Patch dynamics based on Prisoner's Dilemma game: superiority of golden rule

There has been much literature on ecological model of Prisoner's Dilemma (PD) game. This game illustrates that cooperation can evolve in situations where individuals tend to look after themselves. In order to explain some behaviors of altruism in animal societies, the strategy All Cooperate (AC), often called the Golden Rule, is more appropriate than other strategies. However, very little is known about the superiority of AC. In the present article, we study patch dynamics based on non-iterated PD game, applying two different methods: island and lattice models. Each patch is assumed to be either vacant or composed of a population of AC or All Defect (AD), where AD means a selfish strategy. Both models exhibit a phase transition between a phase where both AC and AD survive, and a phase where AD is extinct. The latter phase means that AC beats AD completely. In the case of lattice model, the extinction of AD easily occurs and the abundance of AC takes a larger value, compared with the island model. Our models can be also extended to general iterated PD game; we describe the reason why AC can outperform any other strategy.     

Modelling tritrophic interactions mediated by induced defence volatiles

Many plant species defend themselves against herbivorous insects indirectly by producing and releasing induced volatiles to attract natural enemies of the herbivores. In this paper, we consider the recruitment of natural enemies attracted by plant-induced volatiles and introduce the An–Liu–Johnson–Lovett model into the Lotka–Volterra model in an attempt to add this missing vital link in tritrophic interaction. Increase in attraction strength of plant-induced volatiles to the natural enemy leads to high fluctuation amplitude of plant biomass and herbivore population. When the attack strength of natural enemies reaches a certain level, fluctuation amplitude of plant biomass and herbivore population will decrease and plant biomass will approach to its environmental carrying capacity. The simulation demonstrates that plant volatile compounds induced by insects have led to the introduction of a third tritrophic level, e.g., natural enemies, into the plant–herbivore system, resulting in the coexistence of plants, insects, and natural enemies during the evolution process.     

Ensemble ecosystem modeling for predicting ecosystem response to predator reintroduction

Introducing a new or extirpated species to an ecosystem is risky, and managers need quantitative methods that can predict the consequences for the recipient ecosystem. Proponents of keystone predator reintroductions commonly argue that the presence of the predator will restore ecosystem function, but this has not always been the case, and mathematical modeling has an important role to play in predicting how reintroductions will likely play out. We devised an ensemble modeling method that integrates species interaction networks and dynamic community simulations and used it to describe the range of plausible consequences of 2 keystone‐predator reintroductions: wolves (Canis lupus) to Yellowstone National Park and dingoes (Canis dingo) to a national park in Australia. Although previous methods for predicting ecosystem responses to such interventions focused on predicting changes around a given equilibrium, we used Lotka–Volterra equations to predict changing abundances through time. We applied our method to interaction networks for wolves in Yellowstone National Park and for dingoes in Australia. Our model replicated the observed dynamics in Yellowstone National Park and produced a larger range of potential outcomes for the dingo network. However, we also found that changes in small vertebrates or invertebrates gave a good indication about the potential future state of the system. Our method allowed us to predict when the systems were far from equilibrium. Our results showed that the method can also be used to predict which species may increase or decrease following a reintroduction and can identify species that are important to monitor (i.e., species whose changes in abundance give extra insight into broad changes in the system). Ensemble ecosystem modeling can also be applied to assess the ecosystem‐wide implications of other types of interventions including assisted migration, biocontrol, and invasive species eradication.