Trade-offs between accuracy and interpretability in von Bertalanffy random-effects models of growth

Accounting for temporal and individual variation in the estimation of Von Bertalanffy growth curves

Growth and growth limitation are important indicators of density dependence and environmental limitation of populations. Estimating individual growth trajectories is therefore an important aspect of understanding and predicting the life history and dynamics of a population. Variation in individual growth trajectories arises due to variation in the environmental factors limiting individual growth. This environmental limitation can vary over time, between cohorts and between individuals within a cohort. For a complete and accurate understanding of individual growth in a population, it is important to include all these sources of variation. So far, statistical models only accounted for a subset of these factors or required an extensive growth history of individuals. Here, we present a novel model describing the growth curves of cohorts in a population. This model is derived from a stochastic form of the Von Bertalanffy growth equation describing individual growth. The model is specifically tailored for use on length-at-age data in which the growth trajectory of an individual is unknown and every individual is only measured once. The presented method can also be used if growth limitation differs strongly between age or length classes. We demonstrate the use of the model for length-at-age data of North Sea plaice (Pleuronectes platessa) from the last 30 years. Fitting this model to length-at-age data can provide new insights in the dynamics of the environmental factors limiting individual growth and provides a useful tool for ecological research and management.

Applying the Properties of Neurons in Machine Learning: A Brain-like Neural Model with Interactive Stimulation for Data Classification

Some neural models achieve outstanding results in image recognition, semantic segmentation and natural language processing. However, their classification performance on structured and small-scale datasets that do not involve feature extraction is worse than that of traditional algorithms, although they require more time to train. In this paper, we propose a brain-like neural model with interactive stimulation (NMIS) that focuses on data classification. It consists of a primary neural field and a senior neural field that play different cognitive roles. The former is used to correspond to real instances in the feature space, and the latter stores the category pattern. Neurons in the primary field exchange information through interactive stimulation and their activation is transmitted to the senior field via inter-field interaction, simulating the mechanisms of neuronal interaction and synaptic plasticity, respectively. The proposed NMIS is biologically plausible and does not involve complex optimization processes. Therefore, it exhibits better learning ability on small-scale and structured datasets than traditional BP neural networks. For large-scale data classification, a nearest neighbor NMIS (NN_NMIS), an optimized version of NMIS, is proposed to improve computational efficiency. Numerical experiments performed on some UCI datasets show that the proposed NMIS and NN_NMIS are significantly superior to some classification algorithms that are widely used in machine learning.

A Primer for Microbiome Time-Series Analysis

Time-series can provide critical insights into the structure and function of microbial communities. The analysis of temporal data warrants statistical considerations, distinct from comparative microbiome studies, to address ecological questions. This primer identifies unique challenges and approaches for analyzing microbiome time-series. In doing so, we focus on (1) identifying compositionally similar samples, (2) inferring putative interactions among populations, and (3) detecting periodic signals. We connect theory, code and data via a series of hands-on modules with a motivating biological question centered on marine microbial ecology. The topics of the modules include characterizing shifts in community structure and activity, identifying expression levels with a diel periodic signal, and identifying putative interactions within a complex community. Modules are presented as self-contained, open-access, interactive tutorials in R and Matlab. Throughout, we highlight statistical considerations for dealing with autocorrelated and compositional data, with an eye to improving the robustness of inferences from microbiome time-series. In doing so, we hope that this primer helps to broaden the use of time-series analytic methods within the microbial ecology research community.

Biological and statistical interpretation of size-at-age, mixed-effects models of growth

The differences in life-history traits and processes between organisms living in the same or different populations contribute to their ecological and evolutionary dynamics. We developed mixed-effect model formulations of the popular size-at-age von Bertalanffy and Gompertz growth functions to estimate individual and group variation in body growth, using as a model system four freshwater fish populations, where tagged individuals were sampled for more than 10 years. We used the software Template Model Builder to estimate the parameters of the mixed-effect growth models. Tests on data that were not used to estimate model parameters showed good predictions of individual growth trajectories using the mixed-effects models and starting from one single observation of body size early in life; the best models had R 2 > 0.80 over more than 500 predictions. Estimates of asymptotic size from the Gompertz and von Bertalanffy models were not significantly correlated, but their predictions of size-at-age of individuals were strongly correlated (r > 0.99), which suggests that choosing between the best models of the two growth functions would have negligible effects on the predictions of size-at-age of individuals. Model results pointed to size ranks that are largely maintained throughout the lifetime of individuals in all populations.

Stochastic optimal switching model for migrating population dynamics

An optimal switching control formalism combined with the stochastic dynamic programming is, for the first time, applied to modelling life cycle of migrating population dynamics with non-overlapping generations. The migration behaviour between habitats is efficiently described as impulsive switching based on stochastic differential equations, which is a new standpoint for modelling the biological phenomenon. The population dynamics is assumed to occur so that the reproductive success is maximized under an expectation. Finding the optimal migration strategy ultimately reduces to solving an optimality equation of the quasi-variational type. We show an effective linkage between our optimality equation and the basic reproduction number. Our model is applied to numerical computation of optimal migration strategy and basic reproduction number of an amphidromous fish Plecoglossus altivelis altivelis in Japan as a target species.

A framework for estimating the determinants of spatial and temporal variation in vital rates and inferring the occurrence of unobserved extreme events

We develop a general framework that combines long-term tag-recapture data and powerful statistical and modelling techniques to investigate how population, environmental and climate factors determine variation in vital rates and population dynamics in an animal species, using as a case study the population of brown trout living in Upper Volaja (Western Slovenia). This population has been monitored since 2004. Upper Volaja is a sink, receiving individuals from a source population living above a waterfall. We estimate the numerical contribution of the source population on the sink population and test the effects of temperature, population density and extreme events on variation in vital rates among 2647 individually tagged brown trout. We found that individuals dispersing downstream from the source population help maintain high population densities in the sink population despite poor recruitment. The best model of survival for individuals older than juveniles includes additive effects of birth cohort and sampling occasion. Fast growth of older cohorts and higher population densities in 2004-2005 suggest very low population densities in the late 1990s, which we hypothesize were caused by a flash flood that strongly reduced population size and created the habitat conditions for faster individual growth and transient higher population densities after the extreme event.