Collective behaviors in social insect societies often emerge from simple local rules. However, little is known about how these behaviors are dynamically regulated in response to environmental changes. Here, we use a compartmental modeling approach to identify factors that allow harvester ant colonies to regulate collective foraging activity in response to their environment. We propose a set of di↵erential equations describing the dynamics of: (1) available foragers inside the nest, (2) active foragers outside the nest, and (3) successful returning foragers, to understand how colony-specific parameters, such as baseline number of foragers, interactions among foragers, food discovery rates, successful forager return rates, and foraging duration might influence collective foraging dynamics, while maintaining functional robustness to perturbations. Our analysis indicates that the model can undergo a forward (transcritical) bifurcation or a backward bifurcation depending on colony-specific parameters. In the former case, foraging activity persists when the average number of recruits per successful returning forager is larger than one. In the latter case, the backward bifurcation creates a region of bistability in which the size and fate of foraging activity depends on the distribution of the foraging workforce among the model's compartments. We validate the model with experimental data from harvester ants (Pogonomyrmex barbatus) and perform sensitivity analysis. Our model provides insights on how simple, local interactions can achieve an emergent and robust regulatory system of collective foraging activity in ant colonies.
Human societies are unique in the level of cooperation among non-kin. Evolutionary models explaining this behavior typically assume pure strategies of cooperation and defection. Behavioral experiments, however, demonstrate that humans are typically conditional cooperators who have other-regarding preferences. Building on existing models on the evolution of cooperation and costly punishment, we use a utilitarian formulation of agent decision making to explore conditions that support the emergence of cooperative behavior. Our results indicate that cooperation levels are significantly lower for larger groups in contrast to the original pure strategy model. Here, defection behavior not only diminishes the public good, but also affects the expectations of group members leading conditional co-operators to change their strategies. Hence defection has a more damaging effect when decisions are based on expectations and not only pure strategies.
Metapopulation (multipatch) models are widely used to study the patterns of spatial spread of epidemics. In this paper we study the impact of inter-patch connection weights on the predictions of these models. We contrast arbitrary, uniform link weights with link weights predicted using a gravity model based on patch populations and distance. In a synthetic system with one large driver city and many small follower cities, we show that under uniform link weights, epidemics in the follower regions are perfectly synchronized. In contrast, gravity-based links allow a more realistic, less synchronized distribution of epidemic peaks in the follower regions. We then fit a three-patch metapopulation model to regional dengue fever data from Peru -a country experiencing yearly, spatially defined epidemics. We use data for [2002][2003][2004][2005][2006][2007][2008] (studying the seasonal disease patterns in the country and the yearly reinfection patterns from jungle to the coast) and 2000-2001 (one large epidemic of a new disease strain across the country).We present numerical results.
Borrelia burgdorferi sensu stricto is a bacterial spirochete prevalent in the Northeastern United States that causes Lyme disease. Lyme disease is the most common arthropod-borne disease in the United States; affecting mice, deer, humans and other mammals. The disease is spread by Ixodes Scapularis, a species of tick whose primary food source are deer and mice. Reducing the population of ticks feeding on both large and small mammals below some critical threshold can decrease the prevalence of Lyme disease among humans. A simplified, sixdimensional Susceptible-Infected, SI, model is used to capture the mice-deer-tick dynamics while considering the impact of varying population-specific death rates on infected population size. We analyzed the stability of the models two equilibria, the unstable disease free equilibrium and the endemic equilibrium. Static forward sensitivity analysis is conducted on the basic reproduction number and the endemic equilibrium. A dynamic approach was explored to observe change in the sensitivity of the death rates over time. These analyses were conducted to determine the efficacy of changing death rates in order to reduce prevalence of Lyme disease.
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