Geometric estimates of heritability in biological shape

The recently developed geometric morphometrics methods represent an important contribution of statistics and geometry to the study of biological shapes. We propose simple protocols using shape distances that incorporate geometric techniques into linear quantitative genetic models that should provide insights into the contribution of genetics to shape variation in organisms. The geometric approaches use Procrustes distances in a curved shape space and distances in tangent spaces within and among families to estimate shape heritability. We illustrate the protocols with an example of wing shape variation in the honeybee, Apis mellifera. The heritability of overall shape variation was small, but some localized components depicting shape changes on distal wing regions showed medium to large heritabilities. The genetic variance-covariance matrix of the geometric shape variables was significantly correlated with the phenotypic shape variance-covariance matrix. A comparison of the results of geometric methods with the traditional multivariate analysis of interlandmark distances indicated that even with a larger dimensionality, the interlandmark distances were not as rich in shape information as the landmark coordinates. Quantitative genetics studies of shape should greatly benefit from the application of geometric methods.     

Developmental Dynamics and G-Matrices: Can Morphometric Spaces be Used to Model Phenotypic Evolution?

Modern morphometrics, especially geometric morphometrics, is a powerful tool for modeling the evolution and development of the phenotype. Complicated morphological transformations can be simulated by using standard evolutionary genetic equations for processes such as selection and drift in the same morphospaces that are used for empirical morphometric studies. Such applications appear to be consistent with the theory of quantitative evolution of the phenotype. Nevertheless, concerns exist whether simulations of phenotypic changes directly in morphospaces is realistic because trajectories traced in such spaces describe continuous gradations in the phenotype and because the gain and loss of structures is often impossible because morphospaces are necessarily constructed from variables shared in common by all the phenotypes being considered. Competing models of phenotypic change emphasize morphological discontinuity and novelty. Recently developed models of phenotypic evolution that introduce a “phenotypic landscape” between evolutionary genetic constructs like the adaptive landscape and morphospace may correct this shortcoming.     

How trophic interaction strength depends on traits

A key problem in community ecology is to understand how individual-level traits give rise to population-level trophic interactions. Here, we propose a synthetic framework based on ecological considerations to address this question systematically. We derive a general functional form for the dependence of trophic interaction coefficients on trophically relevant quantitative traits of consumers and resources. The derived expression encompasses—and thus allows a unified comparison of—several functional forms previously proposed in the literature. Furthermore, we show how a community’s, potentially low-dimens ional, effective trophic niche space is related to its higher-dimensional phenotypic trait space. In this manner, we give ecological meaning to the notion of the “dimensionality of trophic niche space.” Our framework implies a method for directly measuring this dimensionality. We suggest a procedure for estimating the relevant parameters from empirical data and for verifying that such data matches the assumptions underlying our derivation.     

Biometrics,biomathematics and the morphometric synthesis

At the core of contemporarymorphometrics—the quantitative study of biological shape variation—is a synthesis of two originally divergent methodological styles. One contributory tradition is the multivariate analysis of covariance matrices originally developed as biometrics and now dominant across a broad expanse of applied statistics. This approach, couched solely in the linear geometry of covariance structures, ignores biomathematical aspects of the original measurements. The other tributary emphasizes the direct visualization of changes in biological form. However, making objective the biological meaning of the features seen in those diagrams was always problematical; also, the representation of variation, as distinct from pairwise difference, proved infeasible. To combine these two variants of biomathematical modeling into a valid praxis for quantitative studies of biological shape was a goal earnestly sought though most of this century. That goal was finally achieved in the 1980s when techniques from mathematical statistics, multivariate biometrics, non-Euclidean geometry and computer graphics were combined in a coherent new system of tools for the complete regionalized quantitative analysis oflandmark points together with the biomedical images in which they are seen. In this morphometric synthesis, correspondence of landmarks (biologically labeled geometric points, like “bridge of the nose”) across specimens is taken as a biomathematical primitive. The shapes of configurations of landmarks are defined as equivalence classes with respect to the Euclidean similarity group and then represented as single points in David Kendall'sshape space, a Riemannian manifold with Procrustes distance as metric. All conventional multivariate strategies carry over to the study of shape variation and covariation when shapes are interpreted in the tangent space to the shape manifold at an average shape. For biomathematical interpretation of such analyses, one needs a basis for the tangent space compatible with the reality of local biotheoretical processes and explanations at many different geometric scales, and one needs graphics for visualizing average shape differences and other statistical contrasts there. Both of these needs are managed by thethin-plate spline, a deformation function that has an unusually helpful linear algebra. The spline also links the biometrics of landmarks to deformation analysis of the images from which the landmarks originally arose. This article reviews the history and principal tools of this synthesis in their biomathematical and biometrical context and demonstrates their usefulness in a study of focal neuroanatomical anomalies in schizophrenia.     

Advances in Geometric Morphometrics

Geometric morphometrics is the statistical analysis of form based on Cartesian landmark coordinates. After separating shape from overall size, position, and orientation of the landmark configurations, the resulting Procrustes shape coordinates can be used for statistical analysis. Kendall shape space, the mathematical space induced by the shape coordinates, is a metric space that can be approximated locally by a Euclidean tangent space. Thus, notions of distance (similarity) between shapes or of the length and direction of developmental and evolutionary trajectories can be meaningfully assessed in this space. Results of statistical techniques that preserve these convenient properties—such as principal component analysis, multivariate regression, or partial least squares analysis—can be visualized as actual shapes or shape deformations. The Procrustes distance between a shape and its relabeled reflection is a measure of bilateral asymmetry. Shape space can be extended to form space by augmenting the shape coordinates with the natural logarithm of Centroid Size, a measure of size in geometric morphometrics that is uncorrelated with shape for small isotropic landmark variation. The thin-plate spline interpolation function is the standard tool to compute deformation grids and 3D visualizations. It is also central to the estimation of missing landmarks and to the semilandmark algorithm, which permits to include outlines and surfaces in geometric morphometric analysis. The powerful visualization tools of geometric morphometrics and the typically large amount of shape variables give rise to a specific exploratory style of analysis, allowing the identification and quantification of previously unknown shape features.     

Arousal increases the representational capacity of cortical tissue

Arousal patently transforms the faculties of complex organisms. Although typical changes in cortical activity such as seen in EEG and LFP measurements are associated with change in state of arousal, it remains unclear what in the constitution of such state dependent activity enables this profound enhancement of ability. We put forward the hypothesis that arousal modulates cortical activity by rendering it more fit to represent information. We argue that representational capacity is of a dual nature—it requires not only that cortical tissue generate complex activity (i.e. spatiotemporal neuronal events), but also a complex cortical activity space (which is comprised of such spatiotemporal events). We explain that the topological notion of complexity—homology—is the pertinent measure of the complexity of neuronal activity spaces, as homological structure indicates not only the degree to which underlying activity is inherently clustered but also registers the effective dimensionality of the configurations formed by such clusters. Changes of this sort in the structure of cortical activity spaces can serve as the basis of the enhanced capacity to make perceptual/behavioral distinctions brought about by arousal. To show the feasibility of these ideas, we analyzed voltage sensitive dye imaging (VSDI) data acquired from primate visual cortex in disparate states of arousal. Our results lend some support to the theory: first as arousal increased so did the complexity of activity (that is the complexity of VSDI movies). Moreover, the complexity of structure of activity space (that is VSDI movie space) as measured by persistent homology—a multi scale topological measure of complexity—increased with arousal as well.     

QTL analysis of tolerance to a German strain of BYDV-PAV in barley (Hordeum vulgare L.)

One hundred and forty six barley doubled-haploid lines (DH lines) were tested for variation in grain yield, yield components, plant height, and heading date after artificial infection with a German isolate of barley yellow dwarf virus (BYDV-PAV-Braunschweig). Of these 146 lines 76 were derived from the cross of the barley yellow dwarf virus (BYDV) tolerant cultivar ’Post’ to cv ’Vixen’ (Ryd2) and 70 from the cross of Post to cv ’Nixe’. Phenotypic measurements were gathered on both non-infected plants and plants artificially inoculated with BYDV-PAV by viruliferous aphids in pot and field experiments for three years at two locations. For all traits a continuous variation was observed suggesting a quantitative mode of inheritance for tolerance against BYDV-PAV. Using skeleton maps constructed using SSRs, AFLPs and RAPDs, two QTLs for relative grain yield per plant after BYDV infection, explaining about 47% of the phenotypic variance, were identified in Post × Vixen at the telomeric region of chromosome 2HL and at a region containing the Ryd2 gene on chromosome 3HL. In Post × Nixe, a QTL was found in exactly the same chromosome 2HL marker interval. In this cross, additional QTL were mapped on chromosomes 7H and 4H and together these explained about 40% of the phenotypic variance. QTL for effects of BYDV infection on yield components, plant height, and heading date generally mapped to the same marker intervals, or in the vicinity of the QTL for relative grain yield, on chromosomes 2HL and 3HL, suggesting that these regions are of special importance for tolerance to the Braunschweig isolate of BYDV-PAV. Possible applications of marker-assisted selection for BYDV tolerance based on these results are discussed. Received: 1 December 2000 / Accepted: 9 March 2001     

Pattern in craniofacial biology: Evidence from the old world monkeys (Cercopithecidae)

An understanding of craniofacial growth, both evolutionarily and clinically, requires an investigation of pattern —geometric relations that remain relatively constant among growing structures or components of the skull. Several craniofacial biologists have suggested that specific morphological relations remain invariant during growth and in interspecific comparisons of adults of varying size. We tested the hypothesized invariance of a series of craniofacial angles in a sample of adult Old World monkeys. Fifteen angles were determined from lateral cranial radiographs. Criteria for examining angular invariance included tests for significant correlations and regression slopes with palatal length (overall skull size), tests for significant mean differences (ANOVAs) in angular values between the two subfamilies of Cercopithecidae — Cercopithecinae and Colobinae — and the computation and ranking of standard deviations (SDs) and coefficients of variation (CVs). Results indicate that most of the cranial angles purported to be invariant do not in fact meet the criteria for acceptance. One of the few cranial angles that evinces a somewhat constant value is that between the posterior maxillary plane and the neutral axis of the orbits, providing very limited support for Enlow’s (1982) claim that this region represents a fundamental anatomical interface (at least within Old World monkeys). Our analysis suggests that while there may be several relatively invariant structural relations within the skull, most of those previously discussed as representing evidence of pattern in primate-wide or mammal-wide comparisons are incorrect.     

Werner syndrome lymphoblastoid cells are sensitive to camptothecin-induced apoptosis in S-phase

Werner Syndrome (WRN) is an autosomal recessive disorder showing an endogenous mutator phenotype in combination with an elevated risk of predominantly mesenchymal cancer. The gene mutated in WRN patients codes for 3’→5’ DNA helicase and 3’→5’ exonuclease activities. We have found similar S-phase arrest in both WRN and control cells after treatment with the DNA-topoisomerase-I-trapping drug camptothecin; this may be responsible for the drug-exposure-related growth inhibition seen in both cell types. A clearer phenotypic difference between WRN and control immortalized B-cell lines (LCLs) is obtained by examining cell death. The mechanism of camptothecin-induced cell death in WRN-deficient LCLs appears to be through apoptosis, a phenotype that strongly differentiates WRN-deficient from wild-type LCLs. We hypothesize that, in cells deficient for WRN function, a topoisomerase-I-DNA intermediate persists. Conflict with DNA replication may lead to apoptosis, increased mutation rates, and cancer in WRN. Received: 23 September 1998 / Accepted: 26 October 1998     

Euclidean sections of protein conformation space and their implications in dimensionality reduction

Dimensionality reduction is widely used in searching for the intrinsic reaction coordinates for protein conformational changes. We find the dimensionality?reduction methods using the pairwise root?mean?square deviation (RMSD) as the local distance metric face a challenge. We use Isomap as an example to illustrate the problem. We believe that there is an implied assumption for the dimensionality‐reduction approaches that aim to preserve the geometric relations between the objects: both the original space and the reduced space have the same kind of geometry, such as Euclidean geometry vs. Euclidean geometry or spherical geometry vs. spherical geometry. When the protein free energy landscape is mapped onto a 2D plane or 3D space, the reduced space is Euclidean, thus the original space should also be Euclidean. For a protein with N atoms, its conformation space is a subset of the 3N‐dimensional Euclidean space R^3N. We formally define the protein conformation space as the quotient space of R^3N by the equivalence relation of rigid motions. Whether the quotient space is Euclidean or not depends on how it is parameterized. When the pairwise RMSD is employed as the local distance metric, implicit representations are used for the protein conformation space, leading to no direct correspondence to a Euclidean set. We have demonstrated that an explicit Euclidean‐based representation of protein conformation space and the local distance metric associated to it improve the quality of dimensionality reduction in the tetra‐peptide and β‐hairpin systems. Proteins 2014; 82:2585–2596. © 2014 Wiley Periodicals, Inc.     

The Developmental Basis of Variational Modularity: Insights from Quantitative Genetics,Morphometrics, and Developmental Biology

Groups of correlated characters (variational modules) often are considered to be the result of dissociated local developmental factors, i.e., of a modular genotype–phenotype map. But certain sets of pleiotropic factors can equally well induce modular phenotypic variation—no local developmental factors are necessary for a modular covariance structure. It is thus not possible to infer genetic or developmental modularity from standing variation alone. Yet, only for approximately linear genotype–phenotype maps is the induced covariance structure stable over changes of the phenotypic mean. For larger genetic and phenotypic variation, such as on a macroevolutionary level, developmental effects often are nonlinear and variational modularity remains stable only when it is realized by local dissociated developmental factors with no overlap of pleiotropic ranges. The evo-devo concept of modularity concurs only at this macroevolutionary level with the quantitative notion of variational modularity. Empirical evidence on the genetic and developmental architecture underlying phenotypic variation is inconclusive and partly subject to methodological problems. Many studies seem to indicate modularized phenotypic variation and local clusters of QTL effects, whereas other studies find support for several alternative models of modularity and report continuous distributions of QTL effects. This inconsistency partly results from the neglect of spatial relationships among the measured traits. Given the complex development of higher organisms, a combination of pleiotropic factors and more local developmental effects with a hierarchical, overlapping, and more or less continuous distribution appears most likely.     

Cartesian stiffness for wrist joints: analysis on the Lie group of 3D rotations and geometric approximation for experimental evaluation

This paper is concerned with the analysis and the numerical evaluation from experimental measurements of the static, Cartesian stiffness of wrist joints, in particular the human wrist. The primary aim is to extend from Euclidean spaces to so(3), the group of rigid body rotations, previous methods for assessing the end-point stiffness of the human arm, typically performed via a robotic manipulandum. As a first step, the geometric definition of Cartesian stiffness from current literature is specialised to the group so(3). Emphasis is placed on the choice of the unique, natural, affine connection on so(3) which guarantees symmetry of the stiffness matrix in presence of conservative fields for any configuration, also out of equilibrium. As the main contribution of this study, a coordinate-independent approximation based on the geometric notion of geodesics is proposed which provides a working equation for evaluating stiffness directly from experimental measurements. Finally, a graphical representation of the stiffness is discussed which extends the ellipse method often used for end-point stiffness visualisation and which is suitable to compare stiffness matrices evaluated at different configurations.     

Models of Darwinian processes and evolutionary principles

Evolutionary processes are described as stochastic motions in a genotype space (set of sequences with a Hamming distance) and a phenotype space (vector space of phenotypic properties). Real value functions are introduced which form a landscape over these spaces; smoothness postulates are formulated. Evolution is considered as a kind of hill climbing on these adaptive landscapes. A rather simple diffusion approximation for the phenotypic processes is proposed which leads to similar mathematical problems as the Schrödinger equation for disordered potential distributions.     

Genetic analysis of durable leaf rust resistance in winter wheat

Quantitative resistance that delays the epidemic development of leaf rust in wheat is an important source for durable resistance breeding. The Swiss winter wheat variety ’Forno’ shows a high level of quantitative resistance against leaf rust. This resistance has been effective for more than 10 years and can therefore be considered to be durable. In order to map quantitative trait loci (QTL) for durable leaf rust resistance we analysed 204 F₅ recombinant inbred lines (RILs) of the cross between the winter wheat ’Forno’ and the winter spelt ’Oberkulmer’ for their level of leaf rust resistance (LR) and leaf tip necrosis (LTN) in four different environments. Both traits showed a continuous distribution and were significantly correlated (r=−0.5). Across environments we detected 8 QTL for leaf rust resistance (6 inherited from ’Forno’) and 10 QTL for the quantitative expression of LTN (6 inherited from ’Forno’). Of the 6 QTL responsible for the durable leaf rust resistance of ’Forno’, 1 major QTL coincided with a thaumatin locus on 7BL explaining 35% of the phenotypic variance. Four QTL for LR coincided with QTL for LTN. At these loci the alleles of ’Forno’ increased the level of resistance as well as the extent of LTN, indicating pleiotropy. Received: 1 July 1999 / Accepted: 30 July 1999     

Comparison of phenotypic and molecular distances to predict heterosis and F1 performance in Ethiopian mustard (Brassica carinata A. Braun)

Predicting heterosis and F₁ performance from the parental generation could largely enhance the efficiency of breeding hybrid or synthetic cultivars. This study was undertaken to determine the relationship between parental distances estimated from phenotypic traits or molecular markers with heterosis, F₁ performance and general combining ability (GCA) in Ethiopian mustard (Brassica carinata). Nine inbred lines representing seven different geographic regions of Ethiopia were crossed in half-diallel. The nine parents along with their 36 F₁s were evaluated in a replicated field trail at three locations in Ethiopia. Distances among the parents were calculated from 14 phenotypic traits (Euclidean distance, ED) and 182 random amplified polymorphic DNA (RAPD) markers (Jaccard’s distances, JD), and correlated with heterosis, F₁ performance and GCA sum of parents (GCA_sum). The correlation between phenotypic and molecular distances was low (r=0.34, P≤0.05). Parents with low molecular distance also had low phenotypic distance, but parents with high molecular distance had either high, intermediate or low phenotypic distance. Phenotypic distance was highly significantly correlated with mid-parent heterosis (r=0.53), F₁ performance (r=0.61) and GCA (r=0.79) for seed yield. Phenotypic distance was also positively correlated with (1) heterosis, F₁ performance and GCA for plant height and seeds plant⁻¹, (2) heterosis for number of pods plant⁻¹, and (3) F₁ performance for 1,000 seed weight. Molecular distance was correlated with GCA_sum (r=0.36, P≤0.05) but not significantly with heterosis and F₁ performance for seed yield. For each parent a mean distance was calculated by averaging the distances to the eight other parents. Likewise, mean heterosis was estimated by averaging the heterosis obtained when each parent is crossed with the other eight. For seed yield, both mean ED and JD were significantly correlated with GCA (r=0.90, P≤0.01 for ED and r=0.68, P≤0.05 for JD) and mean heterosis (r=0.79, P≤0.05 for ED and r=0.77, P≤0.05 for JD). In conclusion, parental distances estimated from phenotypic traits better predicted heterosis, F₁ performance and GCA than distances estimated from RAPD markers. Electronic Supplementary Material Supplementary material is available for this article at and is accessible for authorized users.     

Hormesis provides a generalized quantitative estimate of biological plasticity

Phenotypic plasticity represents an environmentally-based change in an organism’s observable properties. Since biological plasticity is a fundamental adaptive feature, it has been extensively assessed with respect to its quantitative features and genetic foundations, especially within an ecological evolutionary framework. Toxicological investigations on the dose-response continuum (i.e., very broad dose range) that include documented evidence of the hormetic dose response zone (i.e., responses to doses below the toxicological threshold) can be employed to provide a quantitative estimate of phenotypic plasticity. The low dose hormetic stimulation is an adaptive response that reflects an environmentally-induced altered phenotype and provides a quantitative estimate of biological plasticity. Analysis of nearly 8,000 dose responses within the hormesis database indicates that quantitative features of phenotypic plasticity are highly generalizable, being independent of biological model, endpoint measured and chemical/physical stress inducing agent. The magnitude of phenotype changes indicative of plasticity is modest with maximum responses typically being approximately 30–60% greater than control values. The present findings provide the first quantitative estimates of biological plasticity and its capacity for generalization. Summary This article provides the first quantitative estimate of biological plasticity that may be generalized across plant, microbial, animal systems, and across all levels of biological organization. The quantitative features of plasticity are described by the hormesis dose response model. These findings have important biological, biomedical and evolutionary implications.     

Extending Darwin’s analogy: Bridging differences in concepts of selection between farmers, biologists, and plant breeders

Darwin developed his theory of evolution based on an analogy between artificial selection by breeders of his day and “natural selection.” For Darwin, selection included what biologists came to see as being composed of (1) phenotypic selection of individuals based on phenotypic differences, and, when these are based on heritable genotypic differences, (2) genetic response between generations, which can result in (3) evolution (cumulative directional genetic response over generations). The use of the term “selection” in biology and plant breeding today reflects Darwin’s assumption—phenotypic selection is only biologically significant when it results in evolution. In contrast, research shows that small-scale, traditionally-based farmers select seed as part of an integrated production and consumption system in which selection is often not part of an evolutionary process, but is still useful to farmers. Extending Darwin’s analogy to farmers can facilitate communication between farmers, biologists, and plant breeders to improve selection and crop genetic resource conservation.     

Coevolutionary dynamics of adaptive radiation for food-web development

To investigate how complex food-webs can develop through repeated evolutionary diversification, a predator–prey model was analyzed. In the model, each individual has two traits: trait x as a predator and trait y as a prey. These traits constitute a two-dimensional phenotype space, in which the whole group of individuals are represented as a phenotype distribution. Predator–prey interactions among the phenotypes are determined by their relative positions in the phenotype space. Each phenotypic cluster was treated as a species. Each species evolves in y to escape from predation, while it evolves in x to chase their prey. Analytical investigation provided two predictions. First, coupled evolutionary diversifications of y and x may occur when the x of predators have caught up with their prey’s y, which may be repeated. Second, complex food-webs may develop when species’ competitive strengths are kept similar within the communities. If the functional response is close to the ratio-dependent response, the competitive strengths of all species are similar when the relationship between predators and prey corresponds to the ideal free distribution (IFD). These predictions were confirmed by numerical simulations. Electronic supplementary material  The online version of this article doi:() contains supplementary material, which is available to authorized users.     

Distance-related semi-quantitative estimation of the extramatrical ectomycorrhizal mycelia of <Emphasis Type="Italic">Cortinarius obtusus</Emphasis> and <Emphasis Type="Italic">Tylospora asterophora</Emphasis>

Extramatrical mycelia of ectomycorrhizae (ECM) can markedly differ in their density, organization and extension as well as in their biomass. As these mycelia are very important for nutrient uptake, are sinks for carbohydrates and probably act as potential agents to interfere with mycelia of other ECM, a method allowing calculations of density, extension and amount of extramatrical mycelium could further ecological studies at different scales. As a first step synthesized ECM of Cortinarius obtusus and Tylospora asterophora, which represent two different ‘exploration types’ — T. asterophora belongs to the 'short distance exploration type’ and C. obtusus to the ‘medium distance exploration fringe subtype’ — were compared with respect to their extramatrical mycelia. To investigate the mycelial distribution in detail, flat rhizotrons filled with peat were used to synthesize the ECM on roots of Picea abies (Norway spruce). As both species form white mycelia, they contrast conspicuously to the dark brown peat substrate. This made it favourable to use CD-camera photographs and a consecutive image analysis of the bright mycelium in comparison to the dark background. For that, nine distance areas have been defined as the regions between nine concentric lines placed around the mantle surface of the ectomycorrhizal root (EMR). The distances between these lines were fixed in a regular manner as the square multiples of roughly one diameter of the EMR (0,27 mm). This resulted in lines representing distances of 1, 4, 9, 16, 25, 36, 49, 64, and 81 multiples of the EMR diameter. The distance of 81 EMR diameters equals roughly a real distance of app. 20 mm from the surface of the EMR. The studies showed highly significant differences in mycelial density between the four innermost distance areas, i. e. areas up to a distance of 16 EMR diameters. This applied for both species. Significant differences were found in the same areas when both species were compared. It was shown that C. obtusus still forms a considerable amount of mycelium beyond the 49 distance line, where the substrate was covered by 15–20 %. However, a limited data set did not allow any statistical calculations at these positions. In contrast to C. obtusus, the amount of extramatrical mycelium of T. asterophora decreased more rapidly with increasing distance. Mycelium could not be detected with this method beyond the 49 distance line. We conclude that these two species differ considerably in the amount and extension of their mycelia and this may be in line with their assignment to the respective exploration types. Further studies are needed to substantiate these results with additional species representing the full set of known exploration types. Envisaged correlation studies of these results with mycelial biomass by direct measurement of hyphal length or via quantitative PCR, can possibly result in an estimation of extramatrical mycelia of ECM in natural soil.     

Resource partitioning in rhinolophoid bats revisited

We assessed the ecomorphological structure of a guild of rhinolophoid bats in a Malaysian rainforest first described by Heller and von Helversen (1989). These authors found that the distribution of echolocation call frequencies used by 12 syntopic species was more even than expected from allometric relationships or in randomly generated communities, and that the observed minimal ratio was greater than expected by chance alone. In this study we were able to expand their guild to 15 species, but in doing so it became apparent that call frequencies might be less evenly distributed across the total frequency range than previously proposed. We replicated Heller and von Helversen’s (1989) analyses with the full 15-species complement but were unable to support their suggestion that rhinolophoid bats exhibit resource partitioning through differences in frequency bands. We adopted a multivariate approach and incorporated measures of body size and wing morphology into the analysis. We used phylogenetic autocorrelation to ensure that the species were statistically independentand principal component analysis to describe the morphological space occupied by the 15 species in the community and four additional species representing the extremes of phenotypic variation. We derived interspecific Euclidean distances and tested the mean values and SDs of these distances against those of 100 guilds of ”synthetic” species created randomly within the principal component space. The guild of Rhinolophoidea was not distributed randomly in multivariate space. Instead we found evidence of morphological overdispersion of the most similar species, which suggests niche differentiation in response to competition. Less similar species were nearer in morphological space than expected, and we suggest this is a consequence of ecological constraints on parameter combinations. Despite this underdispersion, many of the more distant neighbours were evenly rather than randomly spaced or clumped in morphospace, suggesting that, given the environmental constraints on morphology, species in this guild do experience limits to their similarity. Finally, we tested the influence of the relative abundance of species on morphological displacement, and found no evidence that abundant, spatially correlated species reduce interspecific overlap in morphological space. Received: 10 April 1999 / Accepted: 28 February 2000