Geritz S, Gyllenberg M, Toivonen J
Department of Mathematics and Statistics, University of Helsinki, Helsinki, 00014, Finland.
Department of Biological and Environmental Science, University of Jyväskylä, Jyväskylä, 40014, Finland.
J Math Biol. 2018 Dec;77(6-7):1943-1968. doi: 10.1007/s00285-018-1232-z. Epub 2018 Apr 20.
We present a model for the coevolution of seed size and germination time within a season when both affect the ability of the seedlings to compete for space. We show that even in the absence of a morphological or physiological constraint between the two traits, a correlation between seed size and germination time is nevertheless likely to evolve. This raises the more general question to what extent a correlation between any two traits should be considered as an a priori constraint or as an evolved means (or "instrument") to actually implement a beneficial combination of traits. We derive sufficient conditions for the existence of a positive or a negative correlation. We develop a toy model for seed and seedling survival and seedling growth and use this to illustrate in practice how to determine correlations between seed size and germination time.
我们提出了一个种子大小和季节内萌发时间共同进化的模型，在这个季节中，二者均会影响幼苗竞争空间的能力。我们表明，即使这两个性状之间不存在形态学或生理学上的限制，种子大小与萌发时间之间的相关性仍有可能进化。这就引出了一个更普遍的问题：任何两个性状之间的相关性在多大程度上应被视为一种先验限制，还是一种实际实现有益性状组合的进化手段（或“工具”）。我们推导出了正相关或负相关存在的充分条件。我们构建了一个关于种子、幼苗存活及幼苗生长的简化模型，并以此实际说明如何确定种子大小与萌发时间之间的相关性。
