Population dynamics of mutualism and intraspecific density dependence: How θ-logistic density dependence affects mutualistic positive feedback

Ecological theory of mutualism: Robust patterns of stability and thresholds in two-species population models

Mutualisms are ubiquitous in nature, provide important ecosystem services, and involve many species of interest for conservation. Theoretical progress on the population dynamics of mutualistic interactions, however, comparatively lagged behind that of trophic and competitive interactions, leading to the impression that ecologists still lack a generalized framework to investigate the population dynamics of mutualisms. Yet, over the last 90 years, abundant theoretical work has accumulated, ranging from abstract to detailed. Here, we review and synthesize historical models of two-species mutualisms. We find that population dynamics of mutualisms are qualitatively robust across derivations, including levels of detail, types of benefit, and inspiring systems. Specifically, mutualisms tend to exhibit stable coexistence at high density and destabilizing thresholds at low density. These dynamics emerge when benefits of mutualism saturate, whether due to intrinsic or extrinsic density dependence in intraspecific processes, interspecific processes, or both. We distinguish between thresholds resulting from Allee effects, low partner density, and high partner density, and their mathematical and conceptual causes. Our synthesis suggests that there exists a robust population dynamic theory of mutualism that can make general predictions.

Stress response and population dynamics: Is Allee effect hormesis?

Hormesis is a fundamental notion in ecotoxicology while competition between organisms is an essential notion in population ecology and species adaptation and evolution. Both sub-disciplines of ecology deal with the response of organisms to abiotic and biotic stresses. In ecotoxicology, the Linear-non-Threshold (LNT), Threshold and Hormetic models are used to describe the dominant responses of a plethora of endpoints to abiotic stress. In population ecology, the logistic, theta-logistic and the Allee effect models are used to describe the growth of populations under different responses to (biotic) stress induced by population density. The per capita rate of population increase (r) measures species fitness. When it is used as endpoint, the responses to population density seem to perfectly correspond to LNT, Threshold and Hormetic responses to abiotic stress, respectively. Our analysis suggests the Allee effect is a hormetic-like response of r to population density, an ultimate biotic stress. This biphasic dose-response model appears across different systems and situations (from molecules to tumor growth to population dynamics), is highly supported by ecological and evolutionary theory, and has important implications in most sub-disciplines of biology as well as in environmental and earth sciences. Joined multi-disciplinary efforts would facilitate the development and application of advanced research approaches for better understanding potential planetary-scale implications.

Synthetic Mutualism and the Intervention Dilemma

Ecosystems are complex networks of interacting individuals co-evolving with their environment. As such, changes to an interaction can influence the whole ecosystem. However, to predict the outcome of these changes, considerable understanding of processes driving the system is required. Synthetic biology provides powerful tools to aid this understanding, but these developments also allow us to change specific interactions. Of particular interest is the ecological importance of mutualism, a subset of cooperative interactions. Mutualism occurs when individuals of different species provide a reciprocal fitness benefit. We review available experimental techniques of synthetic biology focused on engineered synthetic mutualistic systems. Components of these systems have defined interactions that can be altered to model naturally occurring relationships. Integrations between experimental systems and theoretical models, each informing the use or development of the other, allow predictions to be made about the nature of complex relationships. The predictions range from stability of microbial communities in extreme environments to the collapse of ecosystems due to dangerous levels of human intervention. With such caveats, we evaluate the promise of synthetic biology from the perspective of ethics and laws regarding biological alterations, whether on Earth or beyond. Just because we are able to change something, should we?

Disentangling eco-evolutionary effects on trait fixation

In population genetics, fixation of traits in a demographically changing population under frequency-independent selection has been extensively analysed. In evolutionary game theory, models of fixation have typically focused on fixed population sizes and frequency-dependent selection. A combination of demographic fluctuations with frequency-dependent interactions such as Lotka-Volterra dynamics has received comparatively little attention. We consider a stochastic, competitive Lotka-Volterra model with higher order interactions between two traits. The emerging individual-based model allows for stochastic fluctuations in the frequencies of the two traits and the total population size. We calculate the fixation probability of a trait under differing competition coefficients. This fixation probability resembles, qualitatively, the deterministic evolutionary dynamics. Furthermore, we partially disentangle the selection effects into their ecological and evolutionary components. We find that changing the evolutionary selection strength also changes the population dynamics and vice versa. Thus, a clean separation of the ecological and evolutionary effects is not possible. Instead, our results imply a nested interaction of the evolutionary and ecological effects. The entangled eco-evolutionary processes thus cannot be ignored when determining fixation properties in a co-evolutionary system.