Implications of uniformly distributed,empirically informed priors for phylogeographical model selection: A reply to Hickerson et al.

Establishing that a set of population‐splitting events occurred at the same time can be a potentially persuasive argument that a common process affected the populations. Recently, Oaks et al. ( 2013 ) assessed the ability of an approximate‐Bayesian model‐choice method (msBayes ) to estimate such a pattern of simultaneous divergence across taxa, to which Hickerson et al. ( 2014 ) responded. Both papers agree that the primary inference enabled by the method is very sensitive to prior assumptions and often erroneously supports shared divergences across taxa when prior uncertainty about divergence times is represented by a uniform distribution. However, the papers differ about the best explanation and solution for this problem. Oaks et al. ( 2013 ) suggested the method's behavior was caused by the strong weight of uniformly distributed priors on divergence times leading to smaller marginal likelihoods (and thus smaller posterior probabilities) of models with more divergence‐time parameters (Hypothesis 1); they proposed alternative prior probability distributions to avoid such strongly weighted posteriors. Hickerson et al. ( 2014 ) suggested numerical‐approximation error causes msBayes analyses to be biased toward models of clustered divergences because the method's rejection algorithm is unable to adequately sample the parameter space of richer models within reasonable computational limits when using broad uniform priors on divergence times (Hypothesis 2). As a potential solution, they proposed a model‐averaging approach that uses narrow, empirically informed uniform priors. Here, we use analyses of simulated and empirical data to demonstrate that the approach of Hickerson et al. ( 2014 ) does not mitigate the method's tendency to erroneously support models of highly clustered divergences, and is dangerous in the sense that the empirically derived uniform priors often exclude from consideration the true values of the divergence‐time parameters. Our results also show that the tendency of msBayes analyses to support models of shared divergences is primarily due to Hypothesis 1, whereas Hypothesis 2 is an untenable explanation for the bias. Overall, this series of papers demonstrates that if our prior assumptions place too much weight in unlikely regions of parameter space such that the exact posterior supports the wrong model of evolutionary history, no amount of computation can rescue our inference. Fortunately, as predicted by fundamental principles of Bayesian model choice, more flexible distributions that accommodate prior uncertainty about parameters without placing excessive weight in vast regions of parameter space with low likelihood increase the method's robustness and power to detect temporal variation in divergences.     

A predictive model of community assembly that incorporates intraspecific trait variation

Community assembly involves two antagonistic processes that select functional traits in opposite directions. Environmental filtering tends to increase the functional similarity of species within communities leading to trait convergence, whereas competition tends to limit the functional similarity of species within communities leading to trait divergence. Here, we introduce a new hierarchical Bayesian model that incorporates intraspecific trait variation into a predictive framework to unify classic coexistence theory and evolutionary biology with recent trait‐based approaches. Model predictions exhibited a significant positive correlation (r = 0.66) with observed relative abundances along a 10 °C gradient in mean annual temperature. The model predicted the correct dominant species in half of the plots, and accurately reproduced species' temperature optimums. The framework is generalizable to any ecosystem as it can accommodate any species pool, any set of functional traits and multiple environmental gradients, and it eliminates some of the criticisms associated with recent trait‐based community assembly models.     

A trait-based approach for modelling microbial litter decomposition

Trait-based models are an emerging tool in ecology with the potential to link community dynamics, environmental responses and ecosystem processes. These models represent complex communities by defining taxa with trait combinations derived from prior distributions that may be constrained by trade-offs. Herein I develop a model that links microbial community composition with physiological and enzymatic traits to predict litter decomposition rates. This approach allows for trade-offs among traits that represent alternative microbial strategies for resource acquisition. The model predicts that optimal strategies depend on the level of enzyme production in the whole community, which determines resource availability and decomposition rates. There is also evidence for facilitation and competition among microbial taxa that co-occur on decomposing litter. These interactions vary with community investment in extracellular enzyme production and the magnitude of trade-offs affecting enzyme biochemical traits. The model accounted for 69% of the variation in decomposition rates of 15 Hawaiian litter types and up to 26% of the variation in enzyme activities. By explicitly representing diversity, trait-based models can predict ecosystem processes based on functional trait distributions in a community. The model developed herein illustrates that traits influencing microbial enzyme production are some of the key controls on litter decomposition rates.     

An approach to analysis of colonization dynamics in community functioning of protozoa for bioassessment of marine pollution

Biological trait analysis is a powerful tool to summarize the spatial/temporal patterns of community functioning and ecosystem process at taxon-free resolutions. To identify the optimal colonization period with high homogeneity in functional patterns of protozoa for bioassessment, 1-month baseline colonization survey was conducted in coastal waters of the Yellow Sea. A fuzzy-coding functional trait system was used to summarize the functional structure of protozoan communities during the colonization process. The functional patterns showed a low homogeneity during the early stage (3–7 days), followed by a stable stage (10–14 days) with high homogeneity, and the last stage (21–28 days) with high heterogeneity. The functional richness showed a low variability, while the functional evenness and divergence generally showed a decreasing trend during the whole colonization process. Furthermore, the functional dispersion and RaoQ indices generally leveled off only during the stable stage. These results suggest that it is necessary to determine the optimal exposure time period with high homogeneity of community functioning for bioassessment using protozoan colonization in marine ecosystems.     

The performance of trait-based indices in an estuarine environment

The performance of several indices of benthic functioning, based on the traits of estuarine macro-invertebrates, was tested in the lower Mondego estuary (Portugal), whose two arms exhibit different disturbance levels related to hydromorphology. The results showed that some indices responded clearly to this type of disturbance and others not so well. We argue that the community-weighted mean trait values (CWM) in combination with the newly developed SR-FRED index provided the best overall picture of how the benthic communities might have been affected by hydromorphological disturbance. This study also showed that certain indices should be used with caution when dealing with communities with few and dominant species, such as in estuarine environments.     

Optimizing ecosystem function by manipulating pasture community composition

The ability to design plant communities to optimize particular ecosystem functions and thus more effectively provide ecosystem services would improve all types of ecosystem management, including agriculture. We propose a novel quantitative multi-step method for selecting mixtures of plant species to meet ecosystem objectives: collecting trait data; identifying suites of traits related to relevant community processes; relating those processes to the ecosystem functions of interest; optimizing the planted mixture; and evaluating trade-offs. This approach was tested using planted mixtures of 14 grassland species common in managed pastures of the northeastern United States. Ordination of trait data from greenhouse and small plot studies was used to relate species traits to community processes, followed by generalized additive modeling to relate community-weighted mean process scores to field estimates of biomass production and resistance to invasion. Multi-criteria optimization identified seed mixtures that maximized or minimized selected ecosystem functions, facilitating quantification of trade-offs in processual ability within species and between ecosystem functions at the community level. In this study, predicted seasonal and annual biomass values were within expected ranges, but the optimal mixtures differed from forage mixtures traditionally planted in the northeastern United States. Perennial ryegrass was the most commonly-selected grass. Legumes were represented less than expected, possibly due to attributes such as longevity and forage quality that are important in pastures but were not directly included in the optimization. Ecosystem function was not linearly related to species richness. While further research on quantitatively relating species traits and community processes is needed, multi-criteria optimization offers a new path for linking ecosystem function to ecosystem management.     

Interactions between stochastic and deterministic processes in stream fish community assembly

Synopsis Numerous studies have attempted to determine whether stream fish communities are structured primarily by deterministic or stochastic processes. Previous work has assumed that stream fish communities will show either persistence about an equilibrium because of strong density-dependent processes or random variation in structure as a result of environmental stochasticity. In a 10-year study of a California stream, fish community structure changed under the influence of storm-induced high discharge events that impacted recruitment. Species' relative abundances were altered as pre-recruitment stream discharges differentially influenced year-class strength among species with contrasting life histories. Simulation of stream fish community assembly under flow-driven recruitment variation indicates that community structure will vary depending on how particular high-flow events affect species' relative abundances and ongoing density-dependent processes, including competition and predation. Results suggest that stream fish communities are likely to show alternate states rather than a single persistent equilibrium. However, community assembly will not be random but will depend on situation-specific interactions between density-independent and density-dependent processes.     

Quantifying relationships between traits and explicitly measured gradients of stress and disturbance in early successional plant communities

Questions: How can one explicitly quantify, and separately measure, stress and disturbance gradients? How do these gradients affect functional composition in early successional plant communities and to what extent? Can we accurately predict trait composition from knowledge of these gradients? Location: Southern Quebec, Canada. Methods: Using eight environmental variables measured in 48 early successional plant communities, we estimated stress and disturbance gradients through structural equation modelling. We then measured 10 functional traits on the most abundant species of these 48 communities and calculated their community‐level mean and variance weighted by the relative abundance of each species. Finally, we related these community‐weighted means and variances to the estimated stress and disturbance gradients using general linear models or generalized additive models. Results: We obtained a well‐fitting measurement model of the stress and disturbance gradients existing in our sites. Of the 10 studied traits, only average plant reproductive height was strongly correlated with the stress (r²=0.464) and disturbance (r²=0.543) gradients. Leaf traits were not significantly related to either the stress or disturbance gradients. Conclusions: The well‐fitting measurement model of the stress and disturbance gradients, combined with the generally weak trait–environment linkages, suggests that community assembly in these early successional plant communities is driven primarily by stochastic processes linked to the history of arrival of propagules and not to trait‐based environmental filtering.     

A bivariate quantitative genetic model for a threshold trait and a survival trait

Many of the functional traits considered in animal breeding can be analyzed as threshold traits or survival traits with examples including disease traits, conformation scores, calving difficulty and longevity. In this paper we derive and implement a bivariate quantitative genetic model for a threshold character and a survival trait that are genetically and environmentally correlated. For the survival trait, we considered the Weibull log-normal animal frailty model. A Bayesian approach using Gibbs sampling was adopted in which model parameters were augmented with unobserved liabilities associated with the threshold trait. The fully conditional posterior distributions associated with parameters of the threshold trait reduced to well known distributions. For the survival trait the two baseline Weibull parameters were updated jointly by a Metropolis-Hastings step. The remaining model parameters with non-normalized fully conditional distributions were updated univariately using adaptive rejection sampling. The Gibbs sampler was tested in a simulation study and illustrated in a joint analysis of calving difficulty and longevity of dairy cattle. The simulation study showed that the estimated marginal posterior distributions covered well and placed high density to the true values used in the simulation of data. The data analysis of calving difficulty and longevity showed that genetic variation exists for both traits. The additive genetic correlation was moderately favorable with marginal posterior mean equal to 0.37 and 95% central posterior credibility interval ranging between 0.11 and 0.61. Therefore, this study suggests that selection for improving one of the two traits will be beneficial for the other trait as well.     

Phylogeny, traits, environment, and space in cerrado plant communities at Emas National Park (Brazil)

Soil, drought, and fire are abiotic factors that may act as environmental filters in the cerrado, the Brazilian savanna. We used a framework to analyze environmental filtering in geographic and phylogenetic context, sampling woody species in one of the largest cerrado reserves. In 100 quadrats, we measured 10 functional traits on each woody individual. We also measured several soil variables, altitude and slope as a rough surrogate of water availability, interval between fires, and time since last fire. Almost all environmental variables were spatially auto-correlated. We found an overall trait clustering, but not an overall phylogenetic clustering. Nevertheless, we found a phylogenetic signal for some traits. Linking phylogeny, traits, environment, and space, we were able to detect a major dichotomy between two geomorphological units. The flat tableland was positively related with altitude, fire frequency, and nutrient-richer soil. Environmental filtering caused by water availability and fire lead to trait clustering, with smaller shrubs and trees that presented thicker barks, denser woods, sclerophyllous leaves, highlighted by the prevalance of Myrtaceae. The other geomorphological unit, hilly terrain, was positively related with slope, low fire frequency, and nutrient-poorer soil. Environmental filtering was caused especially by nutrient-poor soil that lead to trait clustering, assembling taller trees, with thinner barks, lighter woods, and compound, large, tender, nutrient-richer leaves, distributed across many lineages, including Fabaceae. Hence, the high environmental variability in space with different environmental filters assembled different combination of plant traits and lineages, increasing the overall diversity in cerrado.     

A stochastic metapopulation model accounting for habitat dynamics

A stochastic metapopulation model accounting for habitat dynamics is presented. This is the stochastic SIS logistic model with the novel aspect that it incorporates varying carrying capacity. We present results of Kurtz and Barbour, that provide deterministic and diffusion approximations for a wide class of stochastic models, in a form that most easily allows their direct application to population models. These results are used to show that a suitably scaled version of the metapopulation model converges, uniformly in probability over finite time intervals, to a deterministic model previously studied in the ecological literature. Additionally, they allow us to establish a bivariate normal approximation to the quasi-stationary distribution of the process. This allows us to consider the effects of habitat dynamics on metapopulation modelling through a comparison with the stochastic SIS logistic model and provides an effective means for modelling metapopulations inhabiting dynamic landscapes.     

Functional diversity analysis helps to identify filters affecting community assembly after fen restoration by top-soil removal and hay transfer

Top-soil removal followed by species introduction through hay transfer has appeared as a method to restore drained fens. This method addresses abiotic constraints by restoring hydrology and nutrient status, and biotic constraints by removing an unwanted seed bank and counteracting dispersal-limitation. Restoration works by altering environmental filters. Knowledge about the restoration actions effect on functional traits is necessary to understand which types of species may establish. In this study we analyse which factors in top-soil removal followed by hay transfer influence selection and composition of functional traits. Top-soil removal followed by hay transfer from reference sites was conducted at two sites in the Całowanie fen, 33 km SE of Warsaw, Poland. Species and abundance data were recorded for three consecutive years. These data, combined with data on functional traits were used to analyse the effect of the restoration actions on four functional diversity-indices and the community weighted mean of functional traits. Our results reveal a strong habitat filter in the restoration site that follows an elevation gradient. At low elevation this filter selects low values of autochory and specific leaf area and high values of clonal lateral spread, Ellenberg moisture values, and dispersal through hydrochory. The transferred hay differs in trait characteristics compared to the reference site vegetation by having species of higher specific leaf area, lower Ellenberg moisture value and lower dispersal by autochory and hydrochory. The result presented here has three important implications for fen restoration. First, the difference in trait-characteristics between the transferred hay and the reference site it was harvested from limits the restoration potential. Second, since for several fen species important functional traits are filtered along an elevation-gradient, careful planning regarding depth of top-soil removal is needed. Finally the results illustrate how a functional analysis can be used to detect environmental filters acting during ecological restoration.     

Identifying models of trait‐mediated community assembly using random forests and approximate Bayesian computation

Ecologists often use dispersion metrics and statistical hypothesis testing to infer processes of community formation such as environmental filtering, competitive exclusion, and neutral species assembly. These metrics have limited power in inferring assembly models because they rely on often‐violated assumptions. Here, we adapt a model of phenotypic similarity and repulsion to simulate the process of community assembly via environmental filtering and competitive exclusion, all while parameterizing the strength of the respective ecological processes. We then use random forests and approximate Bayesian computation to distinguish between these models given the simulated data. We find that our approach is more accurate than using dispersion metrics and accounts for uncertainty in model selection. We also demonstrate that the parameter determining the strength of the assembly processes can be accurately estimated. This approach is available in the R package CAMI; Community Assembly Model Inference. We demonstrate the effectiveness of CAMI using an example of plant communities living on lava flow islands.