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

Temperature dependence of competitive ability is cold-shifted compared to that of growth rate in marine phytoplankton

The effect of climate warming on community composition is expected to be contingent on competitive outcomes, yet approaches to projecting ecological outcomes often rely on measures of density-independent performance across temperatures. Recent theory suggests that the temperature response of competitive ability differs in shape from that of population growth rate. Here, we test this hypothesis empirically and find thermal performance curves of competitive ability in aquatic microorganisms to be systematically left-shifted and flatter compared to those of exponential growth rate. The minimum resource requirement for growth, R*-an inverse indicator of competitive ability-changes with temperature following a U-shaped pattern in all four species tested, contrasting from their left-skewed density-independent growth rate thermal performance curves. Our results provide new evidence that exploitative competitive success is highest at temperatures that are sub-optimal for growth, suggesting performance estimates of density-independent variables might underpredict performance in cooler competitive environments.

The Stochastic Nature of Functional Responses

Functional responses are non-linear functions commonly used to describe the variation in the rate of consumption of resources by a consumer. They have been widely used in both theoretical and empirical studies, but a comprehensive understanding of their parameters at different levels of description remains elusive. Here, by depicting consumers and resources as stochastic systems of interacting particles, we present a minimal set of reactions for consumer resource dynamics. We rigorously derived the corresponding system of ODEs, from which we obtained via asymptotic expansions classical 2D consumer-resource dynamics, characterized by different functional responses. We also derived functional responses by focusing on the subset of reactions describing only the feeding process. This involves fixing the total number of consumers and resources, which we call chemostatic conditions. By comparing these two ways of deriving functional responses, we showed that classical functional response parameters in effective 2D consumer-resource dynamics differ from the same parameters obtained by measuring (or deriving) functional responses for typical feeding experiments under chemostatic conditions, which points to potential errors in interpreting empirical data. We finally discuss possible generalizations of our models to systems with multiple consumers and more complex population structures, including spatial dynamics. Our stochastic approach builds on fundamental ecological processes and has natural connections to basic ecological theory.

Global Dynamics of a Reaction-Diffusion Model of Zika Virus Transmission with Seasonality

In this paper, we propose a periodic reaction-diffusion model of Zika virus with seasonal and spatial heterogeneous structure in host and vector population. We introduce the basic reproduction ratio [Formula: see text] for this model and show that the disease-free periodic solution is globally asymptotically stable if [Formula: see text], while the system admits a globally asymptotically stable positive periodic solution if [Formula: see text]. Numerically, we study the Zika transmission in Rio de Janeiro Municipality, Brazil, and investigate the effects of some model parameters on [Formula: see text]. We find that the neglect of seasonality underestimates the value of [Formula: see text] and the maximum carrying capacity affects the spread of Zika virus.

Climate predicts geographic and temporal variation in mosquito-borne disease dynamics on two continents

Climate drives population dynamics through multiple mechanisms, which can lead to seemingly context-dependent effects of climate on natural populations. For climate-sensitive diseases, such as dengue, chikungunya, and Zika, climate appears to have opposing effects in different contexts. Here we show that a model, parameterized with laboratory measured climate-driven mosquito physiology, captures three key epidemic characteristics across ecologically and culturally distinct settings in Ecuador and Kenya: the number, timing, and duration of outbreaks. The model generates a range of disease dynamics consistent with observed Aedes aegypti abundances and laboratory-confirmed arboviral incidence with variable accuracy (28–85% for vectors, 44–88% for incidence). The model predicted vector dynamics better in sites with a smaller proportion of young children in the population, lower mean temperature, and homes with piped water and made of cement. Models with limited calibration that robustly capture climate-virus relationships can help guide intervention efforts and climate change disease projections.

The effects of climate on vector-borne disease systems are highly context-dependent. Here, the authors incorporate laboratory-measured physiological traits of the mosquito Aedes aegypti into climate-driven mechanistic models to predict number, timing, and duration of outbreaks in Ecuador and Kenya.

Temperature alters the shape of predator-prey cycles through effects on underlying mechanisms

Background

Predicting the effects of climate warming on the dynamics of ecological systems requires understanding how temperature influences birth rates, death rates and the strength of species interactions. The temperature dependance of these processes—which are the underlying mechanisms of ecological dynamics—is often thought to be exponential or unimodal, generally supported by short-term experiments. However, ecological dynamics unfold over many generations. Our goal was to empirically document shifts in predator–prey cycles over the full range of temperatures that can possibly support a predator–prey system and then to uncover the effect of temperature on the underlying mechanisms driving those changes.

Methods

We measured the population dynamics of the Didinium-Paramecium predator–prey system across a wide range of temperatures to reveal systematic changes in the dynamics of the system. We then used ordinary differential equation fitting to estimate parameters of a model describing the dynamics, and used these estimates to assess the long-term temperature dependance of all the underlying mechanisms.

Results

We found that predator–prey cycles shrank in state space from colder to hotter temperatures and that both cycle period and amplitude varied with temperature. Model parameters showed mostly unimodal responses to temperature, with one parameter (predator mortality) increasing monotonically with temperature and one parameter (predator conversion efficiency) invariant with temperature. Our results indicate that temperature can have profound, systematic effects on ecological dynamics, and these can arise through diverse and simultaneous changes in multiple underlying mechanisms. Predicting the effects of temperature on ecological dynamics may require additional investigation into how the underlying drivers of population dynamics respond to temperature beyond a short-term, acute response.

Increased Temperature Disrupts the Biodiversity-Ecosystem Functioning Relationship

Gaining knowledge of how ecosystems provide essential services to humans is of primary importance, especially with the current threat of climate change. Yet little is known about how increased temperature will impact the biodiversity-ecosystem functioning (BEF) relationship. We tackled this subject theoretically and experimentally. We developed a BEF theory based on mechanistic population dynamic models, which allows the inclusion of the effect of temperature. Using experimentally established relationships between attack rate and temperature, the model predicts that temperature increase will intensify competition, and consequently the BEF relationship will flatten or even become negative. We conducted a laboratory experiment with natural microbial microcosms, and the results were in agreement with the model predictions. The experimental results also revealed that an increase in both temperature average and variation had a more intense effect than an increase in temperature average alone. Our results indicate that under climate change, high diversity may not guarantee high ecosystem functioning.

Nonlinear averaging of thermal experience predicts population growth rates in a thermally variable environment

As thermal regimes change worldwide, projections of future population and species persistence often require estimates of how population growth rates depend on temperature. These projections rarely account for how temporal variation in temperature can systematically modify growth rates relative to projections based on constant temperatures. Here, we tested the hypothesis that time-averaged population growth rates in fluctuating thermal environments differ from growth rates in constant conditions as a consequence of Jensen's inequality, and that the thermal performance curves (TPCs) describing population growth in fluctuating environments can be predicted quantitatively based on TPCs generated in constant laboratory conditions. With experimental populations of the green alga Tetraselmis tetrahele, we show that nonlinear averaging techniques accurately predicted increased as well as decreased population growth rates in fluctuating thermal regimes relative to constant thermal regimes. We extrapolate from these results to project critical temperatures for population growth and persistence of 89 phytoplankton species in naturally variable thermal environments. These results advance our ability to predict population dynamics in the context of global change.

Seasonal temperature variation influences climate suitability for dengue, chikungunya, and Zika transmission

Dengue, chikungunya, and Zika virus epidemics transmitted by Aedes aegypti mosquitoes have recently (re)emerged and spread throughout the Americas, Southeast Asia, the Pacific Islands, and elsewhere. Understanding how environmental conditions affect epidemic dynamics is critical for predicting and responding to the geographic and seasonal spread of disease. Specifically, we lack a mechanistic understanding of how seasonal variation in temperature affects epidemic magnitude and duration. Here, we develop a dynamic disease transmission model for dengue virus and Aedes aegypti mosquitoes that integrates mechanistic, empirically parameterized, and independently validated mosquito and virus trait thermal responses under seasonally varying temperatures. We examine the influence of seasonal temperature mean, variation, and temperature at the start of the epidemic on disease dynamics. We find that at both constant and seasonally varying temperatures, warmer temperatures at the start of epidemics promote more rapid epidemics due to faster burnout of the susceptible population. By contrast, intermediate temperatures (24–25°C) at epidemic onset produced the largest epidemics in both constant and seasonally varying temperature regimes. When seasonal temperature variation was low, 25–35°C annual average temperatures produced the largest epidemics, but this range shifted to cooler temperatures as seasonal temperature variation increased (analogous to previous results for diurnal temperature variation). Tropical and sub-tropical cities such as Rio de Janeiro, Fortaleza, and Salvador, Brazil; Cali, Cartagena, and Barranquilla, Colombia; Delhi, India; Guangzhou, China; and Manila, Philippines have mean annual temperatures and seasonal temperature ranges that produced the largest epidemics. However, more temperate cities like Shanghai, China had high epidemic suitability because large seasonal variation offset moderate annual average temperatures. By accounting for seasonal variation in temperature, the model provides a baseline for mechanistically understanding environmental suitability for virus transmission by Aedes aegypti. Overlaying the impact of human activities and socioeconomic factors onto this mechanistic temperature-dependent framework is critical for understanding likelihood and magnitude of outbreaks.

Mosquito-borne viruses like dengue, Zika, and chikungunya have recently caused large epidemics that are partly driven by temperature. Using a mathematical model built from laboratory experimental data for Aedes aegypti mosquitoes and dengue virus, we examine the impact of variation in seasonal temperature regimes on epidemic size and duration. At constant temperatures, both low and high temperatures (20°C and 35°C) produce small epidemics, while intermediate temperatures like 25°C and 30°C produce much larger epidemics. In seasonally varying temperature environments, epidemics peak more rapidly at higher starting temperatures, while intermediate starting temperatures produce the largest epidemics. Seasonal mean temperatures of 25–35°C are most suitable for large epidemics when seasonality is low, but in more variable seasonal environments epidemic suitability peaks at lower annual average temperatures. Tropical and sub-tropical cities have the highest temperature suitability for epidemics, but more temperate cities with high seasonal variation also have the potential for very large epidemics.

The effects of demographic stochasticity and parameter uncertainty on predicting the establishment of introduced species

Invasive species are a serious threat to biodiversity worldwide and predicting whether an introduced species will first establish and then become invasive can be useful to preserve ecosystem services. Establishment is influenced by multiple factors, such as the interactions between the introduced individuals and the resident community, and demographic and environmental stochasticity. Field observations are often incomplete or biased. This, together with an imperfect knowledge of the ecological traits of the introduced species, makes the prediction of establishment challenging. Methods that consider the combined effects of these factors on our ability to predict the establishment of an introduced species are currently lacking. We develop an inference framework to assess the combined effects of demographic stochasticity and parameter uncertainty on our ability to predict the probability of establishment following the introduction of a small number of individuals. We find that even moderate levels of demographic stochasticity influence both the probability of establishment, and, crucially, our ability to correctly predict that probability. We also find that estimation of the demographic parameters of an introduced species is fundamental to obtain precise estimates of the interaction parameters. For typical values of demographic stochasticity, the drop in our ability to predict an establishment can be 30% when having priors on the demographic parameters compared to having their accurate values. The results from our study illustrate how demographic stochasticity may bias the prediction of the probability of establishment. Our method can be applied to estimate probability of establishment of introduced species in field scenarios, where time series data and prior information on the demographic traits of the introduced species are available.