McCarthy Maeve L, Wallace Dorothy, Whiteman Howard H, Rheingold Evan T, Dunham Ann M, Prosper Olivia, Chen Michelle, Hu-Wang Eileen
Department of Mathematics & Statistics, Murray State University, Murray KY 42071, USA.
Department of Mathematics, Dartmouth College, 27 N. Main Street, 6188 Kemeny Hall, Hanover, NH 03755-3551, USA.
Math Biosci. 2017 Jun;288:35-45. doi: 10.1016/j.mbs.2017.02.011. Epub 2017 Feb 24.
Phenotypic plasticity is the ability of an organism to change its phenotype in response to changes in the environment. General mathematical descriptions of the phenomenon rely on an abstract measure of "viability" that, in this study, is instantiated in the case of the Tiger Salamander, Ambystoma tigrinum. This organism has a point in its development when, upon maturing, it may take two very different forms. One is a terrestrial salamander (metamorph)that visits ponds to reproduce and eat, while the other is an aquatic form (paedomorph) that remains in the pond to breed and which consumes a variety of prey including its own offspring. A seven dimensional nonlinear system of ordinary differential equations is developed, incorporating small (Z) and large (B) invertebrates, Ambystoma young of the year (Y), juveniles (J), terrestrial metamorphs (A) and aquatic paedomorphs (P). One parameter in the model controls the proportion of juveniles maturing into A versus P. Solutions are shown to remain non-negative. Every effort was made to justify parameters biologically through studies reported in the literature. A sensitivity analysis and equilibrium analysis of model parameters demonstrate that morphological choice is critical to the overall composition of the Ambystoma population. Various population viability measures were used to select optimal percentages of juveniles maturing into metamorphs, with optimal choices differing considerably depending on the viability measure. The model suggests that the criteria for viability for this organism vary, both from location to location and also in time. Thus, optimal responses change with spatiotemporal variation, which is consistent with other phenotypically plastic systems. Two competing hypotheses for the conditions under which metamorphosis occurs are examined in light of the model and data from an Ambystoma tigrinum population at Mexican Cut, Colorado. The model clearly supports one of these over the other for this data set. There appears to be a mathematical basis to the general tenet of spatiotemporal variation being important for the maintenance of polyphenisms, and our results suggest that such variation may have cascading effects on population, community, and perhaps ecosystem dynamics because it drives the production of a keystone, cannibalistic predator.
表型可塑性是生物体根据环境变化改变其表型的能力。对这一现象的一般数学描述依赖于一种抽象的“生存能力”度量，在本研究中，这种度量在虎螈（Ambystoma tigrinum）的案例中得以体现。这种生物体在其发育过程中有一个阶段，成熟后可能呈现两种截然不同的形态。一种是陆生螈（变态体），会前往池塘繁殖和觅食，另一种是水生形态（幼态体），留在池塘中繁殖，并捕食包括其自身后代在内的各种猎物。构建了一个七维非线性常微分方程组，纳入了小型（Z）和大型（B）无脊椎动物、当年的虎螈幼体（Y）、幼螈（J）、陆生变态体（A）和水生幼态体（P）。模型中的一个参数控制着幼螈发育为A形态与P形态的比例。结果表明解始终为非负。通过文献报道的研究，尽一切努力从生物学角度对参数进行论证。对模型参数的敏感性分析和平衡分析表明，形态选择对虎螈种群的整体构成至关重要。使用了各种种群生存能力度量来选择发育为变态体的幼螈的最佳百分比，最佳选择因生存能力度量而异。该模型表明，这种生物体的生存能力标准在不同地点和不同时间都有所不同。因此，最佳反应会随着时空变化而改变，这与其他表型可塑性系统一致。根据该模型以及来自科罗拉多州墨西哥卡特的虎螈种群的数据，研究了变态发生条件的两种相互竞争的假说。对于该数据集，模型明确支持其中一种假说而非另一种。时空变化对于维持多型现象很重要这一普遍原则似乎有数学依据，我们的结果表明，这种变化可能对种群、群落乃至生态系统动态产生连锁反应，因为它驱动了一种关键的自相残杀捕食者的产生。
