Contemporary studies of species coexistence are underpinned by deterministic models that assume that competing species have continuous (i.e., noninteger) densities, live in infinitely large landscapes, and coexist over infinite time horizons. By contrast, in nature, species are composed of discrete individuals subject to demographic stochasticity and occur in habitats of finite size where extinctions occur in finite time. One consequence of these discrepancies is that metrics of species’ coexistence derived from deterministic theory may be unreliable predictors of the duration of species coexistence in nature. These coexistence metrics include invasion growth rates and niche and fitness differences, which are now commonly applied in theoretical and empirical studies of species coexistence. In this study, we tested the efficacy of deterministic coexistence metrics on the duration of species coexistence in a finite world. We introduce new theoretical and computational methods to estimate coexistence times in stochastic counterparts of classic deterministic models of competition. Importantly, we parameterized this model using experimental field data for 90 pairwise combinations of 18 species of annual plants, allowing us to derive biologically informed estimates of coexistence times for a natural system. Strikingly, we found that for species expected to deterministically coexist, community sizes containing only 10 individuals had predicted coexistence times of more than 1000 years. We also found that invasion growth rates explained 60% of the variation in intrinsic coexistence times, reinforcing their general usefulness in studies of coexistence. However, only by integrating information on both invasion growth rates and species' equilibrium population sizes could most (>99%) of the variation in species coexistence times be explained. This integration was achieved with demographically uncoupled single‐species models solely determined by the invasion growth rates and equilibrium population sizes. Moreover, because of a complex relationship between niche overlap/fitness differences and equilibrium population sizes, increasing niche overlap and increasing fitness differences did not always result in decreasing coexistence times, as deterministic theory would predict. Nevertheless, our results tend to support the informed use of deterministic theory for understanding the duration of species’ coexistence while highlighting the need to incorporate information on species' equilibrium population sizes in addition to invasion growth rates.
Deterministic compartmental models for infectious diseases give the mean behaviour of stochastic agent-based models. These models work well for counterfactual studies in which a fully mixed large-scale population is relevant. However, with finite size populations, chance variations may lead to significant departures from the mean. In real-life applications, finite size effects arise from the variance of individual realizations of an epidemic course about its fluid limit. In this article, we consider the classical stochastic Susceptible-Infected-Recovered (SIR) model, and derive a martingale formulation consisting of a deterministic and a stochastic component. The deterministic part coincides with the classical deterministic SIR model and we provide an upper bound for the stochastic part. Through analysis of the stochastic component depending on varying population size, we provide a theoretical explanation of finite size effects. Our theory is supported by quantitative and direct numerical simulations of theoretical infinitesimal variance. Case studies of coronavirus disease 2019 (COVID-19) transmission in smaller populations illustrate that the theory provides an envelope of possible outcomes that includes the field data.
more » « less- NSF-PAR ID:
- 10321186
- Date Published:
- Journal Name:
- Networks & Heterogeneous Media
- Volume:
- 0
- Issue:
- 0
- ISSN:
- 1556-1801
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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We investigated the influence of spatial and ontogenetic variance in local densities within an insect population by comparing a model integrating both types of local density variance with models including only spatial variance, only ontogenetic variance, or no variance. We parameterized the models with experimental data, then used elasticity and invasion analyses to characterize selection on traits that affect either the local density an individual experiences (mean clutch size) or individuals' sensitivity to density (effect of larval crowding on pupal mass).
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Ontogenetic variance weakened selection on mean clutch size and sensitivity to larval crowding by disrupting the relationship between trait values and performance during critical life stages.
We demonstrate that local density variance can strongly modify selection at empirically observed interaction strengths and identify mechanisms for the effects of spatial and ontogenetic variance. Our findings reveal the potential for local density variance to mediate eco‐evolutionary feedback by shaping selection on demographically important traits.
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3934/nhm.2022009
