Unlimited niche packing in a Lotka–Volterra competition game

Abstract

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?

Life history variation is maintained by fitness trade-offs and negative frequency-dependent selection

“…To test whether the observed variation in the continuous strategy of age at reproduction could be theoretically maintained by negative frequency dependence (NFD), we examined two complimentary models: first, we adapted a well-known, preexisting evolutionary game theoretic model that incorporates continuous ecological and evolutionary dynamics (38)(39)(40) and has been extensively analyzed previously, and second, we developed an individual-based model in which the fitness of each individual depends on its age at spawning and its relative frequency within the population in accordance with the fitness values and slopes illustrating NFD (i.e., Fig. 3 B and C).…”

Non-Equilibrial Dynamics in Under-Saturated Communities

“…Allowing for speciation, the number of species begins to multiply indefinitely. As seen in Cressman et al (2017), the Roughgarden model does not show non-equilibrial evolutionary dynamics in under-saturated communities. We conjecture the reason for this may have to do with the manipulation of the adaptive landscape.…”

“…The MA model seems to have unlimited niche packing (a continuum of an infinite number of species) though evolutionary dynamics for a certain finite number of species can result in the collapse of the system as some of the species evolve higher and higher strategy values resulting in their extinction. It must be noted that this is in contrast to other single function competition models of unlimited niche packing (Gyllenberg and Meszéna , 2005;Meszéna et al, 2005;Szabó and Meszéna, 2006;Parvinen and Meszéna, 2009;Barabas et al, 2012;Barabas et al, 2013;Cressman et al 2017). For example, in the absence of a predator, the BV model becomes the Roughgarden model (1979).…”

“…For example, with the parameters used for analysis of the BV model, the prey only diversified due to aposematic selection from the predators. Changing the parameters could allow for independent diversification within the prey, likely enhancing community instability (Roughgarden, 1976;Ripa et al, 2009;Cressman et al, 2017). Additionally, asymmetric interactions could be added to the predator capture rate and prey competition within the predator-prey models.…”

“…16b). Examination of the adaptive landscapes under increasing numbers of species suggests that the entire system is permanently under-saturated and could, in fact, be a situation of unlimited niche packing (Roughgarden, 1979;Barabas et al, 2012;Cressman et al, 2017).…”