Discrete-Time Model of an Exploited Population with Age and Sex Structures: Instability and the Hydra Effect
This study proposes a discrete-time mathematical model to investigate the impact of selective harvesting on the dynamics of a population with age and sex structures. The model assumes that the birth rate depends on the sex ratio of the population and the number of breeding pairs. The growth rate is...
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| Format: | Article |
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MDPI AG
2024-02-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/12/4/535 |
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| author | Oksana Revutskaya Galina Neverova Efim Frisman |
| author_facet | Oksana Revutskaya Galina Neverova Efim Frisman |
| author_sort | Oksana Revutskaya |
| collection | DOAJ |
| description | This study proposes a discrete-time mathematical model to investigate the impact of selective harvesting on the dynamics of a population with age and sex structures. The model assumes that the birth rate depends on the sex ratio of the population and the number of breeding pairs. The growth rate is regulated by limiting juvenile survival, where an increase in population size decreases the survival of immature individuals. We consider the following selective proportional exploitation: harvesting of juveniles and harvesting of mature males. Depending on the values of population parameters, selective harvesting can lead to the stabilization of population dynamics by dampening oscillations or the emergence and amplification of fluctuations in population size. The model reveals multistability domains in which different dynamic modes coexist, and variations in initial conditions can lead to changes in dynamic modes. Depending on the values of the population parameters, the proposed models with harvest reveal the hydra effect, indicating an increase in the equilibrium abundance of the exploited group after reproduction but before harvesting, with an increase in the harvesting rate. Selective harvesting, resulting in the hydra effect, increases the remaining population size due to reproduction and the number of harvested individuals. |
| first_indexed | 2024-03-07T22:23:12Z |
| format | Article |
| id | doaj.art-d1a0a26306134a379dd6a5d85d1f1933 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-07T22:23:12Z |
| publishDate | 2024-02-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj.art-d1a0a26306134a379dd6a5d85d1f19332024-02-23T15:26:05ZengMDPI AGMathematics2227-73902024-02-0112453510.3390/math12040535Discrete-Time Model of an Exploited Population with Age and Sex Structures: Instability and the Hydra EffectOksana Revutskaya0Galina Neverova1Efim Frisman2Institute for Complex Analysis of Regional Problems, Far East Branch, Russian Academy of Sciences, Birobidzhan 679016, RussiaInstitute of Automation and Control Processes, Far Eastern Branch, Russian Academy of Sciences, Vladivostok 690041, RussiaInstitute for Complex Analysis of Regional Problems, Far East Branch, Russian Academy of Sciences, Birobidzhan 679016, RussiaThis study proposes a discrete-time mathematical model to investigate the impact of selective harvesting on the dynamics of a population with age and sex structures. The model assumes that the birth rate depends on the sex ratio of the population and the number of breeding pairs. The growth rate is regulated by limiting juvenile survival, where an increase in population size decreases the survival of immature individuals. We consider the following selective proportional exploitation: harvesting of juveniles and harvesting of mature males. Depending on the values of population parameters, selective harvesting can lead to the stabilization of population dynamics by dampening oscillations or the emergence and amplification of fluctuations in population size. The model reveals multistability domains in which different dynamic modes coexist, and variations in initial conditions can lead to changes in dynamic modes. Depending on the values of the population parameters, the proposed models with harvest reveal the hydra effect, indicating an increase in the equilibrium abundance of the exploited group after reproduction but before harvesting, with an increase in the harvesting rate. Selective harvesting, resulting in the hydra effect, increases the remaining population size due to reproduction and the number of harvested individuals.https://www.mdpi.com/2227-7390/12/4/535discrete-time modelage and sex structuresdensity-dependent regulationselective harvestingstabilitydynamic modes |
| spellingShingle | Oksana Revutskaya Galina Neverova Efim Frisman Discrete-Time Model of an Exploited Population with Age and Sex Structures: Instability and the Hydra Effect Mathematics discrete-time model age and sex structures density-dependent regulation selective harvesting stability dynamic modes |
| title | Discrete-Time Model of an Exploited Population with Age and Sex Structures: Instability and the Hydra Effect |
| title_full | Discrete-Time Model of an Exploited Population with Age and Sex Structures: Instability and the Hydra Effect |
| title_fullStr | Discrete-Time Model of an Exploited Population with Age and Sex Structures: Instability and the Hydra Effect |
| title_full_unstemmed | Discrete-Time Model of an Exploited Population with Age and Sex Structures: Instability and the Hydra Effect |
| title_short | Discrete-Time Model of an Exploited Population with Age and Sex Structures: Instability and the Hydra Effect |
| title_sort | discrete time model of an exploited population with age and sex structures instability and the hydra effect |
| topic | discrete-time model age and sex structures density-dependent regulation selective harvesting stability dynamic modes |
| url | https://www.mdpi.com/2227-7390/12/4/535 |
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