基于集合种群理论框架的榕树-榕小蜂互惠系统动力学模型

互惠共生指双方物种都能通过对方增加适合度的种间关系。榕树与榕小蜂的传粉关系是自然界中典型的互惠共生系统,这种互惠关系发生在榕果中,也就是榕果是种间作用的场所,榕小蜂在其中传粉和产卵。由此,可以把榕果看作榕小蜂的生境斑块,利用集合种群理论框架构建榕树与榕小蜂互惠关系的动力学模型,研究这个互惠系统的稳定性和续存条件。由于这里的生境斑块(榕果)的动态变化性(榕果产生和掉落),模型不同于传统的生境斑块固定不变的集合种群模型,增加了描述生境动态的维度。模型表明:(1)榕果产生率足够大(大于一个阈值)是榕树与榕小蜂互惠系统能够续存的必要条件;(2)榕树和榕小蜂互惠系统存在双稳态现象(Allee效应),这个互惠系统续存需要种群大小超过一个阈值,换言之,种群大小低于这个阈值时,系统必然灭绝;(3)榕果产生率增加使榕小蜂种群增加,但不会影响未被占据的榕果数量。我们的模型不但可用来研究榕树与榕小蜂互惠系统的动力学性质,而且也是集合种群理论斑块动态化的发展。

The dynamical models based on the theory framework of metapopulations for the mutualism system of figs and pollinating wasps

Mutualistic symbiosis in general implies that both species can receive survival and reproductive benefits through the interaction each other, which usually increases the species fitness of both species. Mutualistic symbiosis plays an indispensable role in maintaining biodiversity and ecosystem functioning, and the loss of such interactions has the potential to lead to the collapse of entire local ecosystems, thus exacerbating the impact of global changes on biodiversity loss and ecosystem destruction. Therefore, it is essential to investigate the mechanisms that maintain the stability of the reciprocal relationship. The interaction between fig trees and their pollinating wasps is a typical example of mutualism in nature. Due to their close obligate mutualism, the system of fig trees and fig wasps is an ideal model system for studying mutualistic symbiosis. This reciprocal relationship occurs in the syconia, meaning that syconia are the site of interspecific interactions in which fig wasps pollinate flowers and lay eggs. Thus, we could consider syconia as habitat patches for fig wasps, and utilized the framework of metapopulation theory to construct dynamical model of the reciprocal relationship between fig tree and fig wasp species, and studied the stability and conditions for the persistence of this mutualistic system. Since the habitat patches (i.e., syconia) here are dynamic and changing (due to the production and loss of syconia in a fig tree), our models differ from the traditional metapopulation model (the total number of habitat patches is fixed) by adding dimensions that describe the dynamics of the habitats. The models showed that: (1) a sufficiently large production rate of syconia (greater than a threshold) was a necessary condition for the reciprocal mutualism between fig trees and fig wasps to persist. (2) Theoretical analysis revealed the existence of bi-stability property (i.e., the Allee effect) in the mutualistic system of fig trees and fig wasps, whereby the persistence of the mutualistic system depended on the initial size of the population exceeding a threshold. In other words, the system was destined to become extinct when the size of the population fell below the threshold. (3) The increase in the production rate of syconia led to a corresponding rise in the population of fig wasps, but had no effect on the abundance of syconia unoccupied by fig wasps. In conclusion, our models could not only facilitate the investigation of the dynamical properties of the mutualistic system between fig trees and fig wasps, but also contributed to the development for the dynamics of patches in the metapopulation theory.