Bayesian analysis of community dynamics

Elucidating the mechanisms responsible for the patterns of species abundance, diversity, and distribution within and across ecological systems is a fundamental research focus in ecology. Species abundance patterns are shaped in a convoluted way by interplays between inter-/intra-specific interactions, environmental forcing, demographic stochasticity, and dispersal. Comprehensive models and suitable inferential and computational tools for teasing out these different factors are quite limited, even though such tools are critically needed to guide the implementation of management and conservation strategies, the efficacy of which rests on a realistic evaluation of the underlying mechanisms. This is even more so in the prevailing context of concerns over climate change progress and its potential impacts on ecosystems. This thesis utilized the flexible hierarchical Bayesian modelling framework in combination with the computer intensive methods known as Markov chain Monte Carlo, to develop methodologies for identifying and evaluating the factors that control the structure and dynamics of ecological communities. These methodologies were used to analyze data from a range of taxa: macro-moths (Lepidoptera), fish, crustaceans, birds, and rodents. Environmental stochasticity emerged as the most important driver of community dynamics, followed by density dependent regulation; the influence of inter-specific interactions on community-level variances was broadly minor. This thesis contributes to the understanding of the mechanisms underlying the structure and dynamics of ecological communities, by showing directly that environmental fluctuations rather than inter-specific competition dominate the dynamics of several systems. This finding emphasizes the need to better understand how species are affected by the environment and acknowledge species differences in their responses to environmental heterogeneity, if we are to effectively model and predict their dynamics (e.g. for management and conservation purposes). The thesis also proposes a model-based approach to integrating the niche and neutral perspectives on community structure and dynamics, making it possible for the relative importance of each category of factors to be evaluated in light of field data

A Trait-Based Clustering for Phytoplankton Biomass Modeling and Prediction

When designing models for predicting phytoplankton biomass or characterizing traits, it is useful to aggregate the myriad of species into a few biologically meaningful groups and focus on group-level attributes, the common practice being to combine phytoplankton species by functional types. However, biogeochemists and plankton ecologists debate the most applicable grouping for describing phytoplankton biomass patterns and predicting future community structure. Although trait-based approaches are increasingly being advocated, methods are missing for the generation of trait-basedtaxaasalternativestofunctionaltypes. Hereweintroducesuchamethodanddemonstrate the usefulness of the resulting clustering with field data. We parameterize a Bayesian model of biomass dynamics and analyze long-term phytoplankton data collected at Station L4 in the Western English Channel between April 2003 and December 2009. We examine the tradeoffs encountered regarding trait characterization and biomass prediction when aggregating biomass by (1) functional types, (2) the trait-based clusters generated by our method, and (3) total biomass. The model conveniently extracted trait values under the trait-based clustering, but required well-constrained priors under the functional type categorization. It also more accurately predicted total biomass under the trait-based clustering and the total biomass aggregation with comparable root mean squared prediction errors, which were roughly five-fold lower than under the functional type grouping. Although the total biomass grouping ignores taxonomic differences in phytoplankton traits,it predicts total biomass change as well as the trait-based clustering. Our results corroborate the value of trait-based approaches in investigating the mechanisms under lying phytoplankton biomass dynamics and predicting the community response to environmental changes

Phytoplankton traits from long-term oceanographic time-series

Trait values are usually extracted from laboratory studies of single phytoplankton species, which presents challenges for understanding the immense diversity of phytoplankton species and the wide range of dynamic ocean environments. Here we use a Bayesian approach and a trait-based model to extract trait values for 4 functional types and 10 diatom species from field data collected at Station L4 in the Western Channel Observatory, English Channel. We find differences in maximum net growth rate, temperature optimum and sensitivity, half-saturation constants for light and nitrogen, and density-dependent loss terms across the functional types. We find evidence of very high linear loss rates, suggesting that grazing may be even more important than commonly assumed and differences in density-dependent loss rates across functional types, indicating the presence of strong niche differentiation among functional types. Low half-saturation constants for nitrogen at the functional type level may indicate widespread mixotrophy. At the species level, we find a wide range of density-dependent effects, which may be a signal of diversity in grazing susceptibility or biotic interactions. This approach may be a way to obtain more realistic and better-constrained trait values for functional types to be used in ecosystem modeling

A Hierarchical Bayesian Approach to Multi-Trait Clinical Quantitative Trait Locus Modeling

Recent advances in high-throughput genotyping and transcript profiling technologies have enabled the inexpensive production of genome-wide dense marker maps in tandem with huge amounts of expression profiles. These large-scale data encompass valuable information about the genetic architecture of important phenotypic traits. Comprehensive models that combine molecular markers and gene transcript levels are increasingly advocated as an effective approach to dissecting the genetic architecture of complex phenotypic traits. The simultaneous utilization of marker and gene expression data to explain the variation in clinical quantitative trait, known as clinical quantitative trait locus (cQTL) mapping, poses challenges that are both conceptual and computational. Nonetheless, the hierarchical Bayesian (HB) modeling approach, in combination with modern computational tools such as Markov chain Monte Carlo (MCMC) simulation techniques, provides much versatility for cQTL analysis. Sillanpää and Noykova (2008) developed a HB model for single-trait cQTL analysis in inbred line cross-data using molecular markers, gene expressions, and marker-gene expression pairs. However, clinical traits generally relate to one another through environmental correlations and/or pleiotropy. A multi-trait approach can improve on the power to detect genetic effects and on their estimation precision. A multi-trait model also provides a framework for examining a number of biologically interesting hypotheses. In this paper we extend the HB cQTL model for inbred line crosses proposed by Sillanpää and Noykova to a multi-trait setting. We illustrate the implementation of our new model with simulated data, and evaluate the multi-trait model performance with regard to its single-trait counterpart. The data simulation process was based on the multi-trait cQTL model, assuming three traits with uncorrelated and correlated cQTL residuals, with the simulated data under uncorrelated cQTL residuals serving as our test set for comparing the performances of the multi-trait and single-trait models. The simulated data under correlated cQTL residuals were essentially used to assess how well our new model can estimate the cQTL residual covariance structure. The model fitting to the data was carried out by MCMC simulation through OpenBUGS. The multi-trait model outperformed its single-trait counterpart in identifying cQTLs, with a consistently lower false discovery rate. Moreover, the covariance matrix of cQTL residuals was typically estimated to an appreciable degree of precision under the multi-trait cQTL model, making our new model a promising approach to addressing a wide range of issues facing the analysis of correlated clinical traits

On the setting of environmental noise and the performance of population dynamical models

Background Environmental noise is ubiquitous in population growth processes, with a well acknowledged potential to affect populations regardless of their sizes. It therefore deserves consideration in population dynamics modelling. The usual approach to incorporating noise into population dynamical models is to make some model parameter(s) (typically the growth rate, the carrying capacity, or both) stochastic and responsive to environment fluctuations. It is however still unclear whether including noise in one or/and another parameter makes a difference to the model performance. Here we investigated this issue with a focus on model fit and predictive accuracy. To do this, we developed three population dynamical models of the Ricker type with the noise included in the growth rate (Model 1), in the carrying capacity (Model 2), and in both (Model 3). We generated several population time series under each model, and used a Bayesian approach to fit the three models to the simulated data. We then compared the model performances in fitting to the data and in forecasting future observations. Results When the mean intrinsic growth rate, r, in the data was low, the three models had roughly comparable performances, irrespective of the true model and the level of noise. As r increased, Models 1 performed best on data generated from it, and Model 3 tended to perform best on data generated from either Models 2 or Model 3. Model 2 was uniformly outcompeted by the other two models, regardless of the true model and the level of noise. The correlation between the deviance information criterion (DIC) and the mean square error (MSE) used respectively as measure of fit and predictive accuracy was broadly positive. Conclusion Our results suggested that the way environmental noise is incorporated into a population dynamical model may profoundly affect its performance. Overall, we found that including noise in one or/and another parameter does not matter as long as the mean intrinsic growth rate, r, is low. As r increased, however, the three models performed differently. Models 1 and 3 broadly outperformed Model 2, the first having the advantage of being simple and more computationally tractable. A comforting result emerging from our analysis is the broad positive correlation between MSEs and DICs, suggesting that the latter may also be informative about the predictive performance of a model.Peer reviewe

Ecological equivalence of species within phytoplankton functional groups

1.There are tens of thousands of species of phytoplankton found throughout the tree of life. Despite this diversity, phytoplankton are often aggregated into a few functional groups according to metabolic traits or biogeochemical role. We investigate the extent to which phytoplankton species dynamics are neutral within functional groups. 2.Seasonal dynamics in many regions of the ocean are known to affect phytoplankton at the functional group level leading to largely predictable patterns of seasonal succession. It is much more difficult to make general statements about the dynamics of individual species. 3.We use a 7 year time-series at station L4 in the Western English Channel with 57 diatom and 17 dinoflagellate species enumerated weekly to test if the abundance of diatom and dinoflagellate species vary randomly within their functional group envelope or if each species is driven uniquely by external factors. 4.We show that the total biomass of the diatom and dinoflagellate functional groups is well predicted by irradiance and temperature and quantify trait values governing the growth rate of both functional groups. The biomass dynamics of the functional groups are not neutral and each has their own distinct responses to environmental forcing. Compared to dinoflagellates, diatoms have faster growth rates, and grow faster under lower irradiance, cooler temperatures, and higher nutrient conditions. 5.The biomass of most species vary randomly within their functional group biomass envelope, most of the time. As a consequence, modelers will find it difficult to predict the biomass of most individual species. Our analysis supports the approach of using a single set of traits for a functional group and suggests that it should be possible to determine these traits from natural communities

Density regulation amplifies environmentally induced population fluctuations

Background Density-dependent regulation is ubiquitous in population dynamics, and its potential interaction with environmental stochasticity complicates the characterization of the random component of population dynamics. Yet, this issue has not received attention commensurate with its relevance for descriptive and predictive modeling of population dynamics. Here we use a Bayesian modeling approach to investigate the contribution of density regulation to population variability in stochastic environments. Methods We analytically derive a formula linking the stationary variance of population abundance/density under Gompertz regulation in a stochastic environment with constant variance to the environmental variance and the strength of density feedback, to investigate whether and how density regulation affects the stationary variance. We examine through simulations whether the relationship between stationary variance and density regulation inferred analytically under the Gompertz model carries over to the Ricker model, widely used in population dynamics modeling. Results The analytical decomposition of the stationary variance under stochastic Gompertz dynamics implies higher variability for strongly regulated populations. Simulation results demonstrate that the pattern of increasing population variability with increasing density feedback found under the Gompertz model holds for the Ricker model as well, and is expected to be a general phenomenon with stochastic population models. We also analytically established and empirically validated that the square of the autoregressive parameter of the Gompertz model in AR(1) form represents the proportion of stationary variance due to density dependence. Discussion Our results suggest that neither environmental stochasticity nor density regulation can alone explain the patterns of population variability in stochastic environments, as these two components of temporal variation interact, with a tendency for density regulation to amplify the magnitude of environmentally induced population fluctuations. This finding has far-reaching implications for population viability. It implies that intense intra-specific resource competition increases the risk of environment-driven population collapse at high density, making opportune harvesting a sensible practice for improving the resistance of managed populations such as fish stocks to environmental perturbations. The separation of density-dependent and density-independent processes will help improve population dynamics modeling, while providing a basis for evaluating the relative importance of these two categories of processes that remains a topic of long-standing controversy among ecologists

Bayesian two-part modeling of phytoplankton biomass and occurrence

Phytoplankton biomass data often involve zero outcomes preventing a description by continuous distributions with positive support such as the lognormal distribution commonly used to describe ecological data. Two usual solutions: ignoring the zeroes and adding a small positive number to all outcomes, induce bias and reduce predictive power. To address these shortcomings, we design a Bayesian two-part model with a binary component for presence or absence and a continuous component involving a lognormal model for non-zero biomass. We specify two equations relating species-specific occurrence probabilities and expected log-biomasses when present to potential covariates, with spike-and-slab priors imposed on linear effects to selectively discard the irrelevant predictors. We analyze the biomass data of 74 phytoplankton (57 diatoms and 17 dinoflagellates) recorded weekly at Station L4 (Western English Channel, UK) between April 2003 and December 2009, along with measurements of abiotic covariates. Our results disclose different combinations of environmental predictors for the occurrence and the biomass of individual species. Overall, the occurrence of dinoflagellates is associated with higher temperature and irradiance levels compared to diatoms, with virtually no dependence on nutrient concentrations. Irradiance emerges as the key predictor of biomass when species are present. Optimum temperatures for biomass accumulation and temperature sensitivities vary widely among and within functional types. Compared to one-stage models based on usual zero handling approaches, our two-part model stands out with higher prediction accuracy. The two-part modeling approach provides a valuable framework for decoupling the predictors of species occurrence and abundance from observational data

A multispecies perspective on ecological impacts of climatic forcing

P>1. In the prevailing context of concerns over climate change and its potential impacts on ecosystems, evaluating ecological consequences of climatic forcing has become a critical issue. 2. Historical data on the abundance of organisms have been extensively used to characterize the ecological effects of climatic forcing through specific weather and/or climatic variables, with most of the studies confined to single population models. 3. However, population responses to environmental fluctuations typically depend upon positive and negative feedbacks induced by interactions with other species. It is therefore important to integrate the insights gained from single population approaches into a multispecies perspective. 4. Here we combine the hierarchical Bayesian modelling approach with the state-space formulation to extend the scope of previously proposed models of population dynamics under climatic forcing to multi-species systems. 5. We use our model to analyse long-term macro-moth (Lepidoptera) community data from the Rothamsted Insect Survey network in the UK, using winter rainfall and winter temperature as environmental covariates. 6. The effects of the two weather variables were consistent across species, being negative for winter rainfall and positive for winter temperature. The two weather variables jointly explained 15-40% of the total environmental variation affecting the dynamics of individual species, and could explain up to 90% of covariances in species dynamics. 7. The contribution of interspecific interactions to community-level variation was found to be weak compared to the contributions of environmental forcing and intraspecific interactions

A two step Bayesian approach for genomic prediction of breeding values

<p>Abstract</p> <p>Background</p> <p>In genomic models that assign an individual variance to each marker, the contribution of one marker to the posterior distribution of the marker variance is only one degree of freedom (df), which introduces many variance parameters with only little information per variance parameter. A better alternative could be to form clusters of markers with similar effects where markers in a cluster have a common variance. Therefore, the influence of each marker group of size <it>p </it>on the posterior distribution of the marker variances will be <it>p </it>df.</p> <p>Methods</p> <p>The simulated data from the 15^thQTL-MAS workshop were analyzed such that SNP markers were ranked based on their effects and markers with similar estimated effects were grouped together. In step 1, all markers with minor allele frequency more than 0.01 were included in a SNP-BLUP prediction model. In step 2, markers were ranked based on their estimated variance on the trait in step 1 and each 150 markers were assigned to one group with a common variance. In further analyses, subsets of 1500 and 450 markers with largest effects in step 2 were kept in the prediction model.</p> <p>Results</p> <p>Grouping markers outperformed SNP-BLUP model in terms of accuracy of predicted breeding values. However, the accuracies of predicted breeding values were lower than Bayesian methods with marker specific variances.</p> <p>Conclusions</p> <p>Grouping markers is less flexible than allowing each marker to have a specific marker variance but, by grouping, the power to estimate marker variances increases. A prior knowledge of the genetic architecture of the trait is necessary for clustering markers and appropriate prior parameterization.</p