TY - JOUR
T1 - Impacts of demographic and environmental stochasticity on population dynamics with cooperative effects
AU - Feng, Tao
AU - Zhou, Hongjuan
AU - Qiu, Zhipeng
AU - Kang, Yun
N1 - Funding Information:
This research was funded by the NSF-DMS (Award Number 1716802 & 2052820 ); the NSF-IOS/DMS (Award Number 1558127 ); and the James S. McDonnell Foundation 21st Century Science Initiative in Studying Complex Systems Scholar Award, United States (UHC Scholar Award 220020472 ). T. Feng was partially funded by the National Natural Science Foundation of China (Award Number 12201548 ), the Natural Science Foundation of Jiangsu Province, China (Award Number BK20220553 ) and the Natural Science Foundation of the Jiangsu Higher Education Institutions of China, China (Award Number 22KJB110006 ). Z. Qiu was partially funded by the National Natural Science Foundation of China (Award Number 12071217 , 11971232 ).
Publisher Copyright:
© 2022 Elsevier Inc.
PY - 2022/11
Y1 - 2022/11
N2 - Different types of stochasticity play essential roles in shaping complex population dynamics. This paper presents a novel approach to model demographic and environmental stochasticity in a single-species model with cooperative components that are measured by component Allee effects. Our work provides rigorous mathematical proof on stochastic persistence and extinction, ergodicity (i.e., the existence of a unique stationary distribution) and the existence of a nontrivial periodic solution to study the impacts of demographic and environmental stochasticity on population dynamics. The theoretical and numerical results suggest that stochasticity may affect the population system in a variety of ways, specifically: (i) In the weak Allee effects case (e.g., strong cooperative efforts), the demographic stochasticity from the attack rate contributes to the expansion of the population size, while the demographic stochasticity from the handling rate and the environmental stochasticity have the opposite role, and may even lead to population extinction; (ii) In the strong Allee effects case (cooperative efforts not strong enough), both demographic and environmental stochasticity play a similar role in the survival of population, and are related to the initial population level: if the initial population level is large enough, demographic stochasticity and environmental stochasticity may be detrimental to the survival of population, otherwise if the initial population level is small enough, demographic stochasticity and environmental stochasticity may bring survival opportunities for the population that deterministically would extinct indefinitely; (iii) In the extinction case, demographic and environmental stochasticity cannot change the trend of population extinction, but they can delay or promote population extinction.
AB - Different types of stochasticity play essential roles in shaping complex population dynamics. This paper presents a novel approach to model demographic and environmental stochasticity in a single-species model with cooperative components that are measured by component Allee effects. Our work provides rigorous mathematical proof on stochastic persistence and extinction, ergodicity (i.e., the existence of a unique stationary distribution) and the existence of a nontrivial periodic solution to study the impacts of demographic and environmental stochasticity on population dynamics. The theoretical and numerical results suggest that stochasticity may affect the population system in a variety of ways, specifically: (i) In the weak Allee effects case (e.g., strong cooperative efforts), the demographic stochasticity from the attack rate contributes to the expansion of the population size, while the demographic stochasticity from the handling rate and the environmental stochasticity have the opposite role, and may even lead to population extinction; (ii) In the strong Allee effects case (cooperative efforts not strong enough), both demographic and environmental stochasticity play a similar role in the survival of population, and are related to the initial population level: if the initial population level is large enough, demographic stochasticity and environmental stochasticity may be detrimental to the survival of population, otherwise if the initial population level is small enough, demographic stochasticity and environmental stochasticity may bring survival opportunities for the population that deterministically would extinct indefinitely; (iii) In the extinction case, demographic and environmental stochasticity cannot change the trend of population extinction, but they can delay or promote population extinction.
KW - Component Allee effects
KW - Cooperative component
KW - Demographic stochasticity
KW - Environmental stochasticity
KW - Population dynamics
KW - Single-species model
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U2 - 10.1016/j.mbs.2022.108910
DO - 10.1016/j.mbs.2022.108910
M3 - Article
C2 - 36152927
AN - SCOPUS:85139310364
SN - 0025-5564
VL - 353
JO - Mathematical Biosciences
JF - Mathematical Biosciences
M1 - 108910
ER -