Are geometric morphometric analyses replicable? Evaluating landmark measurement error and its impact on extant and fossil Microtus classification.

Geometric morphometric analyses are frequently employed to quantify biological shape and shape variation. Despite the popularity of this technique, quantification of measurement error in geometric morphometric datasets and its impact on statistical results is seldom assessed in the literature. Here, we evaluate error on 2D landmark coordinate configurations of the lower first molar of five North American Microtus (vole) species. We acquired data from the same specimens several times to quantify error from four data acquisition sources: specimen presentation, imaging devices, interobserver variation, and intraobserver variation. We then evaluated the impact of those errors on linear discriminant analysis-based classifications of the five species using recent specimens of known species affinity and fossil specimens of unknown species affinity. Results indicate that data acquisition error can be substantial, sometimes explaining >30% of the total variation among datasets. Comparisons of datasets digitized by different individuals exhibit the greatest discrepancies in landmark precision, and comparison of datasets photographed from different presentation angles yields the greatest discrepancies in species classification results. All error sources impact statistical classification to some extent. For example, no two landmark dataset replicates exhibit the same predicted group memberships of recent or fossil specimens. Our findings emphasize the need to mitigate error as much as possible during geometric morphometric data collection. Though the impact of measurement error on statistical fidelity is likely analysis-specific, we recommend that all geometric morphometric studies standardize specimen imaging equipment, specimen presentations (if analyses are 2D), and landmark digitizers to reduce error and subsequent analytical misinterpretations

Allometric trajectories of body and head morphology in three sympatric Arctic charr (Salvelinus alpinus (L.)) morphs

A study of body and head development in three sympatric reproductively isolated Arctic charr (Salvelinus alpinus (L.)) morphs from a subarctic lake (Skogsfjordvatn, northern Norway) revealed allometric trajectories that resulted in morphological differences. The three morphs were ecologically assigned to a littoral omnivore, a profundal benthivore and a profundal piscivore, and this was confirmed by genetic analyses (microsatellites). Principal component analysis was used to identify the variables responsible for most of the morphological variation of the body and head shape. The littoral omnivore and the profundal piscivore morph had convergent allometric trajectories for the most important head shape variables, developing bigger mouths and relatively smaller eyes with increasing head size. The two profundal morphs shared common trajectories for the variables explaining most of the body and head shape variation, namely head size relative to body size, placement of the dorsal and pelvic fins, eye size and mouth size. In contrast, the littoral omnivore and the profundal benthivore morphs were not on common allometric trajectories for any of the examined variables. The findings suggest that different selective pressures could have been working on traits related to their trophic niche such as habitat and diet utilization of the three morphs, with the two profundal morphs experiencing almost identical environmental conditions

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

A Field Comes of Age: Geometric Morphometrics in the 21st Century

Twenty years ago, Rohlf and Marcus proclaimed that a revolution in morphometrics was underway, where classic analyses based on sets of linear distances were being supplanted by geometric approaches making use of the coordinates of anatomical landmarks. Since that time the field of geometric morphometrics has matured into a rich and cohesive discipline for the study of shape variation and covariation. The development of the field is identified with the Procrustes paradigm, a methodological approach to shape analysis arising from the intersection of the statistical shape theory and analytical procedures for obtaining shape variables from landmark data. In this review we describe the Procrustes paradigm and the current methodological toolkit of geometric morphometrics. We highlight some of the theoretical advances that have occurred over the past ten years since our prior review (Adams et al., 2004), what types of anatomical structures are amenable to these approaches, and how they extend the reach of geometric morphometrics to more specialized applications for addressing particular biological hypotheses. We end with a discussion of some possible areas that are fertile ground for future development in the field

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