Stochastic growth reduces population fluctuations inDaphnia–algal systems

Multi-synchronization and other patterns of multi-rhythmicity in oscillatory biological systems

While experimental and theoretical studies have established the prevalence of rhythmic behaviour at all levels of biological organization, less common is the coexistence between multiple oscillatory regimes (multi-rhythmicity), which has been predicted by a variety of models for biological oscillators. The phenomenon of multi-rhythmicity involves, most commonly, the coexistence between two (birhythmicity) or three (trirhythmicity) distinct regimes of self-sustained oscillations. Birhythmicity has been observed experimentally in a few chemical reactions and in biological examples pertaining to cardiac cell physiology, neurobiology, human voice patterns and ecology. The present study consists of two parts. We first review the mechanisms underlying multi-rhythmicity in models for biochemical and cellular oscillations in which the phenomenon was investigated over the years. In the second part, we focus on the coupling of the cell cycle and the circadian clock and show how an additional source of multi-rhythmicity arises from the bidirectional coupling of these two cellular oscillators. Upon bidirectional coupling, the two oscillatory networks generally synchronize in a unique manner characterized by a single, common period. In some conditions, however, the two oscillators may synchronize in two or three different ways characterized by distinct waveforms and periods. We refer to this type of multi-rhythmicity as ‘multi-synchronization’.

Stoichiometric Ecotoxicology for a Multisubstance World

Nutritional and contaminant stressors influence organismal physiology, trophic interactions, community structure, and ecosystem-level processes; however, the interactions between toxicity and elemental imbalance in food resources have been examined in only a few ecotoxicity studies. Integrating well-developed ecological theories that cross all levels of biological organization can enhance our understanding of ecotoxicology. In the present article, we underline the opportunity to couple concepts and approaches used in the theory of ecological stoichiometry (ES) to ask ecotoxicological questions and introduce stoichiometric ecotoxicology, a subfield in ecology that examines how contaminant stress, nutrient supply, and elemental constraints interact throughout all levels of biological organization. This conceptual framework unifying ecotoxicology with ES offers potential for both empirical and theoretical studies to deepen our mechanistic understanding of the adverse outcomes of chemicals across ecological scales and improve the predictive powers of ecotoxicology.

Within-host priority effects and epidemic timing determine outbreak severity in co-infected populations

Co-infections of hosts by multiple pathogen species are ubiquitous, but predicting their impact on disease remains challenging. Interactions between co-infecting pathogens within hosts can alter pathogen transmission, with the impact on transmission typically dependent on the relative arrival order of pathogens within hosts (within-host priority effects). However, it is unclear how these within-host priority effects influence multi-pathogen epidemics, particularly when the arrival order of pathogens at the host-population scale varies. Here, we combined models and experiments with zooplankton and their naturally co-occurring fungal and bacterial pathogens to examine how within-host priority effects influence multi-pathogen epidemics. Epidemiological models parametrized with within-host priority effects measured at the single-host scale predicted that advancing the start date of bacterial epidemics relative to fungal epidemics would decrease the mean bacterial prevalence in a multi-pathogen setting, while models without within-host priority effects predicted the opposite effect. We tested these predictions with experimental multi-pathogen epidemics. Empirical dynamics matched predictions from the model including within-host priority effects, providing evidence that within-host priority effects influenced epidemic dynamics. Overall, within-host priority effects may be a key element of predicting multi-pathogen epidemic dynamics in the future, particularly as shifting disease phenology alters the order of infection within hosts.

Continuous Structured Population Models for Daphnia magna

We continue our efforts in modeling Daphnia magna, a species of water flea, by proposing a continuously structured population model incorporating density-dependent and density-independent fecundity and mortality rates. We collected new individual-level data to parameterize the individual demographics relating food availability and individual daphnid growth. Our model is fit to experimental data using the generalized least-squares framework, and we use cross-validation and Akaike Information Criteria to select hyper-parameters. We present our confidence intervals on parameter estimates.

Approximation of a physiologically structured population model with seasonal reproduction by a stage-structured biomass model

Seasonal reproduction causes, due to the periodic inflow of young small individuals in the population, seasonal fluctuations in population size distributions. Seasonal reproduction furthermore implies that the energetic body condition of reproducing individuals varies over time. Through these mechanisms, seasonal reproduction likely affects population and community dynamics. While seasonal reproduction is often incorporated in population models using discrete time equations, these are not suitable for size-structured populations in which individuals grow continuously between reproductive events. Size-structured population models that consider seasonal reproduction, an explicit growing season and individual-level energetic processes exist in the form of physiologically structured population models. However, modeling large species ensembles with these models is virtually impossible. In this study, we therefore develop a simpler model framework by approximating a cohort-based size-structured population model with seasonal reproduction to a stage-structured biomass model of four ODEs. The model translates individual-level assumptions about food ingestion, bioenergetics, growth, investment in reproduction, storage of reproductive energy, and seasonal reproduction in stage-based processes at the population level. Numerical analysis of the two models shows similar values for the average biomass of juveniles, adults, and resource unless large-amplitude cycles with a single cohort dominating the population occur. The model framework can be extended by adding species or multiple juvenile and/or adult stages. This opens up possibilities to investigate population dynamics of interacting species while incorporating ontogenetic development and complex life histories in combination with seasonal reproduction.

Relating suborganismal processes to ecotoxicological and population level endpoints using a bioenergetic model

Ecological effects of environmental stressors are commonly evaluated using organismal or suborganismal data, such as standardized toxicity tests that characterize responses of individuals (e.g., mortality and reproduction) and a rapidly growing body of "omics" data. A key challenge for environmental risk assessment is relating such information to population dynamics. One approach uses dynamic energy budget (DEB) models that relate growth and reproduction of individuals to underlying flows of energy and elemental matter. We hypothesize that suborganismal information identifies DEB parameters that are most likely impacted by a particular stressor and that the DEB model can then project suborganismal effects on life history and population endpoints. We formulate and parameterize a model of growth and reproduction for the water flea Daphnia magna. Our model resembles previous generic bioenergetic models, but has explicit representation of discrete molts, an important feature of Daphnia life history. We test its ability to predict six endpoints commonly used in chronic toxicity studies in specified food environments. With just one adjustable parameter, the model successfully predicts growth and reproduction of individuals from a wide array of experiments performed in multiple laboratories using different clones of D. magna raised on different food sources. Fecundity is the most sensitive endpoint, and there is broad correlation between the sensitivities of fecundity and long-run growth rate, as is desirable for the default metric used in chronic toxicity tests. Under some assumptions, we can combine our DEB model with the Euler-Lotka equation to estimate longrun population growth rates at different food levels. A review of Daphnia gene-expression experiments on the effects of contaminant exposure reveals several connections to model parameters, in particular a general trend of increased transcript expression of genes involved in energy assimilation and utilization at concentrations affecting growth and reproduction. The sensitivity of fecundity to many model parameters was consistent with frequent generalized observations of decreased expression of genes involved in reproductive physiology, but interpretation of these observations requires further mechanistic modeling. We thus propose an approach based on generic DEB models incorporating few essential species-specific features for rapid extrapolation of ecotoxicogenomic assays for Daphnia-based population risk assessment.

Inferring the temperature dependence of population parameters: the effects of experimental design and inference algorithm

Understanding and quantifying the temperature dependence of population parameters, such as intrinsic growth rate and carrying capacity, is critical for predicting the ecological responses to environmental change. Many studies provide empirical estimates of such temperature dependencies, but a thorough investigation of the methods used to infer them has not been performed yet. We created artificial population time series using a stochastic logistic model parameterized with the Arrhenius equation, so that activation energy drives the temperature dependence of population parameters. We simulated different experimental designs and used different inference methods, varying the likelihood functions and other aspects of the parameter estimation methods. Finally, we applied the best performing inference methods to real data for the species Paramecium caudatum. The relative error of the estimates of activation energy varied between 5% and 30%. The fraction of habitat sampled played the most important role in determining the relative error; sampling at least 1% of the habitat kept it below 50%. We found that methods that simultaneously use all time series data (direct methods) and methods that estimate population parameters separately for each temperature (indirect methods) are complementary. Indirect methods provide a clearer insight into the shape of the functional form describing the temperature dependence of population parameters; direct methods enable a more accurate estimation of the parameters of such functional forms. Using both methods, we found that growth rate and carrying capacity of Paramecium caudatum scale with temperature according to different activation energies. Our study shows how careful choice of experimental design and inference methods can increase the accuracy of the inferred relationships between temperature and population parameters. The comparison of estimation methods provided here can increase the accuracy of model predictions, with important implications in understanding and predicting the effects of temperature on the dynamics of populations.

Modeling habitat split: landscape and life history traits determine amphibian extinction thresholds

Habitat split is a major force behind the worldwide decline of amphibian populations, causing community change in richness and species composition. In fragmented landscapes, natural remnants, the terrestrial habitat of the adults, are frequently separated from streams, the aquatic habitat of the larvae. An important question is how this landscape configuration affects population levels and if it can drive species to extinction locally. Here, we put forward the first theoretical model on habitat split which is particularly concerned on how split distance - the distance between the two required habitats - affects population size and persistence in isolated fragments. Our diffusive model shows that habitat split alone is able to generate extinction thresholds. Fragments occurring between the aquatic habitat and a given critical split distance are expected to hold viable populations, while fragments located farther away are expected to be unoccupied. Species with higher reproductive success and higher diffusion rate of post-metamorphic youngs are expected to have farther critical split distances. Furthermore, the model indicates that negative effects of habitat split are poorly compensated by positive effects of fragment size. The habitat split model improves our understanding about spatially structured populations and has relevant implications for landscape design for conservation. It puts on a firm theoretical basis the relation between habitat split and the decline of amphibian populations.

Predicting population dynamics from the properties of individuals: a cross-level test of dynamic energy budget theory

Individual-based models (IBMs) are increasingly used to link the dynamics of individuals to higher levels of biological organization. Still, many IBMs are data hungry, species specific, and time-consuming to develop and analyze. Many of these issues would be resolved by using general theories of individual dynamics as the basis for IBMs. While such theories have frequently been examined at the individual level, few cross-level tests exist that also try to predict population dynamics. Here we performed a cross-level test of dynamic energy budget (DEB) theory by parameterizing an individual-based model using individual-level data of the water flea, Daphnia magna, and comparing the emerging population dynamics to independent data from population experiments. We found that DEB theory successfully predicted population growth rates and peak densities but failed to capture the decline phase. Further assumptions on food-dependent mortality of juveniles were needed to capture the population dynamics after the initial population peak. The resulting model then predicted, without further calibration, characteristic switches between small- and large-amplitude cycles, which have been observed for Daphnia. We conclude that cross-level tests help detect gaps in current individual-level theories and ultimately will lead to theory development and the establishment of a generic basis for individual-based models and ecology.