Allan E. Clark

Application of the sequential t-test algorithm for analysing regime shifts to the southern Benguela ecosystem

Long-term ecosystem changes, such as regime shifts, have occurred in several marine ecosystems world-wide. Multivariate statistical methods have been used to detect such changes. A new method known as the sequential t-test algorithm for analysing regime shifts (STARS) is applied to a set of biological state variables as well as environmental and anthropogenic forcing variables in the southern Benguela. The method is able to correct for auto-correlation within time-series by a process known as prewhitening. All variables were tested with and without prewhitening. Shifts that were detected with both methods were termed robust. The STARS method detected shifts in relatively short time-series and identified when these shifts occurred without a priori hypotheses. Shifts were generally well detected at the end of time-series, but further development of the method is needed to enhance its performance for auto-correlated time-series. Since 1950, two major long-term ecosystem changes were identified for the southern Benguela. The first change occurred during the 1960s, caused predominantly by heavy fishing pressure but with some environmental forcing. The second change occurred in the early 2000s, caused mainly by environmental forcing. To strengthen these findings, further analyses should be carried out using different methods.

Ridge Regression – A Simulation Study

In this article we assess the suitability of two new ridge estimators by means of a simulation study. We compare these estimators with well-known ridge estimators. We also make direct comparisons between the ordinary least squares (OLS) estimator and the ridge estimators by using ratio of the average total mean square error of the OLS estimator and the ridge estimators. We find that the new estimators perform well under certain conditions.

Regression and ICOMP—A Simulation Study

A regression simulation study investigates the behaviour of ICOMP, AIC, and BIC under various collinearity-, sample size-, and residual variance-levels. When the variation in the design matrix is large, as the collinearity levels in the design matrix increased, the agreement percentages for all of the information criteria decreased monotonically and that ICOMP agreed with the Kullback Leibler model more often. As the residual variance increases, the agreement percentages of all of the information criteria decreases. However, as the sample size increased the agreement percentages of all information criteria increased. When the variation in the design matrix is low and the collinearity is low, as the residual variance increases, the agreement percentages for all of the information criteria decreases monotonically such that ICOMP agreed more often with Kullback Leibler model than both AIC and BIC.

Modelling the effect of bednet coverage on malaria transmission in South Sudan

A campaign for malaria control, using Long Lasting Insecticide Nets (LLINs) was launched in South Sudan in 2009. The success of such a campaign often depends upon adequate available resources and reliable surveillance data which help officials understand existing infections. An optimal allocation of resources for malaria control at a sub-national scale is therefore paramount to the success of efforts to reduce malaria prevalence. In this paper, we extend an existing SIR mathematical model to capture the effect of LLINs on malaria transmission. Available data on malaria is utilized to determine realistic parameter values of this model using a Bayesian approach via Markov Chain Monte Carlo (MCMC) methods. Then, we explore the parasite prevalence on a continued rollout of LLINs in three different settings in order to create a sub-national projection of malaria. Further, we calculate the model’s basic reproductive number and study its sensitivity to LLINs’ coverage and its efficacy. From the numerical simulation results, we notice a basic reproduction number, R0, confirming a substantial increase of incidence cases if no form of intervention takes place in the community. This work indicates that an effective use of LLINs may reduce R0 and hence malaria transmission. We hope that this study will provide a basis for recommending a scaling-up of the entry point of LLINs’ distribution that targets households in areas at risk of malaria.

Imperfect detection distorts depth-related trends in marine macrofaunal species richness

Ecology and biodiversity research are underpinned by species richness patterns and their environmental drivers. However, a key topic in this discussion is the accuracy of these patterns which are greatly dependent on species detection probabilities. Due to variations in detection of species, true ecological patterns may be distorted. This is particularly true for subtidal macro-infaunal communities. We tested three hypothesized relationships between marine benthic macrofaunal diversity and depth using species richness per site estimated with a capture–recapture heterogeneity model that accounts for variable detection probabilities. These metrics were based on data from 42 replicated sites across the continental shelf of the Southern Benguela. Average detection probability decreased with greater depth but species richness increased along the same depth gradient. The conflation of these trends in observed diversity data resulted in a positively near-linear depth–diversity relationship, while accounting for variable species detection revealed a much stronger relationship. Ignoring species detection in ecosystems with imperfect detection could therefore distort species richness patterns, which has implications for ecological theory, management and conservation.

A variational Bayes approach to the analysis of occupancy models

Detection-nondetection data are often used to investigate species range dynamics using Bayesian occupancy models which rely on the use of Markov chain Monte Carlo (MCMC) methods to sample from the posterior distribution of the parameters of the model. In this article we develop two Variational Bayes (VB) approximations to the posterior distribution of the parameters of a single-season site occupancy model which uses logistic link functions to model the probability of species occurrence at sites and of species detection probabilities. This task is accomplished through the development of iterative algorithms that do not use MCMC methods. Simulations and small practical examples demonstrate the effectiveness of the proposed technique. We specifically show that (under certain circumstances) the variational distributions can provide accurate approximations to the true posterior distributions of the parameters of the model when the number of visits per site (K) are as low as three and that the accuracy of the approximations improves as K increases. We also show that the methodology can be used to obtain the posterior distribution of the predictive distribution of the proportion of sites occupied (PAO).

Time Series and Model Selection

In this article, we investigate the behavior of Bozdogans Information criterion (ICOMP) and other information criteria in a time series context. The study entails simulating stationary autoregressive moving average models 1,000 times and then fitting different time series models to the simulated series. Different series will be considered by changing the size of the residual variance as well as the sample size of the time series. It was found that under certain conditions ICOMP selects the correct time series model most often, although it is suggested that no single information criteria should be used independently of other information criteria.