Path integral calculation for emergence of rapid evolution from demographic stochasticity
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arXiv
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| Format: | Preprint |
| Published: |
2014
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| _version_ | 1866912290770518016 |
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| author | Shih, Hong-Yan Goldenfeld, Nigel |
| author_facet | Shih, Hong-Yan Goldenfeld, Nigel |
| contents | Genetic variation in a population can sometimes arise so fast as to modify ecosystem dynamics. Such phenomena have been observed in natural predator-prey systems, and characterized in the laboratory as showing unusual phase relationships in population dynamics, including a $π$ phase shift between predator and prey (evolutionary cycles) and even undetectable prey oscillations compared to those of the predator (cryptic cycles). Here we present a generic individual-level stochastic model of interacting populations that includes a subpopulation of low nutritional value to the predator. Using a master equation formalism, and by mapping to a coherent state path integral solved by a system-size expansion, we show that evolutionary and cryptic quasicycles can emerge generically from the combination of intrinsic demographic fluctuations and clonal mutations alone, without additional biological mechanisms. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1403_7865 |
| institution | arXiv |
| publishDate | 2014 |
| record_format | arxiv |
| spellingShingle | Path integral calculation for emergence of rapid evolution from demographic stochasticity Shih, Hong-Yan Goldenfeld, Nigel Populations and Evolution Statistical Mechanics Genetic variation in a population can sometimes arise so fast as to modify ecosystem dynamics. Such phenomena have been observed in natural predator-prey systems, and characterized in the laboratory as showing unusual phase relationships in population dynamics, including a $π$ phase shift between predator and prey (evolutionary cycles) and even undetectable prey oscillations compared to those of the predator (cryptic cycles). Here we present a generic individual-level stochastic model of interacting populations that includes a subpopulation of low nutritional value to the predator. Using a master equation formalism, and by mapping to a coherent state path integral solved by a system-size expansion, we show that evolutionary and cryptic quasicycles can emerge generically from the combination of intrinsic demographic fluctuations and clonal mutations alone, without additional biological mechanisms. |
| title | Path integral calculation for emergence of rapid evolution from demographic stochasticity |
| topic | Populations and Evolution Statistical Mechanics |
| url | https://arxiv.org/abs/1403.7865 |