Unravelling the dynamics of organisms in a changing world using ecological modelling

Understanding and predicting the dynamics of organisms is a central objective in ecology and conservation biology, and modelling provides a solution to tackling this problem. However, the complex nature of ecological systems means that for a thorough understanding of ecological dynamics at hierarchical scales, a set of modeling approaches need to be adopted. This review illustrates how modelling approaches can be used to understand the dynamics of organisms in applied ecological problems, focussing on mechanistic models at a local scale and statistical models at a broad scale. Mechanistic models incorporate ecological processes explicitly and thus are likely to be robust under novel conditions. Models based on behavioural decisions by individuals represent a typical example of the successful application of mechanistic models to applied problems. Considering the data-hungry nature of such mechanistic models, model complexity and parameterisation need to be explored further for a quick and widespread implementation of this model type. For broad-scale phenomena, statistical models play an important role in dealing with problems that are often inherent in data. Examples include models for quantifying population trends from long-term, large-scale data and those for comparative methods of extinction risk. Novel statistical approaches also allow mechanistic models to be parameterised using readily obtained data at a macro scale. In conclusion, the complementary use and improvement of multiple model types, the increased use of novel model parameterisation, the examination of model transferability and the achievement of wider biodiversity information availability are key challenges for the effective use of modelling in applied ecological problems.     

Bayesian inference in ecology

Bayesian inference is an important statistical tool that is increasingly being used by ecologists. In a Bayesian analysis, information available before a study is conducted is summarized in a quantitative model or hypothesis: the prior probability distribution. Bayes’ Theorem uses the prior probability distribution and the likelihood of the data to generate a posterior probability distribution. Posterior probability distributions are an epistemological alternative to P‐values and provide a direct measure of the degree of belief that can be placed on models, hypotheses, or parameter estimates. Moreover, Bayesian information‐theoretic methods provide robust measures of the probability of alternative models, and multiple models can be averaged into a single model that reflects uncertainty in model construction and selection. These methods are demonstrated through a simple worked example. Ecologists are using Bayesian inference in studies that range from predicting single‐species population dynamics to understanding ecosystem processes. Not all ecologists, however, appreciate the philosophical underpinnings of Bayesian inference. In particular, Bayesians and frequentists differ in their definition of probability and in their treatment of model parameters as random variables or estimates of true values. These assumptions must be addressed explicitly before deciding whether or not to use Bayesian methods to analyse ecological data.     

Assessing variation in life‐history tactics within a population using mixture regression models: a practical guide for evolutionary ecologists

Mixed models are now well‐established methods in ecology and evolution because they allow accounting for and quantifying within‐ and between‐individual variation. However, the required normal distribution of the random effects can often be violated by the presence of clusters among subjects, which leads to multi‐modal distributions. In such cases, using what is known as mixture regression models might offer a more appropriate approach. These models are widely used in psychology, sociology, and medicine to describe the diversity of trajectories occurring within a population over time (e.g. psychological development, growth). In ecology and evolution, however, these models are seldom used even though understanding changes in individual trajectories is an active area of research in life‐history studies. Our aim is to demonstrate the value of using mixture models to describe variation in individual life‐history tactics within a population, and hence to promote the use of these models by ecologists and evolutionary ecologists. We first ran a set of simulations to determine whether and when a mixture model allows teasing apart latent clustering, and to contrast the precision and accuracy of estimates obtained from mixture models versus mixed models under a wide range of ecological contexts. We then used empirical data from long‐term studies of large mammals to illustrate the potential of using mixture models for assessing within‐population variation in life‐history tactics. Mixture models performed well in most cases, except for variables following a Bernoulli distribution and when sample size was small. The four selection criteria we evaluated [Akaike information criterion (AIC), Bayesian information criterion (BIC), and two bootstrap methods] performed similarly well, selecting the right number of clusters in most ecological situations. We then showed that the normality of random effects implicitly assumed by evolutionary ecologists when using mixed models was often violated in life‐history data. Mixed models were quite robust to this violation in the sense that fixed effects were unbiased at the population level. However, fixed effects at the cluster level and random effects were better estimated using mixture models. Our empirical analyses demonstrated that using mixture models facilitates the identification of the diversity of growth and reproductive tactics occurring within a population. Therefore, using this modelling framework allows testing for the presence of clusters and, when clusters occur, provides reliable estimates of fixed and random effects for each cluster of the population. In the presence or expectation of clusters, using mixture models offers a suitable extension of mixed models, particularly when evolutionary ecologists aim at identifying how ecological and evolutionary processes change within a population. Mixture regression models therefore provide a valuable addition to the statistical toolbox of evolutionary ecologists. As these models are complex and have their own limitations, we provide recommendations to guide future users.     

A parsimonious view of the parsimony principle in ecology and evolution

The idea that simplicity of explanation is important in science is as old as science itself. However, scientists often assume that parsimonious theories, hypothesis and models are more plausible than complex ones, forgetting that there is no empirical evidence to connect parsimony with credibility. The justification for the parsimony principle is strongly dependent on philosophical and statistical inference. Parsimony may have a true epistemic value in the evaluation of correlative and predictive models, as simpler models are less prone to overfitting. However, when natural mechanisms are explicitly modelled to represent the causes of biological phenomena, the application of the parsimony principle to judge the plausibility of mechanistic models would entail an unsupported belief that nature is simple. Here, we discuss the challenges we face in justifying, measuring, and assessing the trade‐off between simplicity and complexity in ecological and evolutionary studies. We conclude that invoking the parsimony principle in ecology and evolution is particularly important in model‐building programs in which models are viewed primarily as an operational tool to make predictions (an instrumentalist view) and in which data play a prominent role in deciding the structure of the model. However, theoretical advances in ecology and evolutionary biology may be derailed by the use of the parsimony principle to judge explanatory mechanistic models that are designed to understand complex natural phenomena. We advocate a parsimonious use of the parsimony principle.     

Inference for nonlinear epidemiological models using genealogies and time series

Phylodynamics - the field aiming to quantitatively integrate the ecological and evolutionary dynamics of rapidly evolving populations like those of RNA viruses - increasingly relies upon coalescent approaches to infer past population dynamics from reconstructed genealogies. As sequence data have become more abundant, these approaches are beginning to be used on populations undergoing rapid and rather complex dynamics. In such cases, the simple demographic models that current phylodynamic methods employ can be limiting. First, these models are not ideal for yielding biological insight into the processes that drive the dynamics of the populations of interest. Second, these models differ in form from mechanistic and often stochastic population dynamic models that are currently widely used when fitting models to time series data. As such, their use does not allow for both genealogical data and time series data to be considered in tandem when conducting inference. Here, we present a flexible statistical framework for phylodynamic inference that goes beyond these current limitations. The framework we present employs a recently developed method known as particle MCMC to fit stochastic, nonlinear mechanistic models for complex population dynamics to gene genealogies and time series data in a Bayesian framework. We demonstrate our approach using a nonlinear Susceptible-Infected-Recovered (SIR) model for the transmission dynamics of an infectious disease and show through simulations that it provides accurate estimates of past disease dynamics and key epidemiological parameters from genealogies with or without accompanying time series data.     

Environmental proteomics, biodiversity statistics and food-web structure

Pioneering studies in environmental proteomics have revealed links between protein diversity and ecological function in simple ecological communities, such as microbial biofilms. In the near future, high-throughput proteomic methods will be applied to more complex ecological systems in which microbes and macrobes interact. Data structures in biodiversity and protein surveys have many similarities, so the statistical methods that ecologists use for analyzing biodiversity data should be adapted for use with quantitative surveys of protein diversity. However, increasing quantities of protein and bioinformatics data will not, by themselves, reveal the functional significance of proteins. Instead, ecologists should be measuring changes in the abundance of protein cohorts in response to replicated field manipulations, including nutrient enrichment and removal of top predators.     

Integrating modelling of biodiversity composition and ecosystem function

There is increasing reliance on ecological models to improve our understanding of how ecological systems work, to project likely outcomes under alternative global change scenarios and to help develop robust management strategies. Two common types of spatiotemporally explicit ecological models are those focussed on biodiversity composition and those focussed on ecosystem function. These modelling disciplines are largely practiced separately, with separate literature, despite growing evidence that natural systems are shaped by the interaction of composition and function. Here we call for the development of new modelling approaches that integrate composition and function, accounting for the important interactions between these two dimensions, particularly under rapid global change. We examine existing modelling approaches that have begun to combine elements of composition and function, identifying their potential contribution to fully integrated modelling approaches. The development and application of integrated models of composition and function face a number of important challenges, including biological data limitations, system knowledge and computational constraints. We suggest a range of promising avenues that could help researchers overcome these challenges, including the use of virtual species, macroecological relationships and hybrid correlative‐mechanistic modelling. Explicitly accounting for the interactions between composition and function within integrated modelling approaches has the potential to improve our understanding of ecological systems, provide more accurate predictions of their future states and transform their management. Synthesis There is increasing attention from researchers and policy makers around the world on both assessing and projecting the state of the planet's biodiversity, its ecosystems and the essential services they provide to society. However, existing modelling approaches largely ignore the interactions between biodiversity composition and ecosystem function. We highlight the key challenges and potential solutions to developing integrated models of composition and function. Such models will require a new effort and focus from ecologists, yet the benefits are likely to be substantial, including better informing the management of natural systems at regional, national and international scales.     

Research frontiers in null model analysis

Null models are pattern‐generating models that deliberately exclude a mechanism of interest, and allow for randomization tests of ecological and biogeographic data. Although they have had a controversial history, null models are widely used as statistical tools by ecologists and biogeographers. Three active research fronts in null model analysis include biodiversity measures, species co‐occurrence patterns, and macroecology. In the analysis of biodiversity, ecologists have used random sampling procedures such as rarefaction to adjust for differences in abundance and sampling effort. In the analysis of species co‐occurrence and assembly rules, null models have been used to detect the signature of species interactions. However, controversy persists over the details of computer algorithms used for randomizing presence–absence matrices. Finally, in the newly emerging discipline of macroecology, null models can be used to identify constraining boundaries in bivariate scatterplots of variables such as body size, range size, and population density. Null models provide specificity and flexibility in data analysis that is often not possible with conventional statistical tests.     

When mechanism matters: Bayesian forecasting using models of ecological diffusion

Ecological diffusion is a theory that can be used to understand and forecast spatio‐temporal processes such as dispersal, invasion, and the spread of disease. Hierarchical Bayesian modelling provides a framework to make statistical inference and probabilistic forecasts, using mechanistic ecological models. To illustrate, we show how hierarchical Bayesian models of ecological diffusion can be implemented for large data sets that are distributed densely across space and time. The hierarchical Bayesian approach is used to understand and forecast the growth and geographic spread in the prevalence of chronic wasting disease in white‐tailed deer (Odocoileus virginianus). We compare statistical inference and forecasts from our hierarchical Bayesian model to phenomenological regression‐based methods that are commonly used to analyse spatial occurrence data. The mechanistic statistical model based on ecological diffusion led to important ecological insights, obviated a commonly ignored type of collinearity, and was the most accurate method for forecasting.     

Application of wavelet analysis to ecological data

Ecological data are difficult to analyze due to complexity residing in the ecological systems with the variables varying in non-linear fashion. Efficient methods are required to properly extract information out of the complex data. Wavelets have good time–frequency (time-scale) localization, can represent data parsimoniously, and can be implemented with very fast algorithms. Brief backgrounds and computational aspects of wavelets were outlined for implementation to ecological data analysis. Wavelets are well suited for building mathematical models of ecological data and the statistical analysis of combined effects of complex factors in ecological network. Wavelet based analysis and synthesis may lead researchers in ecological studies to new insights and novel theories for understanding complex ecological and environmental phenomena.     

Chromatographic parameter determination for complex biological feedstocks

The application of mechanistic models for chromatography requires accurate model parameters. Especially for complex feedstocks such as a clarified cell harvest, this can still be an obstacle limiting the use of mechanistic models. Another commonly encountered obstacle is a limited amount of sample material and time to determine all needed parameters. Therefore, this study aimed at implementing an approach on a robotic liquid handling system that starts directly with a complex feedstock containing a monoclonal antibody. The approach was tested by comparing independent experimental data sets with predictions generated by the mechanistic model using all parameters determined in this study. An excellent agreement between prediction and experimental data was found verifying the approach. Thus, it can be concluded that RoboColumns with a bed volume of 200 μL can well be used to determine isotherm parameters for predictions of larger scale columns. Overall, this approach offers a new way to determine crucial model input parameters for mechanistic modelling of chromatography for complex biological feedstocks. © 2018 The Authors Biotechnology Progress published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers Biotechnol. Prog., 34:1006–1018, 2018     

Machine learning methods without tears: a primer for ecologists

Machine learning methods, a family of statistical techniques with origins in the field of artificial intelligence, are recognized as holding great promise for the advancement of understanding and prediction about ecological phenomena. These modeling techniques are flexible enough to handle complex problems with multiple interacting elements and typically outcompete traditional approaches (e.g., generalized linear models), making them ideal for modeling ecological systems. Despite their inherent advantages, a review of the literature reveals only a modest use of these approaches in ecology as compared to other disciplines. One potential explanation for this lack of interest is that machine learning techniques do not fall neatly into the class of statistical modeling approaches with which most ecologists are familiar. In this paper, we provide an introduction to three machine learning approaches that can be broadly used by ecologists: classification and regression trees, artificial neural networks, and evolutionary computation. For each approach, we provide a brief background to the methodology, give examples of its application in ecology, describe model development and implementation, discuss strengths and weaknesses, explore the availability of statistical software, and provide an illustrative example. Although the ecological application of machine learning approaches has increased, there remains considerable skepticism with respect to the role of these techniques in ecology. Our review encourages a greater understanding of machin learning approaches and promotes their future application and utilization, while also providing a basis from which ecologists can make informed decisions about whether to select or avoid these approaches in their future modeling endeavors.     

Ngongas and ecology: on having a worldview

Ngongas provide a metaphor for some of the opportunities and challenges facing the science of ecology and evolution. Ngongas, the traditional healers of the Shona culture, Zimbabwe, fail in the delivery of quality health by today's standards. Their outdated worldview makes most health related issues seem more complicated and more multi-factorial than when viewed through the worldviews of modern medicine. With the wrong worldview, one can work very hard, be very bright and dedicated, and still be ineffective. With the right worldview, one can work much less hard and still be extremely effective. As ecologists, we should be opinionated and possess clearly articulated worldviews for filtering and interpreting information. As ecologists we are also a bit like ngongas – we often fail to provide answers for society's ecological questions and problems, and we excuse ourselves with a belief that ecological systems are too complex and have too many factors. Unlike ngongas, this invites us to pay a lot of attention to promoting and assessing competing worldviews. We should be open-minded to the anomalies in our worldview and the successes of alternative viewpoints. As an admitted ecological ngonga, I discuss the worldview I use in my own research: the Optimization Research Program, a Darwinian research program that uses game theory to conceptualize and understand ecological systems. I use it illustrate how worldviews can synthesize disparate ideas. (I use kin selection and reciprocal altruism as examples.) I use it to show how new ideas and predictions can be generated. (I use root competition in plants and the possibility that increased crop yield may be forthcoming from knowledge of this game.)     

On the role of spatial stochastic models in understanding landscape indices in ecology

Spatial stochastic models play an important role in understanding and predicting the behaviour of complex systems. Such models may be implemented with explicit knowledge of only a limited number of parameters relating to spatial relationships among locations. Consequently, they are often used instead of deterministic‐mechanistic models, which may potentially require an unrealistically large number of parameters. Currently, in contrast to spatial stochastic models, the parameterization of the joint spatial distribution of objects in landscape models is more often implicit than explicit. Here, we investigate the similarities and differences between bona fide spatial stochastic models and landscape models by focusing mostly on the relationships between processes, their realizations (patterns), representation and measurement, and their use in exploratory as well as confirmatory data analysis. One of the most important outcomes of recognizing the importance of stochastic processes is the acknowledgement that the spatial pattern observed in a landscape is only one realization of that process. Hence, while ecologists have been using landscape pattern indices (LPIs) to characterize landscape heterogeneity and/or make inferences about processes shaping the landscape, no stochastic modelling framework has been developed for their proper statistical elucidation. Consequently, several (mis)uses of LPIs draw conclusions about landscapes which are suspect. We show that several reports about sensitivities of LPIs to measurements have common roots that can be made explicitly manageable by adopting stochastic models of spatial structure. The key parameters of these stochastic models are composition and configuration, which, in general, cannot be estimated independently from each other. We outline how to develop the stochastic framework to interpret observations and make some recommendations to practitioners about everyday usage. The conceptual linkages between patterns and processes are particularly important in light of recent efforts to bridge the static‐structural and the dynamic‐analytic traditions of ecology.     

Climate change,phenological shifts,eco-evolutionary responses and population viability: toward a unifying predictive approach

The debate on emission targets of greenhouse gasses designed to limit global climate change has to take into account the ecological consequences. One of the clearest ecological consequences is shifts in phenology. Linking these shifts to changes in population viability under various greenhouse gasses emission scenarios requires a unifying framework. We propose a box-in-a-box modeling approach that couples population models to phenological change. This approach unifies population modeling with both ecological responses to climate change as well as evolutionary processes. We advocate a mechanistic embedded correlative approach, where the link from genes to population is established using a periodic matrix population model. This periodic model has several major advantages: (1) it can include complex seasonal behaviors allowing an easy link with phenological shifts; (2) it provides the structure of the population at each phase, including the distribution of genotypes and phenotypes, allowing a link with evolutionary processes; and (3) it can incorporate the effect of climate at different time periods. We believe that the way climatologists have approached the problem, using atmosphere–ocean coupled circulation models in which components are gradually included and linked to each other, can provide a valuable example to ecologists. We hope that ecologists will take up this challenge and that our preliminary modeling framework will stimulate research toward a unifying predictive model of the ecological consequences of climate change.     

The neglected tool in the Bayesian ecologist's shed: a case study testing informative priors' effect on model accuracy

Despite benefits for precision, ecologists rarely use informative priors. One reason that ecologists may prefer vague priors is the perception that informative priors reduce accuracy. To date, no ecological study has empirically evaluated data‐derived informative priors' effects on precision and accuracy. To determine the impacts of priors, we evaluated mortality models for tree species using data from a forest dynamics plot in Thailand. Half the models used vague priors, and the remaining half had informative priors. We found precision was greater when using informative priors, but effects on accuracy were more variable. In some cases, prior information improved accuracy, while in others, it was reduced. On average, models with informative priors were no more or less accurate than models without. Our analyses provide a detailed case study on the simultaneous effect of prior information on precision and accuracy and demonstrate that when priors are specified appropriately, they lead to greater precision without systematically reducing model accuracy.     

Ecologists should not use statistical significance tests to interpret simulation model results

Simulation models are widely used to represent the dynamics of ecological systems. A common question with such models is how changes to a parameter value or functional form in the model alter the results. Some authors have chosen to answer that question using frequentist statistical hypothesis tests (e.g. ANOVA). This is inappropriate for two reasons. First, p‐values are determined by statistical power (i.e. replication), which can be arbitrarily high in a simulation context, producing minuscule p‐values regardless of the effect size. Second, the null hypothesis of no difference between treatments (e.g. parameter values) is known a priori to be false, invalidating the premise of the test. Use of p‐values is troublesome (rather than simply irrelevant) because small p‐values lend a false sense of importance to observed differences. We argue that modelers should abandon this practice and focus on evaluating the magnitude of differences between simulations. Synthesis Researchers analyzing field or lab data often test ecological hypotheses using frequentist statistics (t‐tests, ANOVA, etc.) that focus on p‐values. Field and lab data usually have limited sample sizes, and p‐values are valuable for quantifying the probability of making incorrect inferences in that situation. However, modern ecologists increasingly rely on simulation models to address complex questions, and those who were trained in frequentist statistics often apply the hypothesis‐testing approach inappropriately to their simulation results. Our paper explains why p‐values are not informative for interpreting simulation models, and suggests better ways to evaluate the ecological significance of model results.     

Assessing temporal scales and patterns in time series: Comparing methods based on redundancy analysis

Time-series modelling techniques are powerful tools for studying temporal scaling structures and dynamics present in ecological and other complex systems and are gaining popularity for assessing resilience quantitatively. Among other methods, canonical ordinations based on redundancy analysis are increasingly used for determining temporal scaling patterns that are inherent in ecological data. However, modelling outcomes and thus inference about ecological dynamics and resilience may vary depending on the approaches used. In this study, we compare the statistical performance, logical consistency and information content of two approaches: (i) asymmetric eigenvector maps (AEM) that account for linear trends and (ii) symmetric distance-based Moran's eigenvector maps (MEM), which requires detrending of raw data to remove linear trends prior to analysis. Our comparison is done using long-term water quality data (25 years) from three Swedish lakes. This data set therefore provides the opportunity for assessing how the modelling approach used affects performance and inference in time series modelling. We found that AEM models had consistently more explanatory power than MEM, and in two out of three lakes AEM extracted one more temporal scale than MEM. The scale-specific patterns detected by AEM and MEM were uncorrelated. Also individual water quality variables explaining these patterns differed between methods, suggesting that inferences about systems dynamics are dependent on modelling approach. These findings suggest that AEM might be more suitable for assessing dynamics in time series analysis compared to MEM when temporal trends are relevant. The AEM approach is logically consistent with temporal autocorrelation where earlier conditions can influence later conditions but not vice versa. The symmetric MEM approach, which ignores the asymmetric nature of time, might be suitable for addressing specific questions about the importance of correlations in fluctuation patterns where there are no confounding elements of linear trends or a need to assess causality.     

Assessing the impact of climate variation on survival in vertebrate populations

Abstract The impact of the ongoing rapid climate change on natural systems is a major issue for human societies. An important challenge for ecologists is to identify the climatic factors that drive temporal variation in demographic parameters, and, ultimately, the dynamics of natural populations. The analysis of long-term monitoring data at the individual scale is often the only available approach to estimate reliably demographic parameters of vertebrate populations. We review statistical procedures used in these analyses to study links between climatic factors and survival variation in vertebrate populations. We evaluated the efficiency of various statistical procedures from an analysis of survival in a population of white stork, Ciconia ciconia, a simulation study and a critical review of 78 papers published in the ecological literature. We identified six potential methodological problems: (i) the use of statistical models that are not well-suited to the analysis of long-term monitoring data collected at the individual scale; (ii) low ratios of number of statistical units to number of candidate climatic covariates; (iii) collinearity among candidate climatic covariates; (iv) the use of statistics, to assess statistical support for climatic covariates effects, that deal poorly with unexplained variation in survival; (v) spurious detection of effects due to the co-occurrence of trends in survival and the climatic covariate time series; and (vi) assessment of the magnitude of climatic effects on survival using measures that cannot be compared across case studies. The critical review of the ecological literature revealed that five of these six methodological problems were often poorly tackled. As a consequence we concluded that many of these studies generated hypotheses but only few provided solid evidence for impacts of climatic factors on survival or reliable measures of the magnitude of such impacts. We provide practical advice to solve efficiently most of the methodological problems identified. The only frequent issue that still lacks a straightforward solution was the low ratio of the number of statistical units to the number of candidate climatic covariates. In the perspective of increasing this ratio and therefore of producing more robust analyses of the links between climate and demography, we suggest leads to improve the procedures for designing field protocols and selecting a set of candidate climatic covariates. Finally, we present recent statistical methods with potential interest for assessing the impact of climatic factors on demographic parameters.