A pathway for multivariate analysis of ecological communities using copulas

Asymmetric relationships and their effects on coexistence

Species coexistence attracts wide interest in ecology. Modern coexistence theory (MCT) identifies coexistence mechanisms, one of which, storage effects, hinges on relationships between fluctuations in environmental and competitive pressures. However, such relationships are typically measured using covariance, which does not account for the possibility that environment and competition may be more related to each other when they are strong than when weak, or vice versa. Recent work showed that such 'asymmetric tail associations' (ATAs) are common between ecological variables, and are important for extinction risk, ecosystem stability, and other phenomena. We extend MCT, decomposing storage effects to show the influence of ATAs. Analysis of a simple model and an empirical example using diatoms illustrate that ATA influences can be comparable in magnitude to other mechanisms of coexistence and that ATAs can make the difference between species coexistence and competitive exclusion. ATA influences may be an important new mechanism of coexistence.

Exploring the Frequency and Distribution of Ecological Non-monotonicity in Associations among Ecosystem Constituents

Complex links between biotic and abiotic constituents are fundamental for the functioning of ecosystems. Although non-monotonic interactions and associations are known to increase the stability, diversity, and productivity of ecosystems, they are frequently ignored by community-level standard statistical approaches. Using the copula-based dependence measure qad, capable of quantifying the directed and asymmetric dependence between variables for all forms of (functional) relationships, we determined the proportion of non-monotonic associations between different constituents of an ecosystem (plants, bacteria, fungi, and environmental parameters). Here, we show that up to 59% of all statistically significant associations are non-monotonic. Further, we show that pairwise associations between plants, bacteria, fungi, and environmental parameters are specifically characterized by their strength and degree of monotonicity, for example, microbe-microbe associations are on average stronger than and differ in degree of non-monotonicity from plant-microbe associations. Considering directed and non-monotonic associations, we extended the concept of ecosystem coupling providing more complete insights into the internal order of ecosystems. Our results emphasize the importance of ecological non-monotonicity in characterizing and understanding ecosystem patterns and processes.

Supplementary Information

The online version contains supplementary material available at 10.1007/s10021-023-00867-9.

Combining Bayesian Calibration and Copula Models for Age Estimation

Accurately estimating and predicting chronological age from some anthropometric characteristics of an individual without an identity document can be crucial in the context of a growing number of forced migrants. In the related literature, the prediction of chronological age mostly relies upon the use of a single predictor, which is usually represented by a dental/skeletal maturity index, or multiple independent ordinal predictor (stage of maturation). This paper is the first attempt to combine a robust method to predict chronological age, such as Bayesian calibration, and the use of multiple continuous indices as predictors. The combination of these two aspects becomes possible due to the implementation of a complex statistical tool as the copula. Comparing the forecasts from our copula-based method with predictions from an independent model and two single predictor models, we showed that the accuracy increased.

Non-linear models of species' responses to environmental and spatial gradients

Species' responses to broad-scale environmental or spatial gradients are typically unimodal. Current models of species' responses along gradients tend to be overly simplistic (e.g., linear, quadratic or Gaussian GLMs), or are suitably flexible (e.g., splines, GAMs) but lack direct ecologically interpretable parameters. We describe a parametric framework for species-environment non-linear modelling ('senlm'). The framework has two components: (i) a non-linear parametric mathematical function to model the mean species response along a gradient that allows asymmetry, flattening/peakedness or bimodality; and (ii) a statistical error distribution tailored for ecological data types, allowing intrinsic mean-variance relationships and zero-inflation. We demonstrate the utility of this model framework, highlighting the flexibility of a range of possible mean functions and a broad range of potential error distributions, in analyses of fish species' abundances along a depth gradient, and how they change over time and at different latitudes.

A locally relevant framework for assessing the risk of sea level rise under changing temperature conditions: Application in New Caledonia, Pacific Ocean

Sea level rise is a key feature in a warmer world and its impact can be seen globally. Assessing climate change-induced sea level rise, therefore, is urgently needed particularly in small island nations, where the threats of sea level rise are immediate, but the level of preparedness is low. Here, we propose a stochastic simulator to link changes in Mean Annual Temperature (MAT) to Mean Annual Sea Level (MASEL) at the local scale. This is through what-if scenarios that are developed based on the association between local temperature and sea level. The model can provide a basis for a bottom-up impact assessment by addressing limitations of applying large-scale projections in small islands and facilitating the accessibility of the impact assessment to stakeholders. For this purpose, we decompose the MAT and MASEL signals into their linear trend and autocorrelation components as well as independent and identically distributed residual terms. We further explore the association between trend and residual terms of MAT and MASEL. If such dependencies exist, scenarios of sea level can be synthesized based on the trend and residual terms of temperature. We use linear regression to link trends of MAT and MASEL, and copulas to formulate dependencies between residuals. This allows stochastic sampling of MASEL conditioned to trend and random variability in MAT. This framework is used for retrospective and prospective simulations of MASEL in Nouméa, the capital city of New Caledonia, the Pacific. We set up six different model configurations for developing the stochastic sampler, each including various parametric options. By selecting the best setup from each configuration, we provide a multi-model stochastic projection of MASEL, assuming the persistence in current long-term trend in MAT and MASEL. We demonstrate how such simulations can be used for a risk-based impact assessments and discuss sources of uncertainty in future projections.

Data on Gaussian copula modelling of the views of sport club members relating to community sport, Australian sport policy and advocacy

In Australia, community sport plays an essential role in the objectives of national sports organizations and local and national social policy more generally. The opinions of senior community sport club officials (n=53) in rural New South Wales concerning sustainability, policy and advocacy matters impacting upon community sports clubs (CSCs) were identified. Participants were surveyed to establish the level of influence of top-down sport management structures alongside rudimentary views on a coalition to advocate for community sport. Gaussian copula graphical models (GCGMs) were applied to demonstrate the raw and partial correlations between participant responses. While frequently associated with finance, science and medicine, the application of copulas is increasingly common in research in sport where there are multiple variables and relationships involved. GCGMs have been used in, for example, analysis in soccer and across physical education in general.

Trait-based approaches to global change ecology: moving from description to prediction

Trait-based approaches are increasingly recognized as a tool for understanding ecosystem re-assembly and function under intensifying global change. Here we synthesize trait-based research globally (n = 865 studies) to examine the contexts in which traits may be used for global change prediction. We find that exponential growth in the field over the last decade remains dominated by descriptive studies of terrestrial plant morphology, highlighting significant opportunities to expand trait-based thinking across systems and taxa. Very few studies (less than 3%) focus on predicting ecological effects of global change, mostly in the past 5 years and via singular traits that mediate abiotic limits on species distribution. Beyond organism size (the most examined trait), we identify over 2500 other morphological, physiological, behavioural and life-history traits known to mediate environmental filters of species' range and abundance as candidates for future predictive global change work. Though uncommon, spatially explicit process models—which mechanistically link traits to changes in organism distributions and abundance—are among the most promising frameworks for holistic global change prediction at scales relevant for conservation decision-making. Further progress towards trait-based forecasting requires addressing persistent barriers including (1) matching scales of multivariate trait and environment data to focal processes disrupted by global change, and (2) propagating variation in trait and environmental parameters throughout process model functions using simulation.

Building integral projection models with nonindependent vital rates

Population dynamics are functions of several demographic processes including survival, reproduction, somatic growth, and maturation. The rates or probabilities for these processes can vary by time, by location, and by individual. These processes can co-vary and interact to varying degrees, e.g., an animal can only reproduce when it is in a particular maturation state. Population dynamics models that treat the processes as independent may yield somewhat biased or imprecise parameter estimates, as well as predictions of population abundances or densities. However, commonly used integral projection models (IPMs) typically assume independence across these demographic processes. We examine several approaches for modelling between process dependence in IPMs and include cases where the processes co-vary as a function of time (temporal variation), co-vary within each individual (individual heterogeneity), and combinations of these (temporal variation and individual heterogeneity). We compare our methods to conventional IPMs, which treat vital rates independent, using simulations and a case study of Soay sheep (Ovis aries). In particular, our results indicate that correlation between vital rates can moderately affect variability of some population-level statistics. Therefore, including such dependent structures is generally advisable when fitting IPMs to ascertain whether or not such between vital rate dependencies exist, which in turn can have subsequent impact on population management or life-history evolution.

A new approach to interspecific synchrony in population ecology using tail association

Standard methods for studying the association between two ecologically important variables provide only a small slice of the information content of the association, but statistical approaches are available that provide comprehensive information. In particular, available approaches can reveal tail associations, that is, accentuated or reduced associations between the more extreme values of variables. We here study the nature and causes of tail associations between phenological or population-density variables of co-located species, and their ecological importance. We employ a simple method of measuring tail associations which we call the partial Spearman correlation. Using multidecadal, multi-species spatiotemporal datasets on aphid first flights and marine phytoplankton population densities, we assess the potential for tail association to illuminate two major topics of study in community ecology: the stability or instability of aggregate community measures such as total community biomass and its relationship with the synchronous or compensatory dynamics of the community's constituent species; and the potential for fluctuations and trends in species phenology to result in trophic mismatches. We find that positively associated fluctuations in the population densities of co-located species commonly show asymmetric tail associations; that is, it is common for two species' densities to be more correlated when large than when small, or vice versa. Ordinary measures of association such as correlation do not take this asymmetry into account. Likewise, positively associated fluctuations in the phenology of co-located species also commonly show asymmetric tail associations. We provide evidence that tail associations between two or more species' population-density or phenology time series can be inherited from mutual tail associations of these quantities with an environmental driver. We argue that our understanding of community dynamics and stability, and of phenologies of interacting species, can be meaningfully improved in future work by taking into account tail associations.

Should ecologists prefer model- over distance-based multivariate methods?

Ecological data sets often record the abundance of species, together with a set of explanatory variables. Multivariate statistical methods are optimal to analyze such data and are thus frequently used in ecology for exploration, visualization, and inference. Most approaches are based on pairwise distance matrices instead of the sites-by-species matrix, which stands in stark contrast to univariate statistics, where data models, assuming specific distributions, are the norm. However, through advances in statistical theory and computational power, models for multivariate data have gained traction. Systematic simulation-based performance evaluations of these methods are important as guides for practitioners but still lacking. Here, we compare two model-based methods, multivariate generalized linear models (MvGLMs) and constrained quadratic ordination (CQO), with two distance-based methods, distance-based redundancy analysis (dbRDA) and canonical correspondence analysis (CCA). We studied the performance of the methods to discriminate between causal variables and noise variables for 190 simulated data sets covering different sample sizes and data distributions. MvGLM and dbRDA differentiated accurately between causal and noise variables. The former had the lowest false-positive rate (0.008), while the latter had the lowest false-negative rate (0.027). CQO and CCA had the highest false-negative rate (0.291) and false-positive rate (0.256), respectively, where these error rates were typically high for data sets with linear responses. Our study shows that both model- and distance-based methods have their place in the ecologist's statistical toolbox. MvGLM and dbRDA are reliable for analyzing species-environment relations, whereas both CQO and CCA exhibited considerable flaws, especially with linear environmental gradients.