Department of Applied Mathematics, Graduate School of Engineering, Hiroshima University, Kagamiyama 1-4-1, Higashi-hiroshima, Hiroshima Prefecture 739-8527, Japan.
Math Biosci. 2018 Nov;305:55-59. doi: 10.1016/j.mbs.2018.08.006. Epub 2018 Aug 24.
In many cicadas, a phenomenon is observed in which the peak of emergence of males precedes that of females (protandry). Generally, it is known that the ecology of emergence of insects is closely related to mating, and protandry is said to be the strategy of males to eclose early and to attempt mating with virgin females. However, as for the cicadas, males only call females with songs, and as far as the behavior of males is concerned, the necessity of protandry is not felt. Thus, as to cicadas, little is known about the relationship between emergence ecology and mating. Therefore, investigating the temporal distribution of cicada emergence is an important step in considering cicadas mating, and even the evolution of mating system. Unfortunately, it is known that cicadas have a very long lifetime and are known to be difficult to keep, so it is meaningful to predict results mathematically. In this paper, we investigate the influence of male and female emergence spreading in appearance period on the mating rate by using mathematical (stochastic) model. Furthermore, we propose a new mathematical virtual model and try to explain the results that mating rate depends on sexual difference and variance of eclosion date.
在许多蝉类中，观察到一种现象，即雄蝉的出现高峰先于雌蝉（性先熟）。一般来说，人们知道昆虫的出现生态学与交配密切相关，性先熟被认为是雄性提前蜕皮并试图与处女雌性交配的策略。然而，对于蝉来说，雄性只通过歌声来召唤雌性，就雄性的行为而言，性先熟的必要性并不明显。因此，对于蝉类来说，关于出现生态学与交配的关系知之甚少。因此，研究蝉类出现的时间分布是考虑蝉类交配甚至交配系统进化的重要步骤。不幸的是，蝉类的寿命非常长，而且众所周知难以饲养，因此进行数学预测是有意义的。在本文中，我们通过数学（随机）模型研究了在出现期内雄性和雌性出现扩散对交配率的影响。此外，我们提出了一个新的数学虚拟模型，并尝试解释交配率取决于性差和蜕皮日期方差的结果。
