{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,3]],"date-time":"2024-09-03T14:23:44Z","timestamp":1725373424407},"reference-count":31,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2016,4]]},"abstract":"<jats:p> The Ricker model is one of the simplest and most widely-used ecological models displaying complex nonlinear dynamics. We study a discrete-time population model, which is derived from simple assumptions concerning individual organisms\u2019 behavior, using the \u201csite-based\u201d approach, developed by Br\u00e4nnstr\u00f6m, Broomhead, Johansson and Sumpter. In the large-population limit the model converges to the Ricker model, and can thus be considered a mechanistic version of the Ricker model, derived from basic ecological principles, and taking into account the demographic stochasticity inherent to finite populations. We employ several analytical and precise numerical methods to study the model, showing how each approach contributes to understanding the model\u2019s dynamics. Expressing the model as a Markov chain, we employ the concept of quasi-stationary distributions, which are computed numerically, and used to examine the interaction between complex deterministic dynamics and demographic stochasticity, as well as to calculate mean times to extinction. A Gaussian Markov chain approximation is used to obtain quantitative asymptotic approximations for the size of fluctuations of the stochastic model\u2019s time series around the deterministic trajectory, and for the correlations between successive fluctuations. Results of these approximations are compared to results obtained from quasi-stationary distributions and from direct simulations, and are shown to be in good agreement. <\/jats:p>","DOI":"10.1142\/s021812741650067x","type":"journal-article","created":{"date-parts":[[2016,5,5]],"date-time":"2016-05-05T08:18:02Z","timestamp":1462436282000},"page":"1650067","source":"Crossref","is-referenced-by-count":5,"title":["A Mechanistic Stochastic Ricker Model: Analytical and Numerical Investigations"],"prefix":"10.1142","volume":"26","author":[{"given":"Tamar","family":"Gadrich","sequence":"first","affiliation":[{"name":"Department of Industrial Engineering and Management, ORT Braude College, Karmiel 2161002, Israel"}]},{"given":"Guy","family":"Katriel","sequence":"additional","affiliation":[{"name":"Department of Mathematics, ORT Braude College, Karmiel 2161002, Israel"}]}],"member":"219","published-online":{"date-parts":[[2016,5,5]]},"reference":[{"key":"S021812741650067XBIB001","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3800(91)90103-8"},{"key":"S021812741650067XBIB002","first-page":"23","volume":"48","author":"Akcakaya R. 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