constrained ordination
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AbstractColonization of terrestrial environments by filamentous fungi relies on their ability to form networks that can forage for and connect resource patches. Despite the importance of these networks, ecologists rarely consider network features as functional traits because their measurement and interpretation are conceptually and methodologically difficult. To address these challenges, we have developed a pipeline to translate images of fungal mycelia, from both micro- and macro-scales, to weighted network graphs that capture ecologically relevant fungal behaviour. We focus on four properties that we hypothesize determine how fungi forage for resources, specifically: connectivity; relative construction cost; transport efficiency; and robustness against attack by fungivores. Constrained ordination and Pareto front analysis of these traits revealed that foraging strategies can be distinguished predominantly along a gradient of connectivity for micro- and macro-scale mycelial networks that is reminiscent of the qualitative ‘phalanx’ and ‘guerilla’ descriptors previously proposed in the literature. At one extreme are species with many inter-connections that increase the paths for multidirectional transport and robustness to damage, but with a high construction cost; at the other extreme are species with an opposite phenotype. Thus, we propose this approach represents a significant advance in quantifying ecological strategies for fungi using network information.

SummaryIn community ecology, unconstrained ordination can be used to predict latent variables from a multivariate dataset, which generated the observed species composition.Latent variables can be understood as ecological gradients, which are represented as a function of measured predictors in constrained ordination, so that ecologists can better relate species composition to the environment while reducing dimensionality of the predictors and the response data.However, existing constrained ordination methods do not explicitly account for information provided by species responses, so that they have the potential to misrepresent community structure if not all predictors are measured.We propose a new method for model-based ordination with constrained latent variables in the Generalized Linear Latent Variable Model framework, which incorporates both measured predictors and residual covariation to optimally represent ecological gradients. Simulations of unconstrained and constrained ordination show that the proposed method outperforms CCA and RDA.

AbstractBackgroundAt any particular location, frequencies of alleles in organisms that are associated with adaptive traits are expected to change in future climates through local adaption and migration, including assisted migration (human-implemented when climate change is more rapid than natural migration rates). Making the assumption that the baseline frequencies of alleles across environmental gradients can act as a predictor of patterns in changed climates (typically future but possibly paleo-climates), a methodology is provided by AlleleShift of predicting changes in allele frequencies at populations’ locations.MethodsThe prediction procedure involves a first calibration and prediction step through redundancy analysis (RDA), and a second calibration and prediction step through a generalized additive model (GAM) with a binomial family. As such, the procedure is fundamentally different to an alternative approach recently proposed to predict changes in allele frequencies from canonical correspondence analysis (CCA). My methodology of AlleleShift is also different in modelling and predicting allele counts through constrained ordination (not frequencies as in the CCA approach) and modelling both alleles for a locus (not solely the minor allele as in the CCA method; both methods were developed for diploid organisms where individuals are homozygous (AA or BB) or heterozygous (AB)). Whereas the GAM step ensures that allele frequencies are in the range of 0 to 1 (negative values are sometimes predicted by the RDA and CCA approaches), the RDA step is based on the Euclidean distance that is also the typical distance used in Analysis of Molecular Variance (AMOVA). The AlleleShift::amova.rda enables users to verify that the same ‘mean-square’ values are calculated by AMOVA and RDA, and gives the same final statistics with balanced data.ResultsBesides data sets with predicted frequencies, AlleleShift provides several visualization methods to depict the predicted shifts in allele frequencies from baseline to changed climates. These include ‘dot plot’ graphics (function shift.dot.ggplot), pie diagrams (shift.pie.ggplot), moon diagrams (shift.moon.ggplot), ‘waffle’ diagrams (shift.waffle.ggplot) and smoothed surface diagrams of allele frequencies of baseline or future patterns in geographical space (shift.surf.ggplot). As these were generated through the ggplot2 package, methods of generating animations for a climate change time series are straightforward, as shown in the documentation of AlleleShift and in the supplementary materials. In addition, graphical methods are provided of showing shifts of populations in environmental space (population.shift) and to assess how well the predicted frequencies reflect the original frequencies for the baseline climate (freq.ggplot).AvailabilityAlleleShift is available as an open-source R package from https://github.com/RoelandKindt/AlleleShift. Genetic input data is expected to be in the adegenet::genpop format, which can be generated from the adegenet::genind format. Climate data is available from various resources such as WorldClim and Envirem.

AbstractCommunity ecologists and macroecologists have long sought to evaluate the importance of environmental conditions and other drivers in determining species composition across sites. Different methods have been used to estimate species-environment relationships while accounting for or partitioning the variation attributed to environment and spatial autocorrelation, but their differences and respective reliability remain poorly known. We compared the performance of four families of statistical methods in estimating the contribution of the environment and space to explain variation in multi-species occurrence and abundance. These methods included distance-based regression (MRM), constrained ordination (RDA and CCA), generalised linear and additive models (GLM, GAM), and treebased machine learning (regression trees, boosted regression trees, and random forests). Depending on the method, the spatial model consisted of either Moran’s Eigenvector Maps (MEM; in constrained ordination and GLM), smooth spatial splines (in GAM), or tree-based non-linear modelling of spatial coordinates (in machine learning). We simulated typical ecological data to assess the methods’ performance in (1) fitting environmental and spatial effects, and (2) partitioning the variation explained by the environmental and spatial effects. Differences in the fitting performance among major model types – (G)LM, GAM, machine learning – were reflected in the variation partitioning performance of the different methods. Machine learning methods, namely boosted regression trees, performed overall better. GAM performed similarly well, though likelihood optimisation did not converge for some empirical test data. The remaining methods performed worse under most simulated data variations (depending on the type of species data, sample size and coverage, autocorrelation range, and response shape). Our results suggest that tree-based machine learning is a robust approach that can be widely used for variation partitioning. Our recommendations apply to single-species niche models, community ecology, and macroecology studies aiming at disentangling the relative contributions of space vs. environment and other drivers of variation in site-by-species matrices.

AbstractExplorative visualization techniques provide a first summary of microbiome read count datasets through dimension reduction. A plethora of dimension reduction methods exists, but many of them focus primarily on sample ordination, failing to elucidate the role of the bacterial species. Moreover, implicit but often unrealistic assumptions underlying these methods fail to account for overdispersion and differences in sequencing depth, which are two typical characteristics of sequencing data. We combine log-linear models with a dispersion estimation algorithm and flexible response function modelling into a framework for unconstrained and constrained ordination. The method allows easy filtering of technical confounders. As opposed to most existing ordination methods, the assumptions underlying the method are stated explicitly and can be verified using simple diagnostics. The combination of unconstrained and constrained ordination in the same framework is unique in the field and greatly facilitates microbiome data exploration. We illustrate the advantages of our method on simulated and real datasets, while pointing out flaws in existing methods. The algorithms for fitting and plotting are available in the R-packageRCM.

AbstractBackgroundUsing metagenomics to determine animal diet offers a new and promising alternative to current methods. Here we show that rapid and inexpensive diet quantification is possible through metagenomic sequencing with the portable Oxford Nanopore Technologies (ONT) MinION. Using an amplification-free approach, we profiled the stomach contents from wild-caught rats.ResultsWe conservatively identified diet items from over 50 taxonomic orders, ranging across nine phyla that include plants, vertebrates, invertebrates, and fungi. This highlights the wide range of taxa that can be identified using this simple approach. We calibrate the accuracy of this method by comparing the characteristics of reads matching the ground-truth host genome (rat) to those matching diet items, and show that at the family-level, false positive taxon assignments are approximately 97.5% accurate. We also suggest a way to mitigate for database biases in metagenomic approaches. Finally, we implement a constrained ordination analysis and show that we can identify the sampling location of an individual rat within tens of kilometres based on diet content alone.ConclusionsThis work establishes proof-of-principle for long-read metagenomic methods in quantitative diet analysis. We show that diet content can be quantified even with limited expertise, using a simple, amplification free workflow and a relatively inexpensive and accessible next generation sequencing method. Continued increases in the accuracy and throughput of ONT sequencing, along with improved genomic databases, suggests that a metagenomic approach to quantification of animal diets will become an important method in the future.

AbstractIdentifying adaptive loci can provide insight into the mechanisms underlying local adaptation. Genotype-environment association (GEA) methods, which identify these loci based on correlations between genetic and environmental data, are particularly promising. Univariate methods have dominated GEA, despite the high dimensional nature of genotype and environment. Multivariate methods, which analyze many loci simultaneously, may be better suited to these data since they consider how sets of markers covary in response to environment. These methods may also be more effective at detecting adaptive processes that result in weak, multilocus signatures. Here, we evaluate four multivariate methods, and five univariate and differentiation-based approaches, using published simulations of multilocus selection. We found that Random Forest performed poorly for GEA. Univariate GEAs performed better, but had low detection rates for loci under weak selection. Constrained ordinations showed a superior combination of low false positive and high true positive rates across all levels of selection. These results were robust across the demographic histories, sampling designs, sample sizes, and levels of population structure tested. The value of combining detections from different methods was variable, and depended on study goals and knowledge of the drivers of selection. Reanalysis of genomic data from gray wolves highlighted the unique, covarying sets of adaptive loci that could be identified using redundancy analysis, a constrained ordination. Although additional testing is needed, this study indicates that constrained ordinations are an effective means of detecting adaptation, including signatures of weak, multilocus selection, providing a powerful tool for investigating the genetic basis of local adaptation.