Jonsson T, Ebenman B
Department of Biology, Linköping University, S-581 83 Linköping, Sweden
J Theor Biol. 1998 Aug 7;193(3):407-417. doi: 10.1006/jtbi.1998.0708.
The effects of predator-prey body size ratios on the resilience and probability of stability in linear Lotka-Volterra food chains have been analysed. The prey per capita interaction strengths of the model is assumed to be negatively correlated to the relative size difference between a predator and its prey. The relationship between prey interaction strength and predator-prey body size ratios is motivated by energetical arguments. Analytical results show that, given this assumption (on prey interaction strengths) and if average (relative) size differences between predators and their prey decrease with the trophic position of the consumer (as found in a large number of "real food webs") the probability of local stability in model food chains is increased (when compared to model chains with a constant predator-prey body size ratio). Numerical simulations show that in most cases, the effect on the probability of stability is accompanied by an increase in resilience. For example, as model food chain length is increased from two to three trophic levels in one simulation, the return time increases by more than two orders of magnitude with a constant predator-prey body mass ratio while chains longer than four are not feasible. With a decreasing predator-prey body mass ratio on the other hand, the return time does not increase as rapidly and feasible equilibria exist for longer chains. The relationship between resilience and food chain length is, in this model, affected by the relationship between the predator-prey body mass ratio and the trophic position of the predator, that is, how fast this ratio decreases with increasing trophic height. The effect of body mass on consumer mortality rates, and subsequently on the probability of stability and resilience is also analysed. Decreasing mortality rates with increasing body size does not change the results qualitatively, it only increases the probability that an equilibrium is feasible.Copyright 1998 Academic Press
分析了捕食者与猎物体型比在线性Lotka-Volterra食物链中对恢复力和稳定性概率的影响。假设模型中猎物的人均相互作用强度与捕食者及其猎物之间的相对大小差异呈负相关。猎物相互作用强度与捕食者-猎物体型比之间的关系是由能量学论据推动的。分析结果表明，在给定这一假设（关于猎物相互作用强度）的情况下，如果捕食者与其猎物之间的平均（相对）大小差异随着消费者营养级的升高而减小（正如在大量“真实食物网”中所发现的那样），那么模型食物链中局部稳定的概率就会增加（与具有恒定捕食者-猎物体型比的模型食物链相比）。数值模拟表明，在大多数情况下，对稳定性概率的影响伴随着恢复力的增加。例如，在一次模拟中，当模型食物链长度从两个营养级增加到三个营养级时，在捕食者-猎物体重比恒定的情况下，恢复时间增加了两个多数量级，而长度超过四个营养级的食物链是不可行的。另一方面，随着捕食者-猎物体重比的降低，恢复时间增加得没有那么快，并且更长的食物链存在可行的平衡。在这个模型中，恢复力与食物链长度之间的关系受到捕食者-猎物体重比与捕食者营养级之间关系的影响，也就是说，这个比例随着营养级升高而降低的速度有多快。还分析了体重对消费者死亡率的影响，以及随后对稳定性和恢复力概率的影响。随着体型增大死亡率降低并不会在质上改变结果，只是增加了平衡可行的概率。版权所有1998年学术出版社
