Structural Perturbations to Population Skeletons: Transient Dynamics, Coexistence of Attractors and the Rarity of Chaos

Simple models of insect populations with non-overlapping generations have been instrumental in understanding the mechanisms behind population cycles, including wild (chaotic) fluctuations. The presence of deterministic chaos in natural populations, however, has never been unequivocally accepted. Recently, it has been proposed that the application of chaos control theory can be useful in unravelling the complexity observed in real population data. This approach is based on structural perturbations to simple population models (population skeletons). The mechanism behind such perturbations to control chaotic dynamics thus far is model dependent and constant (in size and direction) through time. In addition, the outcome of such structurally perturbed models is [almost] always equilibrium type, which fails to commensurate with the patterns observed in population data.We present a proportional feedback mechanism that is independent of model formulation and capable of perturbing population skeletons in an evolutionary way, as opposed to requiring constant feedbacks. We observe the same repertoire of patterns, from equilibrium states to non-chaotic aperiodic oscillations to chaotic behaviour, across different population models, in agreement with observations in real population data. Model outputs also indicate the existence of multiple attractors in some parameter regimes and this coexistence is found to depend on initial population densities or the duration of transient dynamics. Our results suggest that such a feedback mechanism may enable a better understanding of the regulatory processes in natural populations

A polychromatic 'greenbeard' locus determines patterns of cooperation in a social amoeba

Cheaters disrupt cooperation by reaping the benefits without paying their fair share of associated costs. Cheater impact can be diminished if cooperators display a tag (‘greenbeard') and recognise and preferentially direct cooperation towards other tag carriers. Despite its popular appeal, the feasibility of such greenbeards has been questioned because the complex patterns of partner-specific cooperative behaviours seen in nature require greenbeards to come in different colours. Here we show that a locus (‘Tgr') of a social amoeba represents a polychromatic greenbeard. Patterns of natural Tgr locus sequence polymorphisms predict partner-specific patterns of cooperation by underlying variation in partner-specific protein–protein binding strength and recognition specificity. Finally, Tgr locus polymorphisms increase fitness because they help avoid potential costs of cooperating with incompatible partners. These results suggest that a polychromatic greenbeard can provide a key mechanism for the evolutionary maintenance of cooperation