Dynamic complexities in a single-species discrete population model with stage structure and birth pulses☆

Gao, Shujing; Chen, Lansun

doi:10.1016/j.chaos.2004.05.047

Cited by 32 publications

(14 citation statements)

References 26 publications

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“…Nevertheless, this problem concerns the variable studied (fertility), and any other technique used for the study of birth probabilities will also need data collected throughout the year. The resulting information might be useful for simulations of mammalian single-species population dynamics (Gao and Chen, 2005).…”

Section: Resultsmentioning

confidence: 99%

A model to search for birth probabilities of mammal populations using fertility data

et al. 2009

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A model was constructed to predict monthly birth probabilities using mammalian fertility data. We used a sample of 147 female capybaras (Hydrochoerus hydrochaeris) hunted on a farm on Marajó Island, Brazil. In the model each month was treated as a multinomial with six cells representing the six possible reproductive states (five months gestation). A hypothesis test was carried out to see whether a cosine curve would fit the birth probabilities. The results offer no support for a seasonal component (F 2,9 = 1.84, P = 0.21), whereas results from a direct census do (F 3,23 = 87.29, P < 0.01). Some hunting techniques were biased towards killing pregnant females (χ 2 1 = 7.2, P< 0.01), thereby spreading reproduction throughout the year (F 2,9 = 1.84, P = 0.21). The model remained a powerful predictive tool to be used with mammalian fertility data as long as the data are not biased towards pregnant females.Keywords: capybara, Hydrochoerus hydrochaeris, model, breeding season, fertility. Um modelo para busca por probabilidades de nascimentos de populações de mamíferos utilizando dados de fertilidade ResumoUm modelo foi desenvolvido para predizer as probabilidades de nascimentos mensais utilizando dados de fertilidade de mamíferos. Utilizamos uma amostra de 147 fêmeas de capivaras (Hydrochoerus hydrochaeris) caçadas em fazenda da Ilha de Marajó, Brasil. Cada mês foi tratado no modelo como um multinômio com seis células representando os seis possíveis estados reprodutivos (cinco meses de gestação). Um teste de hipótese foi realizado para avaliar se uma curva cossena se ajustava às probabilidades de nascimentos. Os resultados não apoiaram um componente sazonal (F 2,9 = 1,84, P = 0,21), enquanto houve apoio por parte dos resultados de censo direto (F 3,23 = 87,29, P < 0,01). Algumas técnicas de abate eram tendenciosas ao abate de fêmeas prenhas (χ 2 1 = 7,2, P < 0,01), consequentemente dispersando a reprodução por todo o ano (F 2,9 = 1,84, P = 0,21). O modelo continuou como uma poderosa ferramenta de previsão para uso com dados de fertilidade de mamíferos, desde que os dados não se encontrem tendenciosos para fêmeas prenhas.Palavras-chave: capivara, Hydrochoerus hydrochaeris.

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Section: Resultsmentioning

confidence: 99%

A model to search for birth probabilities of mammal populations using fertility data

et al. 2009

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“…The differential algebraic system (12) is stable at the interior equilibrium point, P 2 ðx Ã ; y Ã ; z Ã ; E Ã 2 Þ, of the model system…”

Section: Qualitative Analysis Of Differential Algebraic Model Systemmentioning

confidence: 99%

“…Therefore, seasonally reproducing species that produce offspring during a short annual period have birth pulse dynamics usually described with discrete population models. Gao and Chen [12] proposed an exploited single-species discrete model with stage structure for the dynamics in a fish population for which births occur in a single pulse once per time period. They constructed bifurcation diagrams through considering birth rate as the bifurcation parameter, and displayed the complex dynamic behaviors of the model system.…”

Section: Introductionmentioning

confidence: 99%

Optimal control of harvest and bifurcation of a prey–predator model with stage structure

Chakraborty¹,

Chakraborty

Kar

2011

Applied Mathematics and Computation

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“…In this paper, we suggest impulsive differential equations to model the process of periodic birth pulse and pulse fishing. Impulsive equations are found in almost every domain of applied science and has been studied in many investigations [7][8][9][10]. The questions that arise are: How do birth pulse and harvesting pulse affect the dynamics of the population?…”

Section: Introductionmentioning

confidence: 99%

Optimal pulse fishing policy in stage-structured models with birth pulses

Gao

Chen

Sun

2005

Chaos, Solitons & Fractals

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Dynamic complexities in a single-species discrete population model with stage structure and birth pulses☆

Cited by 32 publications

References 26 publications

A model to search for birth probabilities of mammal populations using fertility data

A model to search for birth probabilities of mammal populations using fertility data

Optimal control of harvest and bifurcation of a prey–predator model with stage structure

Optimal pulse fishing policy in stage-structured models with birth pulses

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