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

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

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

Competitor Identification for Sustainable Survival Strategies: Illustration with Supply Chain Versus Supply Chain Competition

We describe a methodology for identifying competitors from first principles, drawing on the ecological niche theory which stipulates that competition arises from the dependence of interacting entities on the same limiting resources or, in ecological terms, from overlap in their niches. Depending on the context, the entities of interest may be species, products, firms, countries, or supply chains. We discuss the concepts of niche breadth and niche overlap and provide a mathematical expression for computing the competitive effects of interacting entities on one another from niche breadth and overlap measures. We illustrate the competitor identification procedure with simulated data mimicking a situation where supply chains compete over logistics modes on which they rely for moving goods from point to point. Competition identification is invaluable to business sustainability as it allows the entities involved to remain sustainable and persist in a competitive environment by crafting effective strategies that allow them to continuously adapt to changes and mitigate the negative impacts of competition

Extended Bayesian LASSO for Multiple Quantitative Trait Loci Mapping and Unobserved Phenotype Prediction

The Bayesian LASSO (BL) has been pointed out to be an effective approach to sparse model representation and successfully applied to quantitative trait loci (QTL) mapping and genomic breeding value (GBV) estimation using genome-wide dense sets of markers. However, the BL relies on a single parameter known as the regularization parameter to simultaneously control the overall model sparsity and the shrinkage of individual covariate effects. This may be idealistic when dealing with a large number of predictors whose effect sizes may differ by orders of magnitude. Here we propose the extended Bayesian LASSO (EBL) for QTL mapping and unobserved phenotype prediction, which introduces an additional level to the hierarchical specification of the BL to explicitly separate out these two model features. Compared to the adaptiveness of the BL, the EBL is “doubly adaptive” and thus, more robust to tuning. In simulations, the EBL outperformed the BL in regard to the accuracy of both effect size estimates and phenotypic value predictions, with comparable computational time. Moreover, the EBL proved to be less sensitive to tuning than the related Bayesian adaptive LASSO (BAL), which introduces locus-specific regularization parameters as well, but involves no mechanism for distinguishing between model sparsity and parameter shrinkage. Consequently, the EBL seems to point to a new direction for QTL mapping, phenotype prediction, and GBV estimation

What drives community dynamics?

The search for general mechanisms of community assembly is a major focus of community ecology. The common practice so far has been to examine alternative assembly theories using dichotomist approaches of the form neutrality versus niche, or compensatory dynamics versus environmental forcing. In reality, all these mechanisms will be operating, albeit with different strengths. While there have been different approaches to community structure and dynamics, including neutrality and niche differentiation, less work has gone into separating out the temporal variation in species abundances into relative contributions from different components. Here we use a refined statistical machinery to decompose temporal fluctuations in species abundances into contributions from environmental stochasticity and inter-/intraspecific interactions, to see which ones dominate. We apply the methodology to community data from a range of taxa. Our results show that communities are largely driven by environmental fluctuations, and that member populations are, to different extents, regulated through intraspecific interactions, the effects of interspecific interactions remaining broadly minor. By decomposing the temporal variation in this way, we have been able to show directly what has been previously inferred indirectly: compensatory dynamics are in fact largely outweighed by environmental forcing, and the latter tends to synchronize the population dynamics