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Contemporary theory of predator coexistence through relative non-linearity in their functional responses strongly relies on the Rosenzweig and MacArthur (1963) equations in which the (autotrophic) prey exhibits logistic growth in the absence of the predators. This implies that the prey is limited by a resource such as light or space, which availability is independent of the predators. This assumption does not hold under nutrient limitation where both prey and predators bind resources such as nitrogen and phosphorus in their biomass. Furthermore, the prey’s resource uptake rate is assumed to be linear and the predator-prey system is considered to be closed. All these assumptions are unrealistic for many natural systems. Here, we show that nutrient retention in predator biomass strongly hampers the coexistence of two predators on one prey because it stabilizes the dynamics. In contrast, a non-linear resource uptake rate of the prey slightly promotes predator coexistence. Our study highlights that predator coexistence does depend not only on differences in the curvature of their functional responses but also on the type of resource constraining the growth of their prey. This has far-reaching consequences for the relative importance of fluctuation-dependent and fluctuation-independent mechanisms of species coexistence in natural systems where autotrophs experience light or nutrient limitation.

It is widely recognized that coupled socio-ecological dynamics can be qualitatively different from the dynamics of social or ecological systems in isolation from one another. The influence of the type of ecological dynamics on the dynamics of the larger socio-ecological system is less well studied, however. Here, we carry out such a comparison using a mathematical model of a common pool resource problem. A population must make decisions about harvesting a renewable resource. Individuals may either be cooperators, who harvest at a sustainable level, or defectors, who overharvest. Cooperators punish defectors through social ostracism. Individuals can switch strategies according to the costs and benefits of harvesting and the strength of social ostracism. These mechanisms are represented by a differential equation for social dynamics, which is coupled to three different types of resource dynamics: logistic growth, constant inflow, and threshold growth. We find that when human influence is sufficiently weak, the form of resource dynamics leaves a strong imprint on the socio-ecological dynamics, and human social dynamics are qualitatively very different from resource dynamics. However, stronger human influence introduces a broad intermediate parameter regime where dynamical patterns converge to a common type: the three types of ecological systems exhibit similar dynamics, but also, social and ecological dynamics mirror one another. This regime of strong human influence includes generation of stable limit cycles at high rates of social learning. Such oscillations are a consequence of stronger coupling and are reminiscent of synchrony in other fields, such as the classic problem of coupled oscillators. Socio-ecological convergence has implications for how we understand and manage complex socio-ecological systems. In an era of growing human influence on ecological systems, further empirical and theoretical work is required to determine whether socio-ecological convergence is present in real systems.

The demographic rates (e.g., birth, death, migration) of many organisms have been shown to respond strongly to short- and long-term environmental change, including variation in temperature and precipitation. While ecologists have long accounted for such nonhomogeneous demography in deterministic population models, nonhomogeneous stochastic population models are largely absent from the literature. This is especially the case for models that use exact stochastic methods, such as Gillespie’s stochastic simulation algorithm (SSA), which commonly assumes that demographic rates do not respond to external environmental change (i.e., assumes homogeneous demography). In other words, ecologists are currently accounting for the effects of demographic stochasticity or environmental variability, but not both. In this paper, we describe an extension of Gillespie’s SSA (SSA + ) that allows for nonhomogeneous demography and examine how its predictions differ from a method that is partly naive to environmental change (SSAn) for two fundamental ecological models (exponential and logistic growth). We find important differences in the predicted population sizes of SSA + versus SSAn simulations, particularly when demography responds to fluctuating and irregularly changing environments. Further, we outline a computationally inexpensive approach for estimating when and under what circumstances it can be important to fully account for nonhomogeneous demography for any class of model.

Competition in ecology is often modeled in terms of direct, negative effects of one individual on another. An example is logistic growth, modeling the effects of intraspecific competition, while the Lotka-Volterra equations for competition extend this to systems of multiple species, with varying strengths of intra- and inter-specific competition. These equations are a classic and well-used staple of quantitative ecology, providing a framework to understand species interactions, species coexistence, and community assembly. They can be derived from an assumption of random mixing of organisms, and an outcome of each interaction that removes one or more individuals. However, this framing is some-what unsatisfactory, and ecologists may prefer to think of phenomenological equations for competition as deriving from competition for a set of resources required for growth, which in turn may undergo their own complex dynamics. While it is intuitive that these frameworks are connected, and the connection is well-understood near to equilibria, here we ask the question: when can consumer dynamics alone become an exact description of a full system of consumers and resources? We identify that consumer-resource systems with this property must have some kind of redundancy in the original description, or equivalently there is one or more conservation laws for quantities that do not change with time. Such systems are known in mathematics as integrable systems. We suggest that integrability in consumer-resource dynamics can only arise in cases where each species in an assemblage requires a distinct and unique combination of resources, and even in these cases it is not clear that the resulting dynamics will lead to Lotka-Volterra competition.I acknowledge the Simons Foundation Grant #376199 and the McDonnell Foundation Grant #220020439.

Interaction strength (IS) has been theoretically shown to play a major role in governing the stability and dynamics of food webs. Nonetheless, its definition has been varied and problematic, including a range of recent definitions based on biological rates associated with model parameters (e.g., attack rate). Results from food web theory have been used to argue that IS metrics based on energy flux ought to have a clear relationship with stability. Here, we use simple models to elucidate the actual relationship between local stability and a number of common IS metrics (total flux and per capita fluxes) as well as a more recently suggested metric. We find that the classical IS metrics map to stability in a more complex way than suggested by existing food web theory and that the new IS metric has a much clearer, and biologically interpretable, relationship with local stability. The total energy flux metric falls off existing theoretical predictions when the total resource productivity available to the consumer is reduced despite increased consumer attack rates. The density of a consumer can hence decrease when its attack rate increases. This effect, called the paradox of attack rate, is similar to the well-known hydra effect and can even cascade up a food chain to exclude a predator when consumer attack rate is increased.

Consumer-resource models have been used extensively to study the evolution and coexistence of generalist and specialist consumers. However, current consumer-resource models do not take into account competition between resources or only incorporate intraspecific competition phenomenologically with, for example, a logistic growth function. Here, we mechanistically incorporate competition in an existing two-resource model, by introducing nutrient-limited resource growth and setting the total amount of nutrients (free or contained in consumers and resources) to a fixed value. In addition to the three combinations of generalists and specialists found in previous models, we find four other evolutionary outcomes, depending on the strength of the consumer trade-off: coexistence of one specialist and a generalist and three types of evolutionary cycling. Furthermore, which outcomes are most likely depends strongly on the combination of intrinsic growth rate of resources and the total amount of nutrients in the system. Our results suggest that the realistic assumption of nutrient competition may shed new light on the evolution of the multitude of strategies in real systems.

Among-individual variation in vital parameters such as birth and death rates that is unrelated to age, stage, sex, or environmental fluctuations is referred to as demographic heterogeneity. This kind of heterogeneity is prevalent in ecological populations, but is almost always left out of models. Demographic heterogeneity has been shown to affect demographic stochasticity in small populations and to increase growth rates for density-independent populations. The latter is due to “cohort selection,” where the most frail individuals die out first, lowering the cohort’s average mortality as it ages. The importance of cohort selection to population dynamics has only recently been recognized. We use a continuous-time model with density dependence, based on the logistic equation, to study the effects of demographic heterogeneity in mortality and reproduction. Reproductive heterogeneity is introduced in three ways: parent fertility, offspring viability, and parent–offspring correlation. We find that both the low-density growth rate and the equilibrium population size increase as the magnitude of mortality heterogeneity increases or as parent–offspring phenotypic correlation increases. Population dynamics are affected by complex interactions among the different types of heterogeneity, and trade-off scenarios are examined which can sometimes reverse the effect of increased heterogeneity. We show that there are a number of different homogeneous approximations to heterogeneous models, but all fail to capture important parts of the dynamics of the full model.