Barraquand Frédéric, Yoccoz Nigel G
Department of Arctic and Marine Biology, University of Tromsø, Norway.
Theor Popul Biol. 2013 Nov;89:1-11. doi: 10.1016/j.tpb.2013.07.002. Epub 2013 Jul 29.
Using models for unstructured populations, we investigate the effect of environmental variability on population growth when the environment affects vital rates through nonlinear functions. We focus here especially on interannual variation in food resources availability, for which sigmoid functions are relevant. Considering first unregulated populations in stochastic environments, we show that classic sigmoid annual growth rates cannot lead to positive effects of increased environmental variability on population growth. This is true even when the temporal average of food availability is low, and Jensen's inequality predicts an increased arithmetic mean of the annual growth rate. The result is due to the log-concavity of many sigmoid (and other accelerating) functions, as convexity of the logarithm of the annual growth rate is needed for positive effects of variability to appear. Then, separating the effects of a food availability variable on reproduction and survival rates, we show that populations with less sensitive survival rate to food are more likely to benefit from food variability-as opposed to populations that have survival rates accelerating with food availability, which is rather counterintuitive given Jensen's inequality. Again, this is explained by log-convexity properties of nonlinear functions. We further extend these results to regulated populations, in which similar positive effects of food variability can affect average population size. Positive variability effects seem however more likely to occur in regulated populations. Finally, we extend our results to stage-structured populations. We connect to the previous work showing positive effects of environmental variability with matrix models, and show that these effects are well captured by simpler unstructured models.
使用针对非结构化种群的模型，我们研究当环境通过非线性函数影响生命率时环境变异性对种群增长的影响。我们在此特别关注食物资源可利用性的年际变化，对于这种变化，S 型函数是相关的。首先考虑随机环境中的无调控种群，我们表明经典的 S 型年增长率不会导致环境变异性增加对种群增长产生积极影响。即使食物可利用性的时间平均值较低且詹森不等式预测年增长率的算术平均值会增加，情况也是如此。该结果是由于许多 S 型（以及其他加速型）函数的对数凹性，因为变异性要产生积极影响需要年增长率的对数具有凸性。然后，分离食物可利用性变量对繁殖率和存活率的影响，我们表明对食物不太敏感的种群更有可能从食物变异性中受益——这与存活率随食物可利用性加速增加的种群相反，考虑到詹森不等式，这相当违反直觉。同样，这是由非线性函数的对数凸性性质所解释的。我们进一步将这些结果扩展到有调控的种群，在这类种群中食物变异性的类似积极影响会影响平均种群规模。然而，积极的变异性影响似乎更有可能出现在有调控的种群中。最后，我们将结果扩展到阶段结构种群。我们将其与先前用矩阵模型表明环境变异性具有积极影响的工作联系起来，并表明这些影响可以由更简单的非结构化模型很好地捕捉到。
