• Journal of Ecology and Environment
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• v.32 no.2
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• pp.103-107
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• 2009

We investigated colonization and extinction patterns in a meta population of the gold-spotted pond frog (Rana planeyi ehoseniea) near the Korea National University of Education, Chungbuk, Korea, by surveying the frogs in the nine occupied habitat patches in the study area four times per breeding season for three years (2006$\sim$2008) and recording whether the patches were occupied by frogs as well as how many frogs were calling in the patches. We then developed five a priori year-specific models using the Akaike Information Criterion (AIC). The models predicted that: 1) probabilities of colonization and local extinction of the frogs were better explained by year-dependent models than by constant models, 2) there are high local extinction and low colonization probabilities, 3) approximately 31% number of patches will be occupied at equilibrium, and 4) that considerable variation in occupation rate should occur over a 30-year period, due to demographic stochasticity (in our model, the occupation rate ranged from 0.222 to 0.889). Our results suggest that colonization is important in this metapopulation system, which is governed by mainly stochastic components, and that more constructive conservation effects are needed to increase local colonization rates.

• Journal of the Korean Physical Society
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• v.73 no.11
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• pp.1774-1786
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• 2018

Phenotypic variation among clones (individuals with identical genes, i.e. isogenic individuals) has been recognized both theoretically and experimentally. We investigate the effects of phenotypic variation on evolutionary dynamics of a population. In a population, the individuals are assumed to be haploid with two genotypes : one genotype shows phenotypic variation and the other does not. We use an individual-based Moran model in which the individuals reproduce according to their fitness values and die at random. The evolutionary dynamics of an individual-based model is formulated in terms of a master equation and is approximated as the Fokker-Planck equation (FPE) and the coupled non-linear stochastic differential equations (SDEs) with multiplicative noise. We first analyze the deterministic part of the SDEs to obtain the fixed points and determine the stability of each fixed point. We find that there is a discrete phase transition in the population distribution when the probability of reproducing the fitter individual is equal to the critical value determined by the stability of the fixed points. Next, we take demographic stochasticity into account and analyze the FPE by eliminating the fast variable to reduce the coupled two-variable FPE to the single-variable FPE. We derive a quasi-stationary distribution of the reduced FPE and predict the fixation probabilities and the mean fixation times to absorbing states. We also carry out numerical simulations in the form of the Gillespie algorithm and find that the results of simulations are consistent with the analytic predictions.