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Estimating parameters from multiple time series of population dynamics using bayesian inference
(2019)
Empirical time series of interacting entities, e.g., species abundances, are highly useful to study ecological mechanisms. Mathematical models are valuable tools to further elucidate those mechanisms and underlying processes. However, obtaining an agreement between model predictions and experimental observations remains a demanding task. As models always abstract from reality one parameter often summarizes several properties. Parameter measurements are performed in additional experiments independent of the ones delivering the time series. Transferring these parameter values to different settings may result in incorrect parametrizations. On top of that, the properties of organisms and thus the respective parameter values may vary considerably. These issues limit the use of a priori model parametrizations. In this study, we present a method suited for a direct estimation of model parameters and their variability from experimental time series data. We combine numerical simulations of a continuous-time dynamical population model with Bayesian inference, using a hierarchical framework that allows for variability of individual parameters. The method is applied to a comprehensive set of time series from a laboratory predator-prey system that features both steady states and cyclic population dynamics. Our model predictions are able to reproduce both steady states and cyclic dynamics of the data. Additionally to the direct estimates of the parameter values, the Bayesian approach also provides their uncertainties. We found that fitting cyclic population dynamics, which contain more information on the process rates than steady states, yields more precise parameter estimates. We detected significant variability among parameters of different time series and identified the variation in the maximum growth rate of the prey as a source for the transition from steady states to cyclic dynamics. By lending more flexibility to the model, our approach facilitates parametrizations and shows more easily which patterns in time series can be explained also by simple models. Applying Bayesian inference and dynamical population models in conjunction may help to quantify the profound variability in organismal properties in nature.
Advances in nanotechnology lead to an increasing interest in how nanoparticles interact with biomembranes. Nanoparticles are wrapped spontaneously by biomembranes if the adhesive interactions between the particles and membranes compensate for the cost of membrane bending. In the last years, the cooperative wrapping of spherical nanoparticles in membrane tubules has been observed in experiments and simulations. For spherical nanoparticles, the stability of the particle-filled membrane tubules strongly depends on the range of the adhesive particle-membrane interactions. In this article, it is shown via modeling and energy minimization that elongated and patchy particles are wrapped cooperatively in membrane tubules that are highly stable for all ranges of the particle-membrane interactions, compared to individual wrapping of the particles. The cooperative wrapping of linear chains of elongated or patchy particles in membrane tubules may thus provide an efficient route to induce membrane tubulation, or to store such particles in membranes.
Global change threatens the maintenance of ecosystem functions that are shaped by the persistence and dynamics of populations. It has been shown that the persistence of species increases if they possess larger trait adaptability. Here, we investigate whether trait adaptability also affects the robustness of population dynamics of interacting species and thereby shapes the reliability of ecosystem functions that are driven by these dynamics. We model co‐adaptation in a predator–prey system as changes to predator offense and prey defense due to evolution or phenotypic plasticity. We investigate how trait adaptation affects the robustness of population dynamics against press perturbations to environmental parameters and against pulse perturbations targeting species abundances and their trait values. Robustness of population dynamics is characterized by resilience, elasticity, and resistance. In addition to employing established measures for resilience and elasticity against pulse perturbations (extinction probability and return time), we propose the warping distance as a new measure for resistance against press perturbations, which compares the shapes and amplitudes of pre‐ and post‐perturbation population dynamics. As expected, we find that the robustness of population dynamics depends on the speed of adaptation, but in nontrivial ways. Elasticity increases with speed of adaptation as the system returns more rapidly to the pre‐perturbation state. Resilience, in turn, is enhanced by intermediate speeds of adaptation, as here trait adaptation dampens biomass oscillations. The resistance of population dynamics strongly depends on the target of the press perturbation, preventing a simple relationship with the adaptation speed. In general, we find that low robustness often coincides with high amplitudes of population dynamics. Hence, amplitudes may indicate the robustness against perturbations also in other natural systems with similar dynamics. Our findings show that besides counteracting extinctions, trait adaptation indeed strongly affects the robustness of population dynamics against press and pulse perturbations.
The mineral and biochemical food quality of prey may limit predator production. This well-studied direct bottom-up effect is especially prominent for herbivore-plant interactions. Low-quality prey species, particularly when defended, are generally considered to be less prone to predator-driven extinction. Undefended high-quality prey species sustain high predator production thereby potentially increasing their own extinction risk. The food quality of primary producers is highly species-specific. In communities of competing prey species, predators thus may supplement their diets of low-quality prey with high-quality prey, leading to indirect horizontal interactions between prey species of different food quality. We explore how these predator-mediated indirect interactions affect species coexistence in a general predator-prey model that is parametrized for an experimental algae-rotifer system. To cover a broad range of three essential functional traits that shape many plant-herbivore interactions we consider differences in 1) the food quality of the prey species, 2) their competitive ability for nutrient uptake and 3) their defence against predation. As expected, low food quality of prey can, similarly to defence, provide protection against extinction by predation. Counterintuitively, our simulations demonstrate that being of high food quality also prevents extinction of that prey species and additionally promotes coexistence with a competing, low-quality prey. The persistence of the high-quality prey enables a high conversion efficiency and control of the low-quality prey by the predator and allows for re-allocation of nutrients to the high-quality competitor. Our results show that high food quality is not necessarily detrimental for a prey species but instead can protect against extinction and promote species richness and functional biodiversity.
Swimming is of vital importance for aquatic organisms because it determines several aspects of fitness, such as encounter rates with food, predators, and mates. Generally, rotifer swimming speed is measured by manual tracking of the swimming paths filmed in videos. Recently, an open-source package has been developed that integrates different open-source software and allows direct processing and analysis of the swimming paths of moving organisms. Here, we filmed groups of females and males of Keratella cochlearis separately and in a mixed experimental setup. We extracted movement trajectories and swimming speeds and applied the classification method random forest to assign sex to individuals of the mixed setup. Finally, we used advanced statistical methods of movement ecology, namely a hidden Markov model, to investigate swimming states of females and males. When not discriminating swimming states, females swam faster than males, while when discriminating states males swam faster. Specifically, females and males showed two main states of movement with many individuals switching between states resulting in four modes of swimming. We suggest that switching between states is related to predator avoidance. Males of K. cochlearis especially exhibited switching between turning in a restricted area and swimming over longer distances. No mating or other male-female interactions were observed. Our study elucidates the steps necessary for automatic analysis of rotifer trajectories with open-source software. Application of sophisticated software and analytical models will broaden our understanding of zooplankton ecology from the individual to the population level.
Theory predicts that resource variability hinders consumer performance. How this effect depends on the temporal structure of resource fluctuations encountered by individuals remains poorly understood. Combining modelling and growth experiments with Daphnia magna, we decompose the complexity of resource fluctuations and test the effect of resource variance, supply peak timing (i.e. phase) and co-limiting resource covariance along a gradient from high to low frequencies reflecting fine- to coarse-grained environments. Our results show that resource storage can buffer growth at high frequencies, but yields a sensitivity of growth to resource peak timing at lower ones. When two resources covary, negative covariance causes stronger growth depression at low frequencies. However, negative covariance might be beneficial at intermediate frequencies, an effect that can be explained by digestive acclimation. Our study provides a mechanistic basis for understanding how alterations of the environmental grain size affect consumers experiencing variable nutritional quality in nature.