Dataset Information

Population dynamics with spatial structure and an Allee effect.

ABSTRACT: Population dynamics including a strong Allee effect describe the situation where long-term population survival or extinction depends on the initial population density. A simple mathematical model of an Allee effect is one where initial densities below the threshold lead to extinction, whereas initial densities above the threshold lead to survival. Mean-field models of population dynamics neglect spatial structure that can arise through short-range interactions, such as competition and dispersal. The influence of non-mean-field effects has not been studied in the presence of an Allee effect. To address this, we develop an individual-based model that incorporates both short-range interactions and an Allee effect. To explore the role of spatial structure we derive a mathematically tractable continuum approximation of the IBM in terms of the dynamics of spatial moments. In the limit of long-range interactions where the mean-field approximation holds, our modelling framework recovers the mean-field Allee threshold. We show that the Allee threshold is sensitive to spatial structure neglected by mean-field models. For example, there are cases where the mean-field model predicts extinction but the population actually survives. Through simulations we show that our new spatial moment dynamics model accurately captures the modified Allee threshold in the presence of spatial structure.

SUBMITTER: Surendran A

PROVIDER: S-EPMC7655738 | biostudies-literature |

REPOSITORIES: biostudies-literature

ACCESS DATA

Similar Datasets

Project description:Reconstructing the dynamics of populations is complicated by the different types of stochasticity experienced by populations, in particular if some forms of stochasticity introduce bias in parameter estimation in addition to error. Identification of systematic biases is critical when determining whether the intrinsic dynamics of populations are stable or unstable and whether or not populations exhibit an Allee effect, i.e., a minimum size below which deterministic extinction should follow. Using a simulation model that allows for Allee effects and a range of intrinsic dynamics, we investigated how three types of stochasticity--demographic, environmental, and random catastrophes--affect our ability to reconstruct the intrinsic dynamics of populations. Demographic stochasticity aside, which is only problematic in small populations, we find that environmental stochasticity--positive and negative environmental fluctuations--caused increased error in parameter estimation, but bias was rarely problematic, except at the highest levels of noise. Random catastrophes, events causing large-scale mortality and likely to be more common than usually recognized, caused immediate bias in parameter estimates, in particular when Allee effects were large. In the latter case, population stability was predicted when endogenous dynamics were actually unstable and the minimum viable population size was overestimated in populations with small or non-existent Allee effects. Catastrophes also generally increased extinction risk, in particular when endogenous Allee effects were large. We propose a method for identifying data points likely resulting from catastrophic events when such events have not been recorded. Using social spider colonies (Anelosimus spp.) as models for populations, we show that after known or suspected catastrophes are accounted for, reconstructed growth parameters are consistent with intrinsic dynamical instability and substantial Allee effects. Our results are applicable to metapopulation or time series data and are relevant for predicting extinction in conservation applications or the management of invasive species.

Dataset Information

Population dynamics with spatial structure and an Allee effect.

Similar Datasets

OmicsDI is part of the ELIXIR infrastructure

Tweets