Fish distribution predictions from different points of view: comparing associative neural networks,geostatistics and regression models

Accurate prediction of species distributions based on sampling and environmental data is essential for further scientific analysis, such as stock assessment, detection of abundance fluctuation due to climate change or overexploitation, and to underpin management and legislation processes. The evolution of computer science and statistics has allowed the development of sophisticated and well-established modelling techniques as well as a variety of promising innovative approaches for modelling species distribution. The appropriate selection of modelling approach is crucial to the quality of predictions about species distribution. In this study, modelling techniques based on different approaches are compared and evaluated in relation to their predictive performance, utilizing fish density acoustic data. Generalized additive models and mixed models amongst the regression models, associative neural networks (ANNs) and artificial neural networks ensemble amongst the artificial neural networks and ordinary kriging amongst the geostatistical techniques are applied and evaluated. A verification dataset is used for estimating the predictive performance of these models. A combination of outputs from the different models is applied for prediction optimization to exploit the ability of each model to explain certain aspects of variation in species acoustic density. Neural networks and especially ANNs appear to provide more accurate results in fitting the training dataset while generalized additive models appear more flexible in predicting the verification dataset. The efficiency of each technique in relation to certain sampling and output strategies is also discussed.     

Four years host–parasitoid food web: testing sampling effort on trophic levels

Incomplete sampling is a major problem affecting data quality with respect to food webs. We described a host–parasitoid food web based on data from four years of sampling, evaluated the dataset robustness of the food web, and tested the hypothesis that different trophic levels require different sampling efforts. We sampled Senegalia tenuifolia fruits at eight sampling sites in three areas, during four years (2011–2014) in the Brazilian cerrado (savanna). We recorded 26 insect species in three trophic levels associated with S. tenuifolia. For species accumulation curves, all insect trophic levels, areas and years reached the asymptote, except for one area. The cumulative species richness in each trophic level suggested that the third level (primary parasitoid) should be sampled for a longer time than the second and fourth levels, supporting our hypothesis. In conclusion, the sampling effort employed was sufficient to assess most of the insect species richness, and provided a high-quality and well-represented host-parasitoid food web, even though trophic levels require different efforts.     

Application of the multiensemble sampling to the equilibrium folding of proteins

MOTIVATION: Conventional Monte Carlo and molecular dynamics simulations of proteins in the canonical ensemble are of little use, because they tend to get trapped in states of energy local minima at low temperatures. One way to surmount this difficulty is to use a non-Boltzmann sampling method in which conformations are sampled upon a general weighting function instead of the conventional Boltzmann weighting function. The multiensemble sampling (MES) method is a non-Boltzmann sampling method that was originally developed to estimate free energy differences between systems with different potential energies and/or at different thermodynamic states. The method has not yet been applied to studies of complex molecular systems such as proteins. RESULTS: MES Monte Carlo simulations of small proteins have been carried out using a united-residue force field. The proteins at several temperatures from the unfolded to the folded states were simulated in a single MC run at a time and their equilibrium thermodynamic properties were calculated correctly. The distributions of sampled conformations clearly indicate that, when going through states of energy local minima, the MES simulation did not get trapped in them but escaped from them so quickly that all the relevant parts of conformation space could be sampled properly. A two-step folding process consisting of a collapse transition followed by a folding transition is observed. This study demonstrates that the use of MES alleviates the multiple-minima problem greatly. AVAILABILITY: Available on request from the authors.     

Prediction of marine species distribution from presence–absence acoustic data: comparing the fitting efficiency and the predictive capacity of conventional and novel distribution models

The accurate representation of species distribution derived from sampled data is essential for management purposes and to underpin population modelling. Additionally, the prediction of species distribution for an expanded area, beyond the sampling area can reduce sampling costs. Here, several well-established and recently developed habitat modelling techniques are investigated in order to identify the most suitable approach to use with presence–absence acoustic data. The fitting efficiency of the modelling techniques are initially tested on the training dataset while their predictive capacity is evaluated using a verification set. For the comparison among models, Receiver Operating Characteristics (ROC), Kappa statistics, correlation and confusion matrices are used. Boosted Regression Trees (BRT) and Associative Neural Networks (ASNN), which are both within the machine learning category, outperformed the other modelling approaches tested.     

Parameter estimation in stochastic biochemical reactions

Gene regulatory, signal transduction and metabolic networks are major areas of interest in the newly emerging field of systems biology. In living cells, stochastic dynamics play an important role; however, the kinetic parameters of biochemical reactions necessary for modelling these processes are often not accessible directly through experiments. The problem of estimating stochastic reaction constants from molecule count data measured, with error, at discrete time points is considered. For modelling the system, a hidden Markov process is used, where the hidden states are the true molecule counts, and the transitions between those states correspond to reaction events following collisions of molecules. Two different algorithms are proposed for estimating the unknown model parameters. The first is an approximate maximum likelihood method that gives good estimates of the reaction parameters in systems with few possible reactions in each sampling interval. The second algorithm, treating the data as exact measurements, approximates the number of reactions in each sampling interval by solving a simple linear equation. Maximising the likelihood based on these approximations can provide good results, even in complex reaction systems.     

Spatially autocorrelated sampling falsely inflates measures of accuracy for presence‐only niche models

Aim Environmental niche models that utilize presence‐only data have been increasingly employed to model species distributions and test ecological and evolutionary predictions. The ideal method for evaluating the accuracy of a niche model is to train a model with one dataset and then test model predictions against an independent dataset. However, a truly independent dataset is often not available, and instead random subsets of the total data are used for ‘training’ and ‘testing’ purposes. The goal of this study was to determine how spatially autocorrelated sampling affects measures of niche model accuracy when using subsets of a larger dataset for accuracy evaluation. Location The distribution of Centaurea maculosa (spotted knapweed; Asteraceae) was modelled in six states in the western United States: California, Oregon, Washington, Idaho, Wyoming and Montana. Methods Two types of niche modelling algorithms – the genetic algorithm for rule‐set prediction (GARP) and maximum entropy modelling (as implemented with Maxent) – were used to model the potential distribution of C. maculosa across the region. The effect of spatially autocorrelated sampling was examined by applying a spatial filter to the presence‐only data (to reduce autocorrelation) and then comparing predictions made using the spatial filter with those using a random subset of the data, equal in sample size to the filtered data. Results The accuracy of predictions from both algorithms was sensitive to the spatial autocorrelation of sampling effort in the occurrence data. Spatial filtering led to lower values of the area under the receiver operating characteristic curve plot but higher similarity statistic (I) values when compared with predictions from models built with random subsets of the total data, meaning that spatial autocorrelation of sampling effort between training and test data led to inflated measures of accuracy. Main conclusions The findings indicate that care should be taken when interpreting the results from presence‐only niche models when training and test data have been randomly partitioned but occurrence data were non‐randomly sampled (in a spatially autocorrelated manner). The higher accuracies obtained without the spatial filter are a result of spatial autocorrelation of sampling effort between training and test data inflating measures of prediction accuracy. If independently surveyed data for testing predictions are unavailable, then it may be necessary to explicitly account for the spatial autocorrelation of sampling effort between randomly partitioned training and test subsets when evaluating niche model predictions.     

Statistical approaches to paternity analysis in natural populations and applications to the North Atlantic humpback whale

We present a new method for paternity analysis in natural populations that is based on genotypic data that can take the sampling fraction of putative parents into account. The method allows paternity assignment to be performed in a decision theoretic framework. Simulations are performed to evaluate the utility and robustness of the method and to assess how many loci are necessary for reliable paternity inference. In addition we present a method for testing hypotheses regarding relative reproductive success of different ecologically or behaviorally defined groups as well as a new method for estimating the current population size of males from genotypic data. This method is an extension of the fractional paternity method to the case where only a proportion of all putative fathers have been sampled. It can also be applied to provide abundance estimates of the number of breeding males from genetic data. Throughout, the methods were applied to genotypic data collected from North Atlantic humpback whales (Megaptera novaeangliae) to test if the males that appear dominant during the mating season have a higher reproductive success than the subdominant males.     

A cautionary note on the use of hypervolume kernel density estimators in ecological niche modelling

Blonder et al. ( 2014 , Global Ecology and Biogeography, 23, 595–609) introduced a new multivariate kernel density estimation (KDE) method to infer Hutchinsonian hypervolumes in the modelling of ecological niches. The authors argued that their KDE method matches or outperforms several methods for estimating hypervolume geometries and for conducting species distribution modelling. Further clarification, however, is appropriate with respect to the assumptions and limitations of KDE as a method for species distribution modelling. Using virtual species and controlled environmental scenarios, we show that KDE both under‐ and overestimates niche volumes depending on the dimensionality of the dataset and the number of occurrence records considered. We suggest that KDE may be a viable approach when dealing with large sample sizes, limited sampling bias and only a few environmental dimensions.     

Forecasting insect species richness scores in poorly surveyed territories: the case of the Portuguese dung beetles (Col. Scarabaeinae)

Large-scale biodiversity assessment of faunal distribution is needed in poorly sampled areas. In this paper, Scarabaeinae dung beetle species richness in Portugal is forecasted from a model built with a data set from areas identified as well sampled. Generalized linear models are used to relate the number of Scarabaeinae species in each Portuguese UTM 50 × 50 grid square with a set of 25 predictor variables (geographic, topographic, climatic and land cover) extracted from a geographic information system (GIS). Between-squares sampling effort unevenness, spatial autocorrelation of environmental data, non-linear relationships between variables and an assessment of the models' predictive power, the main shortcomings in geographic species richness modelling, are addressed. This methodological approach has proved to be reliable and accurate enough in estimating species richness distribution, thus providing a tool to identify areas as potential targets for conservation policies in poorly inventoried countries.     

On Estimating the Population of Aphids in A Potato Field

This appendix to the preceding paper by L. Broadbent deals with the statistical problem of estimating the population of aphids per plant in a field of growing potatoes. An unbiased method is described, in which a definite proportion of a number of plants is sampled, and also a more rapid, method of stratified sampling. (An account of the statistical principles involved has been given by Yates (1946).) Sampling for purposes of inspection is then considered, using practices current in industrial statistics and described, for example, by Peach (1947). Finally, some counts on Myzus persicae are examined, to obtain information on the. type of variation in aphid numbers to be expected.     

A new method for handling missing species in diversification analysis applicable to randomly or nonrandomly sampled phylogenies

Chronograms from molecular dating are increasingly being used to infer rates of diversification and their change over time. A major limitation in such analyses is incomplete species sampling that moreover is usually nonrandom. While the widely used γ statistic with the Monte Carlo constant-rates test or the birth-death likelihood analysis with the δ AICrc test statistic are appropriate for comparing the fit of different diversification models in phylogenies with random species sampling, no objective automated method has been developed for fitting diversification models to nonrandomly sampled phylogenies. Here, we introduce a novel approach, CorSiM, which involves simulating missing splits under a constant rate birth-death model and allows the user to specify whether species sampling in the phylogeny being analyzed is random or nonrandom. The completed trees can be used in subsequent model-fitting analyses. This is fundamentally different from previous diversification rate estimation methods, which were based on null distributions derived from the incomplete trees. CorSiM is automated in an R package and can easily be applied to large data sets. We illustrate the approach in two Araceae clades, one with a random species sampling of 52% and one with a nonrandom sampling of 55%. In the latter clade, the CorSiM approach detects and quantifies an increase in diversification rate, whereas classic approaches prefer a constant rate model; in the former clade, results do not differ among methods (as indeed expected since the classic approaches are valid only for randomly sampled phylogenies). The CorSiM method greatly reduces the type I error in diversification analysis, but type II error remains a methodological problem.     

On a Basic Assumption in the Line Transect Method

This paper deals with one of the basic assumptions made in estimating population density by the line transect sampling method. Theory has been developed in this paper for estimating, density using a gamma distribution. The results have been applied to data on ruffed grouse.     

On formation‐based sampling proxies and why they should not be used to correct the fossil record

The fossil record is a unique resource on the history of life, but it is well known to be incomplete. In a series of high‐profile papers, a residual modelling technique has been applied to correct the raw palaeodiversity signal for this bias and incompleteness, and the claim is made that the processed time series are more accurate than the raw data. We apply empirical and simulation approaches to test for correlation and directionality of any relationships between rock and fossil data. The empirical data comprise samples of the global fossil record through the Phanerozoic, and we use simulations to assess whether randomly sampled subsets of modelled data can be improved by application of the residual modelling technique. Our results show that using formation counts as a sampling proxy to correct the fossil record via residual modelling is ill founded. The supposedly independent model of sampling is information‐redundant with respect to the raw palaeodiversity data it seeks to correct, and so the outputs are generally likely to be further from the truth than the raw data. We recommend that students of palaeodiversity cease to use residual modelling estimates based on formation counts, and suggest that results from a substantial number of papers published in the past ten years require re‐evaluation.     

Quantification of the intra-plot correlation in plant abundance data: A possible test of the neutral theory

A method for summarising the degree of spatial covariance (intra-plot correlation) among different plant species using plant abundance data is presented. The method will provide an alternative test of the hypothesis of neutrality in uniform environments, and we apply it in this study to data derived from two different grasslands. There is a significant positive intra-plot correlation in both grasslands that may be due to either sampling effects or deterministic ecological effects. For the calcareous grassland, we also applied the method to a subset of plant species that are expected to be less influenced by sampling effects, and they also has a significant positive intra-plot correlation, which suggests that sampling effects are playing a minor role in the calcareous grassland as an explanation for the spatial aggregated of species. Overall, the results suggest that the deterministic ecological processes that do not contradict the neutral theory are more important than any possible deterministic ecological processes that contradict the neutral theory. Consequently, the hypothesis of neutrality could neither be rejected nor corroborated in the investigated grasslands. We suggest that the spatial aggregation in the sampled calcareous grassland is mainly caused by small local differences in abiotic factors or in the timing of gaps for recolonisation. This in turn may lead to different local niches (ecological adaptation or phenology of establishment from seeds) and possibly local exclusion of plant species by interspecific competition.     

Studies on the effects of bait and sampling intensity on trapping and estimating Wood mice, Apodemus sylvaticus

The effects of baiting a Longworth trap with whole oats and the density of traps on an area, or sampling intensity, on trapping and estimating Wood mice were studied on two neighbouring woodland plots in November 1971. Standard capture-mark-recapture (CMR) methods were used for two weeks followed by five nights of removal trapping.
The presence of bait significantly increased the likelihood of capturing marked and unmarked animals. By increasing the sampling intensity a greater proportion of the population was sampled, although the number of animals captured per trap night decreased. These results have been related to the "effective" number of traps on an area.
Observations on population structure, weather, movement and capturing marked and unmarked animals have been made. CMR population estimates closely resembled the cumulative number of individuals captured in each study and were for the main part lower than the estimates from the removal trapping carried out at the end of the studies.     

Growth rates of young-of-year shovelnose sturgeon in the Upper Missouri River

Information on growth during the larval and young‐of‐year life stages in natural river environments is generally lacking for most sturgeon species. In this study, methods for estimating ages and quantifying growth were developed for field‐sampled larval and young‐of‐year shovelnose sturgeon Scaphirhynchus platorynchus in the upper Missouri River. First, growth was assessed by partitioning samples of young‐of‐year shovelnose sturgeon into cohorts, and regressing weekly increases in cohort mean length on sampling date. This method quantified relative growth because ages of the cohorts were unknown. Cohort increases in mean length among sampling dates were positively related (P < 0.05, r² > 0.59 for all cohorts) to sampling date, and yielded growth rate estimates of 0.80–2.95 mm day⁻¹ (2003) and 0.44–2.28 mm day⁻¹ (2004). Highest growth rates occurred in the largest (and earliest spawned) cohorts. Second, a method was developed to estimate cohort hatch dates, thus age on date of sampling could be determined. This method included quantification of post‐hatch length increases as a function of water temperature (growth capacity; mm per thermal unit, mm TU⁻¹), and summation of mean daily water temperatures to achieve the required number of thermal units that corresponded to post‐hatch lengths of shovelnose sturgeon on sampling dates. For six of seven cohorts of shovelnose sturgeon analyzed, linear growth models (r² ≥ 0.65, P < 0.0001) or Gompertz growth models (r² ≥ 0.83, P < 0.0001) quantified length‐at‐age from hatch through 55 days post‐hatch (98–100 mm). Comparisons of length‐at‐age derived from the growth models indicated that length‐at‐age was greater for the earlier‐hatched cohorts than later‐hatched cohorts. Estimated hatch dates for different cohorts were corroborated based on the dates that newly‐hatched larval shovelnose sturgeon were sampled in the drift. These results provide the first quantification of growth dynamics for field‐sampled age‐0 shovelnose sturgeon in a natural river environment, and provide an accurate method for estimating age of wild‐caught individuals. Methods of age determination used in this study have applications to sturgeons in other regions, but require additional testing and validation.     

The ones we left behind: Comparing plot sampling and floristic habitat sampling for estimating bryophyte diversity

An efficient method for estimating bryophyte diversity in forest stands must consider more than just the dominant forest mesohabitat. We compared two methodologies commonly used for estimating diversity in forest ecosystems. Floristic habitat sampling (FHS) utilizes stratification of all forest mesohabitats, which includes the natural diversity of microhabitats found within and stratifies a mosaic of mesohabitats (e.g. forest, streams, seeps, and cliffs) and microhabitats (e.g. rocks logs, etc.) that are often not considered in forest research projects that use plot sampling to estimate species diversity. In Canadian cedar hemlock forest, FHS methodology recorded more than twice as many bryophyte species as plot sampling (PS). A comparison of the dominant forest mesohabitat concluded that plot sampling was not as efficient as FHS in estimating bryophyte diversity and that plot sampling can result in different interpretations of species diversity. Rare species ordination of stands sampled using FHS showed strong clustering of sites with respect to biogeoclimatic zones and age since the last major disturbance (fire or logging) as compared with rare species ordinations from PS data, which showed no delineation of stands along temporal gradients. Plot sampling has many useful applications in ecology, but floristic habitat sampling is more efficient for quantifying overall bryophyte diversity. FHS provides an excellent way to record a comprehensive list of species.     

Estimation of Spatiotemporal Neural Activity Using Radial Basis Function Networks

We report a method using radial basis function (RBF) networks to estimate the time evolution of population activity in topologically organized neural structures from single-neuron recordings. This is an important problem in neuroscience research, as such estimates may provide insights into systems-level function of these structures. Since single-unit neural data tends to be unevenly sampled and highly variable under similar behavioral conditions, obtaining such estimates is a difficult task. In particular, a class of cells in the superior colliculus called buildup neurons can have very narrow regions of saccade vectors for which they discharge at high rates but very large surround regions over which they discharge at low, but not zero, levels. Estimating the dynamic movement fields for these cells for two spatial dimensions at closely spaced timed intervals is a difficult problem, and no general method has been described that can be applied to all buildup cells. Estimation of individual collicular cells' spatiotemporal movement fields is a prerequisite for obtaining reliable two-dimensional estimates of the population activity on the collicular motor map during saccades. Therefore, we have developed several computational-geometry-based algorithms that regularize the data before computing a surface estimation using RBF networks. The method is then expanded to the problem of estimating simultaneous spatiotemporal activity occurring across the superior colliculus during a single movement (the inverse problem). In principle, this methodology could be applied to any neural structure with a regular, two-dimensional organization, provided a sufficient spatial distribution of sampled neurons is available.     

Bayesian inference of fine-scale recombination rates using population genomic data

Recently, several statistical methods for estimating fine-scale recombination rates using population samples have been developed. However, currently available methods that can be applied to large-scale data are limited to approximated likelihoods. Here, we developed a full-likelihood Markov chain Monte Carlo method for estimating recombination rate under a Bayesian framework. Genealogies underlying a sampling of chromosomes are effectively modelled by using marginal individual single nucleotide polymorphism genealogies related through an ancestral recombination graph. The method is compared with two existing composite-likelihood methods using simulated data.Simulation studies show that our method performs well for different simulation scenarios. The method is applied to two human population genetic variation datasets that have been studied by sperm typing. Our results are consistent with the estimates from sperm crossover analysis.     

Evaluating methods to quantify spatial variation in the velocity of biological invasions

Invading species rarely spread homogeneously through a landscape and invasion patterns typically display irregular frontal boundaries as the invasion progresses through space. Those irregular patterns are generally produced by local environmental factors that may slow or accelerate movement of the frontal boundary. While there is an abundant literature on species distribution modelling methods that quantify local suitability for species establishment, comparatively few studies have examined methods for measuring the local velocity of invasions that can then be statistically analysed in relation to spatially variable environmental factors. Previous studies have used simulations to compare different methods for estimating the overall rate of spread of an invasion. We adopted a similar approach of simulating invasions that resemble two real case‐studies, both in terms of their spatial resolution (i.e. considering the size of one cell as one km) and their spatial extent (> 600 000 km²). Simulations were sampled to compare how different methods used to measure local spread rate, namely the neighbouring, nearest distance and Delaunay methods, perform for spatio‐temporal comparisons. We varied the assessment using three levels of complexity of the spatio‐temporal pattern of invasion, three sample sizes (500, 1000 and 2000 points), three different spatial sampling patterns (stratified, random, aggregated), three interpolation methods (generalized linear model, kriging, thin plate spline regression) and two spatio‐temporal modelling structures (trend surface analysis and boundary displacement), resulting in a total of 486 different scenarios. The thin plate spline regression interpolation method, in combination with trend surface analysis, was found to provide the most robust local spread rate quantification as it was able to reliably accommodate different sampling conditions and invasion patterns. This best approach was successfully applied to two case‐studies, the invasion of France by the horse‐chestnut leafminer Cameraria ohridella and by the bluetongue virus, generally in agreement with previously published values of spread rates. Potential avenues for further research are discussed.