We model spatially expanding populations by means of a spatial Λ-Fleming Viot process (SLFV) with selection : the k-parent SLFV. We fill empty areas with type 0 "ghost" individuals, which have a strong selective disadvantage against "real" type 1 individuals. This model is a special case of the SLFV with selection introduced in [19,22] : natural selection acts during all reproduction events, and the fraction of individuals replaced during a reproduction event is constant equal to 1. Letting the selective advantage k of type 1 individuals over type 0 individuals grow to +∞, and without rescaling time nor space, we obtain a new model for expanding populations, the ∞-parent SLFV.This model is reminiscent of the Eden growth model [13], but with an associated dual process of potential ancestors, making it possible to investigate the genetic diversity in a population sample. In order to obtain the limit k → +∞ of the k-parent SLFV, we introduce an alternative construction of the k-parent SLFV adapted from [38], which allows us to couple SLFVs with different selection strengths.
Seed banks are known to play a key role in plant metapopulations. However, detecting seed banks remains challenging and requires intense monitoring efforts. Assessing the genuine effect of seed banks on plant metapopulation dynamics (rather than their presence) may offer a much easier while still biologically relevant way to overcome this issue. In this study, we developed a new metric: the seed bank characteristic event (SBCE) probability. Instead of detecting seed bank directly, the SBCE probability measures seed bank contribution to the observed metapopulation dynamics. Exploring seed bank parameters (colonization, germination and seed bank death probabilities, initial proportion of patches containing a seed bank), a wide range of monitoring durations (from 3 to 10 years) and number of patches in the metapopulation (from 10 to 1,000 patches), we examined the conditions under which the SBCE probability is correctly estimated. To test the robustness of our approach, we further introduced false negatives, false positives or parameter heterogeneity between patches. Finally, we applied the SBCE probability method to the monitoring of tree bases plant species in Paris, France, to assess the applicability of the method to real‐world datasets and increase the understanding of plant metapopulation dynamics within an urban environment. Our results indicate that the SBCE probability is well‐estimated when enough monitoring years or number of patches are considered, and for probabilities of false negatives or false positives of up to 0.1. However, the SBCE probability estimation is not robust to colonization probability heterogeneity between patches. When we applied the SBCE probability method to the real monitoring dataset, we found a contrasted contribution of the seed bank to the observed metapopulation dynamics from one street and one species to another. The study suggests that the measurement of seed bank contribution is less data‐demanding than assessment of seed bank presence. Applying the estimation method to the monitoring of tree bases plant species highlights a significant contribution of the seed bank to plant metapopulation dynamics in an urban environment, and illustrates how the method can be applied on real‐world datasets.
We model spatially expanding populations by means of two spatial Λ-Fleming Viot processes (or SLFVs) with selection: the k-parent SLFV and the ∞-parent SLFV. In order to do so, we fill empty areas with type 0 "ghost" individuals with a strong selective disadvantage against "real" type 1 individuals, quantified by a parameter k. The reproduction of ghost individuals is interpreted as local extinction events due to stochasticity in reproduction. When k → +∞, the limiting process, corresponding to the ∞-parent SLFV, is reminiscent of stochastic growth models from percolation theory, but is associated to tools making it possible to investigate the genetic diversity in a population sample. In this article, we provide a rigorous construction of the ∞-parent SLFV, and show that it corresponds to the limit of the k-parent SLFV when k → +∞. In order to do so, we introduce an alternative construction of the k-parent SLFV which allows us to couple SLFVs with different selection strengths and is of interest in its own right. We exhibit three different characterizations of the ∞-parent SLFV, which are valid in different settings and link together population genetics models and stochastic growth models.
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