to demonstrate that our spatially explicit simulations and analytic models provide equivalent results, and to use simulation approaches to investigate the evolution of dispersal kernel shape in spatially complex habitats. Our model could be modified in various ways to investigate dispersal evolution in other species and seascapes, providing new insights into patterns of marine larval dispersal.
  • Preprint
    Density dependence in demography and dispersal generates fluctuating invasion speeds
    ( 2017-04) Sullivan, Lauren L. ; Li, Bingtuan ; Miller, Tom E. X. ; Neubert, Michael G. ; Shaw, Allison K.
    Mitigating the spread of invasive species remains difficult—substantial variability in invasion speed is increasingly well-documented, but the sources of this variability are poorly understood. We report a mechanism for invasion speed variability. The combined action of density dependence in demography and dispersal can cause invasions to fluctuate, even in constant environments. Speed fluctuations occur through creation of a pushed invasion wave that moves forward not from small populations at the leading edge but instead, from larger, more established populations that “jump” forward past the previous invasion front. Variability in strength of the push generates fluctuating invasion speeds. Conditions giving rise to fluctuations are widely documented in nature, suggesting that an important source of invasion variability may be overlooked.