How self-regulation, the storage effect and their interaction contribute to coexistence in stochastic and seasonal environments

Explaining coexistence in species-rich communities of primary producers remains a challenge for ecologists because of their likely competition for shared resources. Following Hutchinson's seminal suggestion, many theoreticians have tried to create diversity through a fluctuating environment, which impairs or slows down competitive exclusion. However, fluctuating-environment models often only produce a dozen of coexisting species at best. Here, we investigate how to create richer communities in fluctuating environments, using an empirically parameterized model. Building on the forced Lotka-Volterra model of Scranton and Vasseur (Theor Ecol 9(3):353-363, 2016), inspired by phytoplankton communities, we have investigated the effect of two coexistence mechanisms, namely the storage effect and higher intra- than interspecific competition strengths (i.e., strong self-regulation). We tuned the intra/inter competition ratio based on empirical analyses, in which self-regulation dominates interspecific interactions. Although a strong self-regulation maintained more species (50%) than the storage effect (25%), we show that none of the two coexistence mechanisms considered could ensure the coexistence of all species alone. Realistic seasonal environments only aggravated that picture, as they decreased persistence relative to a random environment. However, strong self-regulation and the storage effect combined superadditively so that all species could persist with both mechanisms at work. Our results suggest that combining different coexistence mechanisms into community models might be more fruitful than trying to find which mechanism best explains diversity. We additionally highlight that while biomass-trait distributions provide some clues regarding coexistence mechanisms, they cannot indicate unequivocally which mechanisms are at play.Comment: 27 pages, 9 figures, Theor Ecol (2019

Fitting stochastic predator-prey models using both population density and kill rate data

Most mechanistic predator-prey modelling has involved either parameterization from process rate data or inverse modelling. Here, we take a median road: we aim at identifying the potential benefits of combining datasets, when both population growth and predation processes are viewed as stochastic. We fit a discrete-time, stochastic predator-prey model of the Leslie type to simulated time series of densities and kill rate data. Our model has both environmental stochasticity in the growth rates and interaction stochasticity, i.e., a stochastic functional response. We examine what the kill rate data brings to the quality of the estimates, and whether estimation is possible (for various time series lengths) solely with time series of population counts or biomass data. Both Bayesian and frequentist estimation are performed, providing multiple ways to check model identifiability. The Fisher Information Matrix suggests that models with and without kill rate data are all identifiable, although correlations remain between parameters that belong to the same functional form. However, our results show that if the attractor is a fixed point in the absence of stochasticity, identifying parameters in practice requires kill rate data as a complement to the time series of population densities, due to the relatively flat likelihood. Only noisy limit cycle attractors can be identified directly from population count data (as in inverse modelling), although even in this case, adding kill rate data - including in small amounts - can make the estimates much more precise. Overall, we show that under process stochasticity in interaction rates, interaction data might be essential to obtain identifiable dynamical models for multiple species. These results may extend to other biotic interactions than predation, for which similar models combining interaction rates and population counts could be developed

Indirect effects of primary prey population dynamics on alternative prey

We develop a theory of generalist predation showing how alternative prey species are affected by changes in both mean abundance and variability (coefficient of variation) of their predator's primary prey. The theory is motivated by the indirect effects of cyclic rodent populations on ground-breeding birds, and developed through progressive analytic simplifications of an empirically-based model. It applies nonetheless to many other systems where primary prey have fast life-histories and can become locally superabundant, which facilitates impact on alternative prey species. In contrast to classic apparent competition theory based on symmetric interactions, our results suggest that predator effects on alternative prey should generally decrease with mean primary prey abundance, and increase with primary prey variability (low to high CV) - unless predators have strong aggregative responses, in which case these results can be reversed. Approximations of models including predator dynamics (general numerical response with possible delays) confirm these results but further suggest that negative temporal correlation between predator and primary prey is harmful to alternative prey. We find in general that predator numerical responses are crucial to predict the response of ecosystems to changes in key prey species exhibiting outbreaks, and extend the apparent competition/mutualism theory to asymmetric interactions

Intense or Spatially Heterogeneous Predation Can Select against Prey Dispersal

Dispersal theory generally predicts kin competition, inbreeding, and temporal variation in habitat quality should select for dispersal, whereas spatial variation in habitat quality should select against dispersal. The effect of predation on the evolution of dispersal is currently not well-known: because predation can be variable in both space and time, it is not clear whether or when predation will promote dispersal within prey. Moreover, the evolution of prey dispersal affects strongly the encounter rate of predator and prey individuals, which greatly determines the ecological dynamics, and in turn changes the selection pressures for prey dispersal, in an eco-evolutionary feedback loop. When taken all together the effect of predation on prey dispersal is rather difficult to predict. We analyze a spatially explicit, individual-based predator-prey model and its mathematical approximation to investigate the evolution of prey dispersal. Competition and predation depend on local, rather than landscape-scale densities, and the spatial pattern of predation corresponds well to that of predators using restricted home ranges (e.g. central-place foragers). Analyses show the balance between the level of competition and predation pressure an individual is expected to experience determines whether prey should disperse or stay close to their parents and siblings, and more predation selects for less prey dispersal. Predators with smaller home ranges also select for less prey dispersal; more prey dispersal is favoured if predators have large home ranges, are very mobile, and/or are evenly distributed across the landscape

Integrated monitoring of mola mola behaviour in space and time

Over the last decade, ocean sunfish movements have been monitored worldwide using various satellite tracking methods. This study reports the near-real time monitoring of finescale (< 10 m) behaviour of sunfish. The study was conducted in southern Portugal in May 2014 and involved satellite tags and underwater and surface robotic vehicles to measure both the movements and the contextual environment of the fish. A total of four individuals were tracked using custom-made GPS satellite tags providing geolocation estimates of fine-scale resolution. These accurate positions further informed sunfish areas of restricted search (ARS), which were directly correlated to steep thermal frontal zones. Simultaneously, and for two different occasions, an Autonomous Underwater Vehicle (AUV) videorecorded the path of the tracked fish and detected buoyant particles in the water column. Importantly, the densities of these particles were also directly correlated to steep thermal gradients. Thus, both sunfish foraging behaviour (ARS) and possibly prey densities, were found to be influenced by analogous environmental conditions. In addition, the dynamic structure of the water transited by the tracked individuals was described by a Lagrangian modelling approach. The model informed the distribution of zooplankton in the region, both horizontally and in the water column, and the resultant simulated densities positively correlated with sunfish ARS behaviour estimator (r(s) = 0.184, p < 0.001). The model also revealed that tracked fish opportunistically displace with respect to subsurface current flow. Thus, we show how physical forcing and current structure provide a rationale for a predator's finescale behaviour observed over a two weeks in May 2014

Parameter Redundancy and Identifiability, by Diana Cole

Most quantitative biologists and applied statisticians interested in identifiability-i.e., whether a unique set of parameter values can be found to maximize the likelihood of a model-currently have to swift through piles of manuscripts that are often only tangentially relevant to their needs. A colleague who fits dynamic models to data recently lamented: 'Is there something that I could recommend to my graduate students and postdocs that would not be a very technical book from the 80s or 90s?' Now there is. Diana Cole's new book, Parameter redundancy and identifiability, explores all facets of model identifiability and its little cousin parameter redundancy (when the model is non-identifiable because it could be re-parameterized with fewer parameters). The book is written with mostly ecological modelling in mind (in the broadest sense-including fisheries science, epidemiology, ...). However, as the author notes in the preface, the methodology is general and applies equally to other fields: for instance, to compartmental models from pharmacokinetics, that are covered to some degree, and many other dynamical systems. In many ways, this book builds on the author's previous work (Cole et al., 2010; Cole & McCrea, 2016), but presents identifiability techniques in a more accessible and comprehensive manner than the original papers, which were more focused on so-called exhaustive summaries

Integrating multiple data sources to fit matrix population models for interacting species

Inferring interactions between populations of different species is a challenging statistical endeavour, which requires a large amount of data. There is therefore some incentive to combine all available sources of data into a single analysis to do so. In demography and single-population studies, Integrated Population Models combine population counts, capture-recapture and reproduction data to fit matrix population models. Here, we extend this approach to the community level in a stage-structured predator-prey context. We develop Integrated Community Models (ICMs), implemented in a Bayesian framework, to fit multispecies nonlinear matrix models to multiple data sources. We assessed the value of the different sources of data using simulations of ICMs under different scenarios contrasting data availability. We found that combining all data types (capture-recapture, counts, and reproduction) allows the estimation of both demographic and interaction parameters, unlike count-only data which typically generate high bias and low precision in interaction parameter estimates for short time series. Moreover, reproduction surveys informed the estimation of interactions particularly well when compared to capture-recapture programs, and have the advantage of being less costly. Overall, ICMs offer an accurate representation of stage structure in community dynamics, and foster the development of efficient observational study designs to monitor communities in the field

Biological conservation in dynamic agricultural landscapes: effectiveness of public policies and trade-offs with agricultural production

Land use change and land management intensification are major drivers of biodiversity loss, especially in agricultural landscapes, that cover a large and increasing share of the world's surface. Incentive-based agrienvironmental policies are designed to influence farmers' land-use decisions in order to mitigate environmental degradation. This paper evaluates the effectiveness of agri-environmental schemes for biological conservation in a dynamic agricultural landscape under economic uncertainty. We develop a dynamic ecological economic model of agricultural land-use and spatially explicit population dynamics. We then relate policies (subsidies to grassland, taxation of agricultural intensity) to the ecological outcome (probability of persistence of a species of interest). We also analyze the associated trade-offs between agricultural production (in value) and biological conservation (in probability of persistence) at the landscape scale.Le changement d'usage des sols et l'intensification des usages contrôles sont deux facteurs majeurs de l'érosion de la biodiversité, tout particulièrement dans les paysages agricoles qui couvrent une part de plus en plus importante des surfaces mondiales. Des mesures environnementales incitatives sont mises en place pour limiter les dégradations environnementales. Cet article évalue l'efficacité de mesures agro-environnementales pour la préservation de la biodiversité dans les paysages agricoles dynamiques soumis aux incertitudes économiques. Les auteurs développent un modèle écologique-économique dynamique décrivant l'usage des sols agricoles et la dynamique spatialement explicite d'une population animale. Les auteurs relient alors l'effet des politiques publiques (subventions aux prairies et taxations des intrants) à l'état écologique du paysage (probabilité de survie persistance de l'espèce). Les auteurs décrivent également les arbitrages nécessaires à l'échelle du paysage entre production agricole (en valeur) et conservation écologique (en probabilité de persistance)

How do MAR(1) models cope with hidden nonlinearities in ecological dynamics?

1.Multivariate autoregressive (MAR) models are an increasingly popular technique to infer interaction strengths between species in a community and to predict the community response to environmental change. The most commonly employed MAR(1) models, with one time lag, can be viewed either as multispecies competition models with Gompertz density‐dependence or, more generally, as a linear approximation of more complex, nonlinear dynamics around stable equilibria. This latter interpretation allows for broader applicability, but may come at a cost in terms of interpretation of estimates and reliability of both short‐ and long‐term predictions. 2.We investigate what these costs might be by fitting MAR(1) models to simulated two‐species competition, consumer‐resource and host‐parasitoid systems, as well as a larger food web influenced by the environment. We review how MAR(1) coefficients can be interpreted and evaluate how reliable are estimates of interaction strength, rank, or sign; accuracy of short‐term forecasts; as well as the ability of MAR(1) models to predict the long‐term responses of communities submitted to environmental change such as PRESS perturbations. 3.The net effects of species j on species i are usually (90 to 95%) well recovered in terms of sign or rank, with the notable exception of overcompensatory dynamics. In actual values, net effects of species j on species i are not well recovered when the underlying dynamics are nonlinear. MAR(1) models are better at making short‐term, qualitative forecasts (next point going up or down) than at predicting long‐term responses to environmental perturbations, which can be severely over‐ as well as under‐estimated. 4.We conclude that when applying MAR(1) models to ecological data, inferences on net effects among species should be limited to signs, or the Gompertz assumption should be tested and discussed. This particular assumption on density‐dependence (log‐linearity) is also required for unbiased long‐term predictions. Overall, we think that MAR(1) models are highly useful tools to resolve and characterize community dynamics, but we recommend to use them in conjunction with alternative, nonlinear models resembling the ecological context in order to improve their interpretation in specific applications

Schematic depiction of predation in the individual-based model.

<p>Predators are pictured as open circles while prey individuals are represented as black dots. Thick black lines represent the spatial distribution of foraging effort for each predator (i.e. the probability density of attack as described by kernel <i>a</i> in the model), while the dotted line, which is the sum of the black curves, represent the relative predation risk for the prey. , the spatial dispersion of the foraging effort distribution, is referred to in the main text as the predator home range size. On average, predators tend to kill more prey in the center of their home range so that prey progressively concentrate at predator home range boundaries; and this creates a negative spatial correlation between predator and prey distributions.</p