Mutualistic cross-feeding in microbial systems generates bistability via an Allee effect.
ABSTRACT: In microbial ecosystems, species not only compete for common resources but may also display mutualistic interactions as a result from metabolic cross-feeding. Such mutualism can lead to bistability. Depending on the initial population sizes, species will either survive or go extinct. Various phenomenological models have been suggested to describe bistability in mutualistic systems. However, these models do not account for interaction mediators such as nutrients. In contrast, nutrient-explicit models do not provide an intuitive understanding of what causes bistability. Here, we reduce a theoretical nutrient-explicit model of two mutualistic cross-feeders in a chemostat, uncovering an explicit relation to a growth model with an Allee effect. We show that the dilution rate in the chemostat leads to bistability by turning a weak Allee effect into a strong Allee effect. This happens as long as there is more production than consumption of cross-fed nutrients. Thanks to the explicit relationship of the reduced model with the underlying experimental parameters, these results allow to predict the biological conditions that sustain or prevent the survival of mutualistic species.
Project description:We theoretically study the dynamics of two interacting microbial species in the chemostat. These species are competitors for a common resource, as well as mutualists due to cross-feeding. In line with previous studies (Assaneo, et al., 2013; Holland, et al., 2010; Iwata, et al., 2011), we demonstrate that this system has a rich repertoire of dynamical behavior, including bistability. Standard Lotka-Volterra equations are not capable to describe this particular system, as these account for only one type of interaction (mutualistic or competitive). We show here that the different steady state solutions can be well captured by an extended Lotka-Volterra model, which better describe the density-dependent interaction (mutualism at low density and competition at high density). This two-variable model provides a more intuitive description of the dynamical behavior than the chemostat equations.
Project description:Recovering populations of carnivores suffering Allee effects risk extinction because positive population growth requires a minimum number of cooperating individuals. Conservationists seldom consider these issues in planning for carnivore recovery because of data limitations, but ignoring Allee effects could lead to overly optimistic predictions for growth and underestimates of extinction risk. We used Bayesian splines to document a demographic Allee effect in the time series of gray wolf (Canis lupus) population counts (1980-2011) in the southern Lake Superior region (SLS, Wisconsin and the upper peninsula of Michigan, USA) in each of four measures of population growth. We estimated that the population crossed the Allee threshold at roughly 20 wolves in four to five packs. Maximum per-capita population growth occurred in the mid-1990s when there were approximately 135 wolves in the SLS population. To infer mechanisms behind the demographic Allee effect, we evaluated a potential component Allee effect using an individual-based spatially explicit model for gray wolves in the SLS region. Our simulations varied the perception neighborhoods for mate-finding and the mean dispersal distances of wolves. Simulation of wolves with long-distance dispersals and reduced perception neighborhoods were most likely to go extinct or experience Allee effects. These phenomena likely restricted population growth in early years of SLS wolf population recovery.
Project description:The Allee effect describes populations that deviate from logistic growth models and arises in applications including ecology and cell biology. A common justification for incorporating Allee effects into population models is that the population in question has altered growth mechanisms at some critical density, often referred to as a threshold effect. Despite the ubiquitous nature of threshold effects arising in various biological applications, the explicit link between local threshold effects and global Allee effects has not been considered. In this work, we examine a continuum population model that incorporates threshold effects in the local growth mechanisms. We show that this model gives rise to a diverse family of Allee effects, and we provide a comprehensive analysis of which choices of local growth mechanisms give rise to specific Allee effects. Calibrating this model to a recent set of experimental data describing the growth of a population of cancer cells provides an interpretation of the threshold population density and growth mechanisms associated with the population.
Project description:A phenomenon that strongly influences the demography of small introduced populations and thereby potentially their genetic diversity is the demographic Allee effect, a reduction in population growth rates at small population sizes. We take a stochastic modeling approach to investigate levels of genetic diversity in populations that successfully overcame either a strong Allee effect, in which populations smaller than a certain critical size are expected to decline, or a weak Allee effect, in which the population growth rate is reduced at small sizes but not negative. Our results indicate that compared to successful populations without an Allee effect, successful populations with a strong Allee effect tend to (1) derive from larger founder population sizes and thus have a higher initial amount of genetic variation, (2) spend fewer generations at small population sizes where genetic drift is particularly strong, and (3) spend more time around the critical population size and thus experience more genetic drift there. In the case of multiple introduction events, there is an additional increase in diversity because Allee-effect populations tend to derive from a larger number of introduction events than other populations. Altogether, a strong Allee effect can either increase or decrease genetic diversity, depending on the average founder population size. By contrast, a weak Allee effect tends to decrease genetic diversity across the entire range of founder population sizes. Finally, we show that it is possible in principle to infer critical population sizes from genetic data, although this would require information from many independently introduced populations.
Project description:Allee effects may arise as the number of individuals decreases, thereby reducing opportunities for cooperation and constraining individual fitness, which can lead to population decrease and extinction. Obligate cooperative breeders rely on a minimum group size to subsist and are thus expected to be particularly susceptible to Allee effects. Although Allee effects in some components of the fitness of cooperative breeders have been detected, empirical confirmation of population extinction due to Allee effects is lacking yet. Because previous studies of cooperation have focused on Allee effects affecting individual fitness (component Allee effect) and population dynamics (demographic Allee effect), we argue that a new conceptual level of Allee effect, the group Allee effect, is needed to understand the special case of cooperative breeders.We hypothesize that whilst individuals are vulnerable to Allee effects, the group could act as a buffer against population extinction if: (i) individual fitness and group fate depend on group size but not on population size and (ii) group size is independent of population size (that is, at any population size, populations comprise both large and small groups). We found that both conditions apply for the African wild dog, Lycaon pictus, and data on this species in Zimbabwe support our hypothesis.The importance of groups in obligate cooperative breeders needs to be accounted for within the Allee effect framework, through a group Allee effect, because the group mediates the relationship between individual fitness and population performance. Whilst sociality is associated with a high probability of Allee effects, we suggest that cooperative individuals organized in relatively autonomous groups within populations might be behaving in ways that diminish extinction risks caused by Allee effects. This study opens new avenues to a better understanding of the role of the evolution of group-living on the probability of extinction faced by social species.
Project description:Microbial populations can be dispersal limited. However, microorganisms that successfully disperse into physiologically ideal environments are not guaranteed to establish. This observation contradicts the Baas-Becking tenet: 'Everything is everywhere, but the environment selects'. Allee effects, which manifest in the relationship between initial population density and probability of establishment, could explain this observation. Here, we experimentally demonstrate that small populations of Vibrio fischeri are subject to an intrinsic demographic Allee effect. Populations subjected to predation by the bacterivore Cafeteria roenbergensis display both intrinsic and extrinsic demographic Allee effects. The estimated critical threshold required to escape positive density-dependence is around 5, 20 or 90 cells ml(-1)under conditions of high carbon resources, low carbon resources or low carbon resources with predation, respectively. This work builds on the foundations of modern microbial ecology, demonstrating that mechanisms controlling macroorganisms apply to microorganisms, and provides a statistical method to detect Allee effects in data.
Project description:Allee effects are an important component in the population dynamics of numerous species. Accounting for these Allee effects in population viability analyses generally requires estimates of low-density population growth rates, but such data are unavailable for most species and particularly difficult to obtain for large mammals. Here, we present a mechanistic modeling framework that allows estimating the expected low-density growth rates under a mate-finding Allee effect before the Allee effect occurs or can be observed. The approach relies on representing the mechanisms causing the Allee effect in a process-based model, which can be parameterized and validated from data on the mechanisms rather than data on population growth. We illustrate the approach using polar bears (Ursus maritimus), and estimate their expected low-density growth by linking a mating dynamics model to a matrix projection model. The Allee threshold, defined as the population density below which growth becomes negative, is shown to depend on age-structure, sex ratio, and the life history parameters determining reproduction and survival. The Allee threshold is thus both density- and frequency-dependent. Sensitivity analyses of the Allee threshold show that different combinations of the parameters determining reproduction and survival can lead to differing Allee thresholds, even if these differing combinations imply the same stable-stage population growth rate. The approach further shows how mate-limitation can induce long transient dynamics, even in populations that eventually grow to carrying capacity. Applying the models to the overharvested low-density polar bear population of Viscount Melville Sound, Canada, shows that a mate-finding Allee effect is a plausible mechanism for slow recovery of this population. Our approach is generalizable to any mating system and life cycle, and could aid proactive management and conservation strategies, for example, by providing a priori estimates of minimum conservation targets for rare species or minimum eradication targets for pests and invasive species.
Project description:Allee effects may render exploited animal populations extinction prone, but empirical data are often lacking to describe the circumstances leading to an Allee effect. Arbitrary assumptions regarding Allee effects could lead to erroneous management decisions so that predictive modelling approaches are needed that identify the circumstances leading to an Allee effect before such a scenario occurs. We present a predictive approach of Allee effects for polar bears where low population densities, an unpredictable habitat and harvest-depleted male populations result in infrequent mating encounters. We develop a mechanistic model for the polar bear mating system that predicts the proportion of fertilized females at the end of the mating season given population density and operational sex ratio. The model is parametrized using pairing data from Lancaster Sound, Canada, and describes the observed pairing dynamics well. Female mating success is shown to be a nonlinear function of the operational sex ratio, so that a sudden and rapid reproductive collapse could occur if males are severely depleted. The operational sex ratio where an Allee effect is expected is dependent on population density. We focus on the prediction of Allee effects in polar bears but our approach is also applicable to other species.
Project description:The demographic Allee effect, or depensation, implies positive association between per capita population growth rate and population size at low abundances, thereby lowering growth ability of sparse populations. This can have far-reaching consequences on population recovery ability and colonization success. In the context of marine fishes, there is a widespread perception that Allee effects are rare or non-existent. However, studies that have failed to detect Allee effects in marine fishes have suffered from several fundamental methodological and data limitations. In the present study, we challenge the prevailing perception about the rarity of Allee effects by analysing nine populations of Atlantic herring (Clupea harengus), using Bayesian statistical methods. We find that populations of the same species can show either strong evidence for Allee effects or compensation. We explicitly demonstrate how the evidence for Allee effects is strongly provisional on observations made at low population abundances. We contrast our statistical approach with previous attempts to detect Allee effects and illustrate methodological issues that can lead to erroneous conclusions about the nature of population dynamics at low abundance. The present study demonstrates that there is no substantive scientific basis to support the perception that Allee effects are rare or non-existent in marine fishes.
Project description:A strong demographic Allee effect in which the expected population growth rate is negative below a certain critical population size can cause high extinction probabilities in small introduced populations. But many species are repeatedly introduced to the same location and eventually one population may overcome the Allee effect by chance. With the help of stochastic models, we investigate how much genetic diversity such successful populations harbor on average and how this depends on offspring-number variation, an important source of stochastic variability in population size. We find that with increasing variability, the Allee effect increasingly promotes genetic diversity in successful populations. Successful Allee-effect populations with highly variable population dynamics escape rapidly from the region of small population sizes and do not linger around the critical population size. Therefore, they are exposed to relatively little genetic drift. It is also conceivable, however, that an Allee effect itself leads to an increase in offspring-number variation. In this case, successful populations with an Allee effect can exhibit less genetic diversity despite growing faster at small population sizes. Unlike in many classical population genetics models, the role of offspring-number variation for the population genetic consequences of the Allee effect cannot be accounted for by an effective-population-size correction. Thus, our results highlight the importance of detailed biological knowledge, in this case on the probability distribution of family sizes, when predicting the evolutionary potential of newly founded populations or when using genetic data to reconstruct their demographic history.