Are Anomalous Invasion Speeds Robust to Demographic Stochasticity?

Elliott, Elizabeth C.; Cornell, Stephen J.

doi:10.1371/journal.pone.0067871

Cited by 7 publications

(9 citation statements)

References 37 publications

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“…While the deterministic model, eqn. (1), predicts anomalous speeds for vanishingly small mutation, it has been shown for N = 2 that demographic stochasticity suppresses anomalous speeds when 220 mutation or populations are small (Elliott and Cornell, 2013). We also find this to be the case for N > 2.…”

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confidence: 69%

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Anomalous invasion dynamics due to dispersal polymorphism and dispersal-reproduction trade-offs

Keenan

Cornell

2020

Preprint

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Dispersal polymorphism and mutation play significant roles during biological invasions, potentially leading to evolution and complex behaviour such as accelerating or decelerating invasion fronts. However, life history theory predicts that reproductive fitness -another key determinant of invasion dynamics -may be lower for more dispersive strains. Here, we use a mathematical 5 model to show that unexpected invasion dynamics emerge from the combination of heritable dispersal polymorphism, dispersal-fitness trade-offs, and mutation between strains. We show that the invasion dynamics are determined by the trade-off relationship between dispersal and population growth rates of the constituent strains. We find that invasion dynamics can be "anomalous" (i.e. faster than any of the strains in isolation), but that the ultimate invasion speed is determined by the 10 traits of at most two strains. The model is simple but generic, so we expect the predictions to apply to a wide range of ecological, evolutionary or epidemiological invasions.

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confidence: 69%

“…It is known that demographic stochasticity can affect anomalous speeds in dimorphic species (Elliott and Cornell, 2013), so to test the robustness of our results we also ran simulations of a stochastic Beverton-Holt model. This is based on the following deterministic model: (4) and (5) (more details in the Supplementary information Appendix S1).…”

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confidence: 99%

Anomalous invasion dynamics due to dispersal polymorphism and dispersal-reproduction trade-offs

Keenan

Cornell

2020

Preprint

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“…Using (4.8), this implies 11) and substituting in the full expression for P and dividing by β(µ 0 ) then yields…”

Section: Spreading Speed C *mentioning

confidence: 99%

“…A knowledge of this speed enables us to predict the ability of a species to keep up with the rate at which the climate changes or the rate at which an exotic species invades, two prominent ecological challenges [28,31]. It is known that traits such as dispersal and population growth affect the rate at which species expands its range, and there has been an intriguing suggestion from recent work that polymorphism in traits can cause a species invasion to occur at a faster rate than a single morph would in isolation [10,11]. Understanding the effect that each of a species traits has, and can potentially have, on its rate of spread is therefore important to understanding how the spread of a species can evolve.…”

Section: Introductionmentioning

confidence: 99%

Individual Variability in Dispersal and Invasion Speed

2019

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We model the growth, dispersal and mutation of two phenotypes of a species using reaction-diffusion equations, focusing on the biologically realistic case of small mutation rates. After verifying that the addition of a small linear mutation rate to a Lotka-Volterra system limits it to only two steady states in the case of weak competition, an unstable extinction state and a stable coexistence state, we prove that under some biologically reasonable condition on parameters the spreading speed of the system is linearly determinate. Using this result we show that the spreading speed is a non-increasing function of the mutation rate and hence that greater mixing between phenotypes leads to slower propagation. Finally, we determine the ratio at which the phenotypes occur at the leading edge in the limit of vanishing mutation.

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“…For example, fluctuations in the speed of an advancing population wave can be estimated by knowing demographic stochasticity, which is dominant at the leading edge of the front (Giometto, Rinaldo, Carrara, & Altermatt, ). Furthermore, demographic stochasticity can slow down biological invasions (Snyder, ) resulting in smaller invasion speeds than the one predicted by simpler deterministic models (Elliott & Cornell, ).…”

Section: Introductionmentioning

confidence: 99%

The effects of demographic stochasticity and parameter uncertainty on predicting the establishment of introduced species

Palamara

Carrara

Smith

et al. 2016

Ecology and Evolution

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Invasive species are a serious threat to biodiversity worldwide and predicting whether an introduced species will first establish and then become invasive can be useful to preserve ecosystem services. Establishment is influenced by multiple factors, such as the interactions between the introduced individuals and the resident community, and demographic and environmental stochasticity. Field observations are often incomplete or biased. This, together with an imperfect knowledge of the ecological traits of the introduced species, makes the prediction of establishment challenging. Methods that consider the combined effects of these factors on our ability to predict the establishment of an introduced species are currently lacking. We develop an inference framework to assess the combined effects of demographic stochasticity and parameter uncertainty on our ability to predict the probability of establishment following the introduction of a small number of individuals. We find that even moderate levels of demographic stochasticity influence both the probability of establishment, and, crucially, our ability to correctly predict that probability. We also find that estimation of the demographic parameters of an introduced species is fundamental to obtain precise estimates of the interaction parameters. For typical values of demographic stochasticity, the drop in our ability to predict an establishment can be 30% when having priors on the demographic parameters compared to having their accurate values. The results from our study illustrate how demographic stochasticity may bias the prediction of the probability of establishment. Our method can be applied to estimate probability of establishment of introduced species in field scenarios, where time series data and prior information on the demographic traits of the introduced species are available.

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Are Anomalous Invasion Speeds Robust to Demographic Stochasticity?

Cited by 7 publications

References 37 publications

Anomalous invasion dynamics due to dispersal polymorphism and dispersal-reproduction trade-offs

Anomalous invasion dynamics due to dispersal polymorphism and dispersal-reproduction trade-offs

Individual Variability in Dispersal and Invasion Speed

The effects of demographic stochasticity and parameter uncertainty on predicting the establishment of introduced species

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