Spatially explicit neutral models for population genetics and community ecology: Extensions of the Neyman–Scott clustering process

Shimatani, Ichiro K.

doi:10.1016/j.tpb.2009.10.006

Cited by 10 publications

(41 citation statements)

References 49 publications

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“…Here all but one simulation with d obs / d ep > 2 concluded wrongly that there were significant effects of the covariates considered. Such a ratio of d obs / d ep > 2 is likely to occur for numerous studies [ N / N e is reported to be generally between 2 and 10 by Frankham (1995); Shimatani (2010) also reports a large variance of fecundity not explained by DBH]. Additional simulations covering a range of scenarios showed that the type I error rate found here (i) was weakly sensitive to the dispersal kernel used, (ii) was not sensitive to the consideration of another covariate (related or unrelated to fecundity), but (iii) was lower for ‘simpler’ covariates (one quantitative covariate < three quantitative covariates < one class covariate < two class covariates), (Data S2).…”

Section: Discussionmentioning

confidence: 92%

Estimating the variance of male fecundity from genotypes of progeny arrays: evaluation of the Bayesian forward approach

2011

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Summary1. Characterizing fine scale mating patterns in plant populations makes it possible to investigate genetic drift, gene flow and selection gradients at a contemporary time scale. Molecular markers are valuable tools for this type of analysis, and numerous statistical methods have been developed to make the best of the information they can provide. In particular, we recently proposed a Bayesian approach based on a paternity analysis wherein we estimate jointly the variance in male fecundity and the pollen dispersal kernel. 2. Here, we use simulated data sets to investigate the accuracy of the Bayesian approach compared to (i) classical maximum likelihood approaches (e.g. Neighbourhood model) that ignore variance in male fecundity or explain it through a few covariates and (ii) indirect methods (KinDist and TwoGener) that integrate the variance in fecundity in an 'effective population density'. 3. The Bayesian estimates correctly considered the over-dispersion resulting from the variance in fecundity, resulting in wider but more accurate confidence intervals, in particular in high-density populations. The maximum likelihood methods resulted in confidence intervals with low coverage probabilities and in widespread false-positive tests when testing the effect of covariates on male fecundity. 4. Estimated individual fecundities and estimated empirical variance in fecundity were robust to the distribution assumed for the individual random fecundities (log-normal or Gamma). In contrast, the theoretical variance estimate critically depended on the assumed distribution. 5. The indirect methods provided much more variable estimators, as expected because they use less information about pollen sources and consider the molecular information only through genetic structure indices. 6. Disentangling the fecundity from the spatial effects in paternity analyses is necessary when studying selection in natura and or when addressing the effects of spatial distribution on effective gene flow. The Bayesian approach studied here successfully accounts for the variance in fecundity when a large fraction of it is not explained by the studied covariates. The Mixed Effect Mating Model computer program introduced here is devoted to its implementation.

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Section: Discussionmentioning

confidence: 92%

Estimating the variance of male fecundity from genotypes of progeny arrays: evaluation of the Bayesian forward approach

2011

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“…The following computation can be considered the generalization of the one contained in Shimatani paper [8] which is the primary source of inspiration for this work. The technical part of the computation is contained in the Supplementary material, Sect.…”

Section: Replicated Neyman-scott Process With a General Dispersal Kernelmentioning

confidence: 99%

“…Therefore the model was rejected by Felsenstein as physically unsound (see however the comment in [7] to Felsenstein paper). Recently the model has been reformulated by Shimatani [8] in the spatial point process framework still considering a Gaussian dispersal kernel but adding the hypothesis that at each generation a fixed fraction of offsprings migrates randomly away from their parents points. In this way the resulting process reaches a finite clustering even if an infinite number of generations is considered.…”

Section: Introductionmentioning

confidence: 99%

“…In this way the resulting process reaches a finite clustering even if an infinite number of generations is considered. In this paper we repeat the computation along the lines of [8] for a general dispersal kernel function. We thus obtain a model of greater generality in which we are able to discuss the role of the choice of dispersal kernel on the issue of divergent clustering.…”

Section: Introductionmentioning

confidence: 99%

“…Gaussian and exponential kernels were commonly considered until the turning of the century, but nowadays are outperformed by various fat tailed dispersal kernels (see Ch.15 in [12]). Replicated point process as pioneered by Shimatani [8,9,10] allow to consider a dynamic and spatially explicit population genetics model. In this way a coalescent theory is recovered.…”

Section: Introductionmentioning

confidence: 99%

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Replicated point processes with application to population dynamics models

Favretti

2018

Preprint

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In this paper we study spatially clustered distribution of individuals using point process theory. In particular we discuss the spatially explicit model of population dynamics of Shimatani (2010) which extend previous works on Malécot theory of isolation by distance. We reformulate Shimatani model of replicated Neyman-Scott process to allow for a general dispersal kernel function and we show that the random immigration hypothesis can be substituted by the long dispersal distance property of the kernel. Moreover, the extended framework presented here is fit to handle spatially explicit statistical estimators of genetic variability like Moran autocorrelation index, Sørensen similarity index, average kinship coefficient. We discuss the pivotal role of the choice of dispersal kernel for the above estimators in a toy model of dynamic population genetics theory.

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2013

Stochastic Geometry and Its Applications

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Spatially explicit neutral models for population genetics and community ecology: Extensions of the Neyman–Scott clustering process

Cited by 10 publications

References 49 publications

Estimating the variance of male fecundity from genotypes of progeny arrays: evaluation of the Bayesian forward approach

Estimating the variance of male fecundity from genotypes of progeny arrays: evaluation of the Bayesian forward approach

Replicated point processes with application to population dynamics models

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