Seeing distinct groups where there are none : spurious patterns from between-group PCA

Using sampling experiments, we found that, when there are fewer groups than variables, between-groups PCA (bgPCA) may suggest surprisingly distinct differences among groups for data in which none exist. While apparently not noticed before, the reasons for this problem are easy to understand. A bgPCA captures the g-1 dimensions of variation among the g group means, but only a fraction of the∑ni-g  dimensions of within-group variation ( are the sample sizes), when the number of variables, p, is greater than g-1. This introduces a distortion in the appearance of the bgPCA plots because the within-group variation will be underrepresented, unless the variables are sufficiently correlated so that the total variation can be accounted for with just g-1 dimensions. The effect is most obvious when sample sizes are small relative to the number of variables, because smaller samples spread out less, but the distortion is present even for large samples. Strong covariance among variables largely reduces the magnitude of the problem, because it effectively reduces the dimensionality of the data and thus enables a larger proportion of the within-group variation to be accounted for within the g-1-dimensional space of a bgPCA. The distortion will still be relevant though its strength will vary from case to case depending on the structure of the data (p, g, covariances etc.). These are important problems for a method mainly designed for the analysis of variation among groups when there are very large numbers of variables and relatively small samples. In such cases, users are likely to conclude that the groups they are comparing are much more distinct than they really are.  Having many variables but just small sample sizes is a common problem in fields ranging from morphometrics (as in our examples) to molecular analyses

Ecological and evolutionary factors in the morphological diversification of South American spiny rats

Understanding the processes underlying morphological diversification is a central goal in ecology and evolutionary biology and requires the integration of information about phylogenetic divergence and ecological niche diversity. In the present study, we use geometric morphometrics and comparative methods to investigate morphological diversification in Neotropical spiny rats of the family Echimyidae. Morphological diversification is studied as shape variation in the skull, comprising a structure composed of four distinct units: vault, base, orognathofacial complex, and mandible. We demonstrate association among patterns of variation in shape in different cranial units, levels of phylogenetic divergence, and ecological niche diversification. At the lower level of phylogenetic divergence, there is significant and positive concordance between patterns of phylogenetic divergence and cranial shape variation in all cranial units. This concordance may be attributable to the phylogenetic and shape distances being calculated between species that occupy the same niche. At higher phylogenetic levels of divergence and with ecological niche diversity, there is significant concordance between shape variation in all four cranial units and the ecological niches. In particular, the orognathofacial complex revealed the most significant association between shape variation and ecological niche diversity. This association may be explained by the great functional importance of the orognathofacial complex.Facultad de Ciencias Naturales y Muse

Analysis of temporal and spatial phytoplankton variability in a Long Island salt marsh

A study of phytoplankton and related variables in a Long Island salt marsh was designed to incorporate three major sources of variation in the sampling regime: spatial, short-term temporal, and long-term temporal. The combination of multivariate (MANOVA and factor analysis) and univariate (ANOVA) data analyses was used to examine the relative importance of each source of variation in 11 variables and to aid in the ecological interpretation of the data. MANOVA confirmed that all three sources of variation were significant with temporal variation (weekly sampling and at different times of the day) more important than spatial variation (sampling at different stations). The analyses also indicated that sampling a dynamic, tidally-driven system, such as a small salt marsh, cannot be carried out on a once-per-day basis; tidal flushing and diurnal changes in primary production induce a large amount of variation into the concentrations of phytoplankton and related variables within the salt marsh.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/24393/1/0000663.pd

Ecological and evolutionary factors in the morphological diversification of South American spiny rats

Understanding the processes underlying morphological diversification is a central goal in ecology and evolutionary biology and requires the integration of information about phylogenetic divergence and ecological niche diversity. In the present study, we use geometric morphometrics and comparative methods to investigate morphological diversification in Neotropical spiny rats of the family Echimyidae. Morphological diversification is studied as shape variation in the skull, comprising a structure composed of four distinct units: vault, base, orognathofacial complex, and mandible. We demonstrate association among patterns of variation in shape in different cranial units, levels of phylogenetic divergence, and ecological niche diversification. At the lower level of phylogenetic divergence, there is significant and positive concordance between patterns of phylogenetic divergence and cranial shape variation in all cranial units. This concordance may be attributable to the phylogenetic and shape distances being calculated between species that occupy the same niche. At higher phylogenetic levels of divergence and with ecological niche diversity, there is significant concordance between shape variation in all four cranial units and the ecological niches. In particular, the orognathofacial complex revealed the most significant association between shape variation and ecological niche diversity. This association may be explained by the great functional importance of the orognathofacial complex.Facultad de Ciencias Naturales y Muse

Morphological Analysis of Size and Shape (MASS): An Integrative Software Program for Morphometric Analyses of Leaves

Morphometric analysis is a common approach for comparing and categorizing botanical samples; however, completing a suite of analyses using existing tools may require a multi-stage, multi-program process. To facilitate streamlined analysis within a single program, Morphological Analysis of Size and Shape (MASS) for leaves was developed. Its utility is demonstrated using exemplar leaf samples from Acer saccharum, Malus domestica, and Lithospermum

Connectivity Conservation and Endangered Species Recovery: A Study in the Challenges of Defining Conservation-Reliant Species

Many species listed under the US Endangered Species Act (ESA) face continuing threats and will require intervention to address those threats for decades. These species, which have been termed conservation-reliant, pose a challenge to the ESA\u27s mandate for recovery of self-sustaining populations. Most references to conservation-reliant species by federal agencies involve the restoration of population connectivity. However, the diverse threats to connectivity faced by different species have contrasting implications in the context of the ESA\u27s mandate. For species facing long-term threats from invasive species or climate change, restoration of natural dispersal may not be technically feasible in the foreseeable future. For other species, restoration of natural dispersal is feasible, but carries economic and political cost. Federal agencies have used a broad definition of conservation reliance to justify delisting of species in the latter group even if they remain dependent on artificial translocation. Distinguishing the two groups better informs policy by distinguishing the technical challenges posed by novel ecological stressors from normative questions such as the price society is willing to pay to protect biodiversity, and the degree to which we should grow accustomed to direct human intervention in species\u27 life cycles as a component of conservation in the Anthropocene Epoch

By hook or by crook? Morphometry, competition and cooperation in rodent sperm

Background Sperm design varies enormously across species and sperm competition is thought to be a major factor influencing this variation. However, the functional significance of many sperm traits is still poorly understood. The sperm of most murid rodents are characterised by an apical hook of the sperm head that varies markedly in extent across species. In the European woodmouse Apodemus sylvaticus (Muridae), the highly reflected apical hook of sperm is used to form sperm groups, or “trains,” which exhibited increased swimming velocity and thrusting force compared to individual sperm. Methodology/Principal Findings Here we use a comparative study of murine rodent sperm and demonstrate that the apical hook and sperm cooperation are likely to be general adaptations to sperm competition in rodents. We found that species with relatively larger testes, and therefore more intense sperm competition, have a longer, more reflected apical sperm hook. In addition, we show that sperm groups also occur in rodents other than the European woodmouse. Conclusions Our results suggest that in rodents sperm cooperation is more widespread than assumed so far and highlight the importance of diploid versus haploid selection in the evolution of sperm design and function

Drift versus selection as drivers of phenotypic divergence at small spatial scales: The case of Belgjarskógur threespine stickleback

Divergence in phenotypic traits is facilitated by a combination of natural selection, phenotypic plasticity, gene flow, and genetic drift, whereby the role of drift is expected to be particularly important in small and isolated populations. Separating the components of phenotypic divergence is notoriously difficult, particularly for multivariate phenotypes. Here, we assessed phenotypic divergence of threespine stickleback (Gasterosteus aculeatus) across 19 semi‐interconnected ponds within a small geographic region (~7.5 km2) using comparisons of multivariate phenotypic divergence (PST), neutral genetic (FST), and environmental (EST) variation. We found phenotypic divergence across the ponds in a suite of functionally relevant phenotypic traits, including feeding, defense, and swimming traits, and body shape (geometric morphometric). Comparisons of PSTs with FSTs suggest that phenotypic divergence is predominantly driven by neutral processes or stabilizing selection, whereas phenotypic divergence in defensive traits is in accordance with divergent selection. Comparisons of population pairwise PSTs with ESTs suggest that phenotypic divergence in swimming traits is correlated with prey availability, whereas there were no clear associations between phenotypic divergence and environmental difference in the other phenotypic groups. Overall, our results suggest that phenotypic divergence of these small populations at small geographic scales is largely driven by neutral processes (gene flow, drift), although environmental determinants (natural selection or phenotypic plasticity) may play a role.ISSN:2045-775