Looking at the bid picture: A framework for identifying reverse auctions in ecological systems.

Biological market theory can be used to explain intraspecific cooperation, interspecific mutualism, and sexual selection through models of game theory. These models describe the interactions between organisms as two classes of traders (buyers/sellers) exchanging commodities in the form of goods (e.g. food, shelter, matings) and services (e.g. warning calls, protection). Here, we expand biological market theory to include auction theory where bidding serves to match buyers and sellers. In a reverse auction, the seller increases the value of the item or decreases the cost until a buyer steps forward. We provide several examples of ecological systems that may have reverse auctions as underlying mechanisms to form mutualistic relationships. We focus on the yellow baboon (Papio cynocephalus) mating system as a case study to propose how the mechanisms of a reverse auction, which have the unintended but emergent consequence of producing a mutually beneficial outcome that improves collective reproductive benefits of the troop in this multi-female multi-male polygynandrous social system. For the yellow baboon, we posit that the "seller" is the reproductively cycling female, and the "buyer" is a male looking to mate with a cycling female. To the male, the "item for the sale" is the opportunity to sire an offspring, the price is providing safety and foraging time (via consortship) to the female. The "increasing value of the item for sale" is the chance of conception, which increases with each cycle since a female has resumed cycling post-partum. The female's sexual swelling is an honest indicator of that cycle's probability of conception, and since resident males can track a female's cycle since resumption, there is transparency. The males presumably know the chance of conception when choosing to bid by offering consortship. Across nature, this reverse auction game likely exists in other inter- and intraspecific social relationships. Considering an ecological system as a reverse auction broadens our view of social evolution and adaptations through the lens of human economic structures.

Unstable population dynamics in obligate co-operators.

Cooperation significantly impacts a species' population dynamics as individuals choose others to associate with based upon fitness opportunities. Models of these dynamics typically assume that individuals can freely move between groups. Such an assumption works well for facultative co-operators (e.g. flocking birds, schooling fish, and swarming locusts) but less so for obligate co-operators (e.g. canids, cetaceans, and primates). With obligate co-operators, the fitness consequences from associations are stronger compared to facultative co-operators. Consequently, individuals within a group should be more discerning and selective over their associations, rejecting new members and even removing current members. Incorporating such aspects into population models may better reflect obligately cooperative species. In this paper, we create and analyze a model of the population dynamics of obligate co-operators. In our model, a behavioral game determines within-group population dynamics that then spill over into between-group dynamics. Our analysis shows that group number increases when population dynamics are stable, but additional groups lead to unstable population dynamics and an eventual collapse of group numbers. Using a more general analysis, we identify a fundamental mismatch between the stability of the behavioral dynamics and the stability of the population dynamics. When one is stable, the other is not. Our results suggest that group turnover may be inherent to the population dynamics of obligate co-operators. The instability arises from a non-chaotic deterministic process, and such dynamics should be predictable and testable.

Unlimited niche packing in a Lotka-Volterra competition game.

A central question in the study of ecology and evolution is: "Why are there so many species?" It has been shown that certain forms of the Lotka-Volterra (L-V) competition equations lead to an unlimited number of species. Furthermore, these authors note how any change in the nature of competition (the competition kernel) leads to a finite or small number of coexisting species. Here we build upon these works by further investigating the L-V model of unlimited niche packing as a reference model and evolutionary game for understanding the environmental factors restricting biodiversity. We also examine the combined eco-evolutionary dynamics leading up to the species diversity and traits of the ESS community in both unlimited and finite niche-packing versions of the model. As an L-V game with symmetric competition, we let the strategies of individuals determine the strength of the competitive interaction (like competes most with like) and also the carrying capacity of the population. We use a mixture of analytic proofs (for one and two species systems) and numerical simulations. For the model of unlimited niche packing, we show that a finite number of species will evolve to specific convergent stable minima of the adaptive landscape (also known as species archetypes). Starting with a single species, faunal buildup can proceed either through species doubling as each diversity-specific set of minima are reached, or through the addition of species one-by-one by randomly assigning a speciation event to one of the species. Either way it is possible for an unlimited number or species to evolve and coexist. We examine two simple and biologically likely ways for breaking the unlimited niche-packing: (1) some minimum level of competition among species, and (2) constrain the fundamental niche of the trait space to a finite interval. When examined under both ecological and evolutionary dynamics, both modifications result in convergent stable ESSs with a finite number of species. When the number of species is held below the number of species in an ESS coalition, we see a diverse array of convergent stable niche archetypes that consist of some species at maxima and some at minima of the adaptive landscape. Our results support those of others and suggest that instead of focusing on why there are so many species we might just as usefully ask, why are there so few species?

When does mutualism offer a competitive advantage? A game-theoretic analysis of host-host competition in mutualism.

Due to their non-motile nature, plants rely heavily on mutualistic interactions to obtain resources and carry out services. One key mutualism is the plant-microbial mutualism in which a plant trades away carbon to a microbial partner for nutrients like nitrogen and phosphorous. Plants show much variation in the use of this partnership from the individual level to entire lineages depending upon ecological, evolutionary and environmental context. We sought to determine how this context dependency could result in the promotion, exclusion or coexistence of the microbial mutualism by asking if and when the partnership provided a competitive advantage to the plant. To that end, we created a 2 × 2 evolutionary game in which plants could either be a mutualist and pair with a microbe or be a non-mutualist and forgo the partnership. Our model includes both frequency dependence and density dependence, which gives us the eco-evolutionary dynamics of mutualism evolution. As in all models, mutualism only evolved if it could offer a competitive advantage and its net benefit was positive. However, surprisingly the model reveals the possibility of coexistence between mutualist and non-mutualist genotypes due to competition between mutualists over the microbially obtained nutrient. Specifically, frequency dependence of host strategies can make the microbial symbiont less beneficial if the microbially derived resources are shared, a phenomenon that increasingly reduces the frequency of mutualism as the density of competitors increases. In essence, ecological competition can act as a hindrance to mutualism evolution. We go on to discuss basic experiments that can be done to test and falsify our hypotheses.