Measures of precision for dissimilarity‐based multivariate analysis of ecological communities

Ecological studies require key decisions regarding the appropriate size and number of sampling units. No methods currently exist to measure precision for multivariate assemblage data when dissimilarity‐based analyses are intended to follow. Here, we propose a pseudo multivariate dissimilarity‐based standard error (MultSE) as a useful quantity for assessing sample‐size adequacy in studies of ecological communities. Based on sums of squared dissimilarities, MultSE measures variability in the position of the centroid in the space of a chosen dissimilarity measure under repeated sampling for a given sample size. We describe a novel double resampling method to quantify uncertainty in MultSE values with increasing sample size. For more complex designs, values of MultSE can be calculated from the pseudo residual mean square of a permanova model, with the double resampling done within appropriate cells in the design. R code functions for implementing these techniques, along with ecological examples, are provided.     

一种模型模拟结果的统计检验方法

模拟结果的准确性是衡量生态学模型是否成功的关键,但采用统计学方法判别模型模拟结果与观察值相符程度的报道较少。根据两个直线回归方程能否合并为一个方程的统计学检验方法,提出了通过检验观察值与模拟值直线回归方程和1∶1直线方程截距与斜率是否相同,进而在统计显著水平上判断生态学模型模拟值与观察值一致性的统计学检验方法。数据检验表明,此方法可以较好解决判断生态学模型模拟结果准确性的问题。     

A new multivariate zero‐adjusted Poisson model with applications to biomedicine

Recently, although advances were made on modeling multivariate count data, existing models really has several limitations: (i) The multivariate Poisson log‐normal model (Aitchison and Ho, 1989) cannot be used to fit multivariate count data with excess zero‐vectors; (ii) The multivariate zero‐inflated Poisson (ZIP) distribution (Li et al., 1999) cannot be used to model zero‐truncated/deflated count data and it is difficult to apply to high‐dimensional cases; (iii) The Type I multivariate zero‐adjusted Poisson (ZAP) distribution (Tian et al., 2017) could only model multivariate count data with a special correlation structure for random components that are all positive or negative. In this paper, we first introduce a new multivariate ZAP distribution, based on a multivariate Poisson distribution, which allows the correlations between components with a more flexible dependency structure, that is some of the correlation coefficients could be positive while others could be negative. We then develop its important distributional properties, and provide efficient statistical inference methods for multivariate ZAP model with or without covariates. Two real data examples in biomedicine are used to illustrate the proposed methods.     

Co‐occurrence is not evidence of ecological interactions

There is a rich amount of information in co‐occurrence (presence–absence) data that could be used to understand community assembly. This proposition first envisioned by Forbes (1907) and then Diamond (1975) prompted the development of numerous modelling approaches (e.g. null model analysis, co‐occurrence networks and, more recently, joint species distribution models). Both theory and experimental evidence support the idea that ecological interactions may affect co‐occurrence, but it remains unclear to what extent the signal of interaction can be captured in observational data. It is now time to step back from the statistical developments and critically assess whether co‐occurrence data are really a proxy for ecological interactions. In this paper, we present a series of arguments based on probability, sampling, food web and coexistence theories supporting that significant spatial associations between species (or lack thereof) is a poor proxy for ecological interactions. We discuss appropriate interpretations of co‐occurrence, along with potential avenues to extract as much information as possible from such data.     

Modelling seasonal changes in the distribution of Common Quail Coturnix coturnix in farmland landscapes using remote sensing

Species’ distribution models are widely used in landscape ecology but usually lack explicit information about species’ responses to ecosystem dynamics, leading to uncertainty when applied to the prediction of seasonal change in distributions. In this study, we aimed to build a species’ distribution model for the Common Quail Coturnix coturnix, a farmland species that shows changes in its distribution in response to seasonal changes in habitat suitability. During the course of three breeding seasons we collected temporal replicates of presence–absence data in 13 sampling locations in four countries (Morocco, Portugal, Spain and France). We used generalized linear mixed models to relate the species’ presence or absence to environmental variables and to the normalized difference vegetation index at each sampling location through the seasons, the latter variable being an indicator of within‐ and between‐season habitat changes. The preferred model showed that occurrence was highly dependent on habitat changes associated with crop seasonality, as measured by the normalized difference vegetation index. Common Quail selected areas with dense vegetation and warm climate and tracked spatial changes in these two parameters. The model allows accurate mapping of within‐ and between‐season distribution changes. Such changes are related to habitat variations caused mainly by drought and agricultural practices. Our results demonstrate that seasonal changes in farmland ecosystems can be incorporated into a simple distribution model, and our approach could be applied to other species to predict the effects of agricultural changes on the distribution of birds inhabiting farmland landscapes.     

A new mixed‐effects regression model for the analysis of zero‐modified hierarchical count data

Count data sets are traditionally analyzed using the ordinary Poisson distribution. However, such a model has its applicability limited as it can be somewhat restrictive to handle specific data structures. In this case, it arises the need for obtaining alternative models that accommodate, for example, (a) zero‐modification (inflation or deflation at the frequency of zeros), (b) overdispersion, and (c) individual heterogeneity arising from clustering or repeated (correlated) measurements made on the same subject. Cases (a)–(b) and (b)–(c) are often treated together in the statistical literature with several practical applications, but models supporting all at once are less common. Hence, this paper's primary goal was to jointly address these issues by deriving a mixed‐effects regression model based on the hurdle version of the Poisson–Lindley distribution. In this framework, the zero‐modification is incorporated by assuming that a binary probability model determines which outcomes are zero‐valued, and a zero‐truncated process is responsible for generating positive observations. Approximate posterior inferences for the model parameters were obtained from a fully Bayesian approach based on the Adaptive Metropolis algorithm. Intensive Monte Carlo simulation studies were performed to assess the empirical properties of the Bayesian estimators. The proposed model was considered for the analysis of a real data set, and its competitiveness regarding some well‐established mixed‐effects models for count data was evaluated. A sensitivity analysis to detect observations that may impact parameter estimates was performed based on standard divergence measures. The Bayesian ‐value and the randomized quantile residuals were considered for model diagnostics.     

Raising the bar for the next generation of biological atlases: using existing data to inform the design and implementation of atlas monitoring

Selecting a sampling design to monitor multiple species across a broad geographical region can be a daunting task and often involves tradeoffs between limited resources and the accurate estimation of population abundance and occurrence. Since the 1950s, biological atlases have been implemented in various regions to document the occurrence of plant and animal species. As next‐generation atlases repeat original surveys, investigators often seek to raise the rigour of atlases by incorporating species abundances. We present a repeatable framework that incorporates existing monitoring data, hierarchical modelling and sampling simulations to augment existing atlas occurrence and breeding status maps with a secondary sampling of species abundances. Using existing information on three bird species with varying abundance and detectability, we evaluated several sampling scenarios for the 2nd Wisconsin Breeding Bird Atlas. In general, we found that most sampling schemes produced accurate mean statewide abundance estimates for species with medium to high abundance and detection probability, but estimates varied significantly for species with low abundance and low detection probability. Our approach provided a statewide point‐count sampling design that: provided precise and unbiased abundance estimates for species of varied prevalence and detectability; ensured suitable spatial coverage across the state and its habitats; and reduced spending on total survey costs. Our framework could benefit investigators conducting atlases and other broad‐scale avian surveys that seek to add systematic, multi‐species sampling for estimating density and abundance across broad geographical regions.     

Population assessment using multivariate time‐series analysis: A case study of rockfishes in Puget Sound

Estimating a population's growth rate and year‐to‐year variance is a key component of population viability analysis (PVA ). However, standard PVA methods require time series of counts obtained using consistent survey methods over many years. In addition, it can be difficult to separate observation and process variance, which is critical for PVA . Time‐series analysis performed with multivariate autoregressive state‐space (MARSS ) models is a flexible statistical framework that allows one to address many of these limitations. MARSS models allow one to combine surveys with different gears and across different sites for estimation of PVA parameters, and to implement replication, which reduces the variance‐separation problem and maximizes informational input for mean trend estimation. Even data that are fragmented with unknown error levels can be accommodated. We present a practical case study that illustrates MARSS analysis steps: data choice, model set‐up, model selection, and parameter estimation. Our case study is an analysis of the long‐term trends of rockfish in Puget Sound, Washington, based on citizen science scuba surveys, a fishery‐independent trawl survey, and recreational fishery surveys affected by bag‐limit reductions. The best‐supported models indicated that the recreational and trawl surveys tracked different, temporally independent assemblages that declined at similar rates (an average of ?3.8% to ?3.9% per year). The scuba survey tracked a separate increasing and temporally independent assemblage (an average of 4.1% per year). Three rockfishes (bocaccio, canary, and yelloweye) are listed in Puget Sound under the US Endangered Species Act (ESA ). These species are associated with deep water, which the recreational and trawl surveys sample better than the scuba survey. All three ESA ‐listed rockfishes declined as a proportion of recreational catch between the 1970s and 2010s, suggesting that they experienced similar or more severe reductions in abundance than the 3.8–3.9% per year declines that were estimated for rockfish populations sampled by the recreational and trawl surveys.     

Floristic inventory and diversity assessment of a lowland African Montane Rainforest at Korup,Cameroon and implications for conservation

Twenty modified‐Whittaker plots were stratified at different sampling locations from February to May of 2008 in the central zone of Korup National Park, Cameroon. Our interest was to assess floristic diversity and investigate their relationship with environmental variables. Diversity profiles and rank abundance–curves were used for diversity analysis while canonical correspondence analysis and species–response curves were used to investigate the relationships between the response and explanatory variables. Of the 66 families identified, the Rubiaceae (999 species) were the most abundant. The Sterculiaceae (basal area = 10.482 m² ha^?1) were the dominant family, while the co‐dominant families included the Ebenaceae (basal area = 9.092 m² ha^?1) and the Euphorbiaceae (basal area = 8.168 m² ha^?1). Soil variables explained 54.3% of total variation in family distribution. Canonical axes were related to different environmental gradients: axis1 was related to increasing canopy cover (r = 0.6951); axis 2, increasing Magnesium (r = 0.8465) and effective cation exchange capacity (r = 0.5899); axis 3, increasing effective cation exchange capacity (r = 0.5536); while axis 4, increasing Phosphorus concentration (r = 0.5232). Our results demonstrate the advantage which diversity profiles have over single or combination of indices, and the importance of using a combination of methodologies in diversity analysis.     

Raw data graphing: an informative but under‐utilized tool for the analysis of multivariate abundances

Abstract In exploring the relationship between multivariate abundance data and environmental variables, a rarely used approach is to graph raw data separately for each different taxon. It is proposed that such raw data graphs become part of the standard toolset for graphing and analysing multivariate abundances. The key advantage of this approach is that axis scales have quantitative interpretations, enabling quantitative interpretation of patterns in abundance. In contrast, ordinations only present qualitative information. Ordinations are useful for inferring overall, qualitative patterns and raw data graphing is a complementary tool of greater use for answering more specific questions, aimed at a deeper understanding the ecology of a community. It is demonstrated using some well‐known examples that our understanding of the nature of associations can be considerably improved by using raw data graphs, even when only plotting a subset of variables. One example describes how an often‐cited dataset has been misinterpreted in key methodological papers, because data were interpreted from ordinations alone, with no consideration of plots of the raw data.     

A composite likelihood approach to latent multivariate Gaussian modeling of SNP data with application to genetic association testing

Many statistical tests have been proposed for case-control data to detect disease association with multiple single nucleotide polymorphisms (SNPs) in linkage disequilibrium. The main reason for the existence of so many tests is that each test aims to detect one or two aspects of many possible distributional differences between cases and controls, largely due to the lack of a general and yet simple model for discrete genotype data. Here we propose a latent variable model to represent SNP data: the observed SNP data are assumed to be obtained by discretizing a latent multivariate Gaussian variate. Because the latent variate is multivariate Gaussian, its distribution is completely characterized by its mean vector and covariance matrix, in contrast to much more complex forms of a general distribution for discrete multivariate SNP data. We propose a composite likelihood approach for parameter estimation. A direct application of this latent variable model is to association testing with multiple SNPs in a candidate gene or region. In contrast to many existing tests that aim to detect only one or two aspects of many possible distributional differences of discrete SNP data, we can exclusively focus on testing the mean and covariance parameters of the latent Gaussian distributions for cases and controls. Our simulation results demonstrate potential power gains of the proposed approach over some existing methods.     

Importance of temporal variability at different spatial scales for diversity of floodplain aquatic communities

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Lessons learnt on the analysis of large sequence data in animal genomics

The ’omics revolution has made a large amount of sequence data available to researchers and the industry. This has had a profound impact in the field of bioinformatics, stimulating unprecedented advancements in this discipline. Mostly, this is usually looked at from the perspective of human ’omics, in particular human genomics. Plant and animal genomics, however, have also been deeply influenced by next‐generation sequencing technologies, with several genomics applications now popular among researchers and the breeding industry. Genomics tends to generate huge amounts of data, and genomic sequence data account for an increasing proportion of big data in biological sciences, due largely to decreasing sequencing and genotyping costs and to large‐scale sequencing and resequencing projects. The analysis of big data poses a challenge to scientists, as data gathering currently takes place at a faster pace than does data processing and analysis, and the associated computational burden is increasingly taxing, making even simple manipulation, visualization and transferring of data a cumbersome operation. The time consumed by the processing and analysing of huge data sets may be at the expense of data quality assessment and critical interpretation. Additionally, when analysing lots of data, something is likely to go awry—the software may crash or stop—and it can be very frustrating to track the error. We herein review the most relevant issues related to tackling these challenges and problems, from the perspective of animal genomics, and provide researchers that lack extensive computing experience with guidelines that will help when processing large genomic data sets.     

The derivation of log‐transformed abundance data for the quantitative analysis of macroinvertebrate traits – an addendum to ‘A macroecological perspective of trait patterns in stream communities’ by Heino et al. ()

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Predictive power of food web models based on body size decreases with trophic complexity

Food web models parameterised using body size show promise to predict trophic interaction strengths (IS) and abundance dynamics. However, this remains to be rigorously tested in food webs beyond simple trophic modules, where indirect and intraguild interactions could be important and driven by traits other than body size. We systematically varied predator body size, guild composition and richness in microcosm insect webs and compared experimental outcomes with predictions of IS from models with allometrically scaled parameters. Body size was a strong predictor of IS in simple modules (r² = 0.92), but with increasing complexity the predictive power decreased, with model IS being consistently overestimated. We quantify the strength of observed trophic interaction modifications, partition this into density‐mediated vs. behaviour‐mediated indirect effects and show that model shortcomings in predicting IS is related to the size of behaviour‐mediated effects. Our findings encourage development of dynamical food web models explicitly including and exploring indirect mechanisms.