Department of Biological Science, Graduate School of Science, Osaka Prefecture University, 1-1 Gakuen-cho, Nakaku, Sakai 599-8531, Japan.
J Theor Biol. 2013 Sep 7;332:1-8. doi: 10.1016/j.jtbi.2013.04.016. Epub 2013 Apr 21.
Evolution and maintenance of mutualism have been one of the major questions in evolutionary ecology, because it is often susceptible of invasion of non-mutualistic strategy. Some previous studies using dual-lattice model suggest that spatial structures of habitat can prevent non-mutualism from prevailing over mutualism, while the detail of the dynamics is not fully revealed. Here we explore population dynamics of the two strategies (mutualism and non-mutualism) in two species engaged in Prisoner's Dilemma game on a dual-lattice space, especially focusing on whether mutualists and non-mutualists can coexist in long-term dynamics. The habitat consists of two layers, each of which a population of species inhabits, and interspecific interaction is restricted between two corresponding sites of the layers. Each individual of the both species is either a mutualist or a non-mutualist and only the former pay cost c for benefit of the partner b. The payoff of the game affects the individuals' fecundity, while the mortality is constant. Reproduction is restricted to neighboring vacant sites of the focal individuals. Our computer simulations of the model show that even if b/c ratio remains constant, mutualists become dominant in both species over wider ranges of basic reproduction rate (reproduction rate without interspecific interaction) as b and c increase. If basic reproduction rates are asymmetric between the species or basic reproduction rates were sufficiently large, mutualists and non-mutualists can coexist in one or both species, while their population sizes often fluctuate. Transition of the final state between mutualism and non-mutualism happens rather discontinuously, then total population sizes change drastically at the transition. Moreover, we also find paradoxical cases of unilateral exploitation, i.e. one species consists of mutualists and other species non-mutualists. Additional simulations reveal that accidental extinction of the non-mutualists of one species can result in extinction of mutualist of the other species.
共生关系的演化和维持一直是进化生态学的主要问题之一，因为它常常容易受到非共生策略的入侵。一些先前使用双格模型的研究表明，栖息地的空间结构可以防止非共生策略战胜共生策略，尽管其动态细节尚未完全揭示。在这里，我们在双格空间上研究了两种策略（共生和非共生）的种群动态，特别是关注共生者和非共生者是否可以在长期动态中共存。栖息地由两层组成，每一层都有一个物种的种群栖息，种间相互作用仅限于两层对应的两个位点之间。两种物种的每个个体都是共生者或非共生者，只有前者为伙伴 b 支付成本 c 以获得利益。博弈的收益影响个体的繁殖力，而死亡率是恒定的。繁殖受到焦点个体相邻空位的限制。我们对该模型的计算机模拟表明，即使 b/c 比保持不变，随着 b 和 c 的增加，共生者在两种物种中都在更宽的基本繁殖率范围内（没有种间相互作用的繁殖率）占据主导地位。如果两个物种之间的基本繁殖率不对称，或者基本繁殖率足够大，共生者和非共生者可以在一个或两个物种中共存，而它们的种群大小通常会波动。从共生到非共生的最终状态的转变相当不连续，然后总种群数量在转变时会发生巨大变化。此外，我们还发现了单边剥削的悖论情况，即一种物种由共生者组成，而另一种物种由非共生者组成。额外的模拟表明，一种物种中非共生者的偶然灭绝可能导致另一种物种中共生者的灭绝。
