A discrete two time scales model of a size-structured population of parasitized trees.

IF 2.6 4区 工程技术 Q1 Mathematics
Rafael Bravo de la Parra, Ezio Venturino
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Abstract

The work presented a general discrete-time model of a population of trees affected by a parasite. The tree population was considered size-structured, and the parasite was represented by a single scalar variable. Parasite dynamics were assumed to act on a faster timescale than tree dynamics. The model was studied based on an associated nonlinear matrix model, in which the presence of the parasites was only reflected in the value of its parameters. For the model in all its generality, an explicit condition of viability/extinction of the parasite/tree community was found. In a simplified model with two size-classes of trees and particular forms of the vital rates, it was shown that the model undergoes a transcritical bifurcation and, likewise, a period-doubling bifurcation. It was found that, for any tree fertility rate that makes them viable without a parasite, if the parasite sufficiently reduces the survival of young trees, it can lead to the extinction of the entire community. The same cannot be assured if the parasite acts on adult trees. In situations where a high fertility rate coupled with a low survival rate of adult trees causes a non-parasitized population of trees to fluctuate, a parasite sufficiently damaging only young trees can stabilize the population. If, instead, the parasite acts on adult trees, we can find a destabilization condition on the tree population that brings them from a stable to an oscillating regime.

寄生树规模结构种群的离散双时间尺度模型。
该研究提出了一个受寄生虫影响的树木群体的一般离散时间模型。树木种群被认为是大小结构的,而寄生虫则由一个单一的标量变量表示。假定寄生虫动力学的时间尺度比树木动力学的时间尺度更快。该模型的研究基于一个相关的非线性矩阵模型,其中寄生虫的存在只反映在其参数值上。针对该模型的所有一般性,我们找到了寄生虫/树木群落的生存/灭绝的明确条件。在一个简化模型中,有两类大小的树木和特定形式的生命率,结果表明,该模型经历了一次临界分岔,同样,也经历了一次周期加倍分岔。研究发现,对于没有寄生虫也能存活的任何树木生育率,如果寄生虫充分降低了幼树的存活率,就会导致整个群落的灭绝。如果寄生虫作用于成年树木,则无法保证同样的结果。在生育率高、成树存活率低的情况下,未被寄生的树木种群会出现波动,如果寄生虫只对幼树造成足够的伤害,就能稳定种群。相反,如果寄生虫作用于成年树木,我们就能找到一个破坏树木种群稳定的条件,使它们从稳定状态进入振荡状态。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Mathematical Biosciences and Engineering
Mathematical Biosciences and Engineering 工程技术-数学跨学科应用
CiteScore
3.90
自引率
7.70%
发文量
586
审稿时长
>12 weeks
期刊介绍: Mathematical Biosciences and Engineering (MBE) is an interdisciplinary Open Access journal promoting cutting-edge research, technology transfer and knowledge translation about complex data and information processing. MBE publishes Research articles (long and original research); Communications (short and novel research); Expository papers; Technology Transfer and Knowledge Translation reports (description of new technologies and products); Announcements and Industrial Progress and News (announcements and even advertisement, including major conferences).
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