简单的进化策略和投资优化如何影响生态模式？广义泰勒定律
How do simple evolutionary strategies and investment optimizations affect ecological patterns? The case of generalized Taylor's Law
摘要：
泰勒定律（TL）通过幂律将方差与随机变量的均值联系起来。在生态学中，它适用于种群，是不同生态系统共有的经验模式.测量给出幂律指数在1和2之间，并且更多地聚集在2周围，而理论模型预测TL指数可以假设任何真实值。本文采用马尔可夫环境下的乘法增长模型框架，研究了演化策略对TL指数在有限范围内的可能性.我们实施了三种不同的策略，个人可以遵循，并为每个策略设置两个不同的优化投资目标。在所有研究的情况下，我们发现TL指数可以假设任何实值，由于存在的区域的模型参数，其中指数可以发散。此外，在对环境动态的自然假设下，这些区域的形状不依赖于所采用的不同策略，也不依赖于优化目标。因此，策略的引入并不影响模型中TL指数的取值范围。在我们的理论框架中，罕见的事件正在塑造TL指数的值，这表明，正如以前的作品所暗示的那样，经验值可能是采样不足的统计伪影。
英文摘要：
Taylor's Law (TL) relates the variance to the mean of a random variable via power law. In ecology it applies to populationsand it is a common empirical pattern shared among different ecosystems. Measurements give power law exponent to be between 1 and 2, and more often to cluster around 2, whereas theoretical models predict TL exponent can assume any real value. In this paper, adopting the framework of multiplicative growth models in a Markovian environment, we investigate the possibility of evolutionary strategies to be responsible for TL exponent to be in a finite range. We implement three different strategies the individuals can follow and for each strategy set two different optimization investment objectives. In all the studied cases we find TL exponent can assume any real value due to the existence of regions of the model parameters in which the exponent can diverge. Furthermore, under natural hypothesis on the dynamics of the environment, the shapes of these regions do not depend on different strategies adopted and nor on the optimization objective. Thus the introduction of strategies dose not affect the range of TL exponent in the model. In our theoretical framework rare events are shaping the value of the TL exponent, suggesting, as hinted by previous works, that empirical values may be a statistical artifact following from under sampling.
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