- Research article
- Open Access
Phenotypic covariance at species’ borders
© Caley et al.; licensee BioMed Central Ltd. 2013
Received: 26 July 2012
Accepted: 24 May 2013
Published: 28 May 2013
Understanding the evolution of species limits is important in ecology, evolution, and conservation biology. Despite its likely importance in the evolution of these limits, little is known about phenotypic covariance in geographically marginal populations, and the degree to which it constrains, or facilitates, responses to selection. We investigated phenotypic covariance in morphological traits at species’ borders by comparing phenotypic covariance matrices (P), including the degree of shared structure, the distribution of strengths of pair-wise correlations between traits, the degree of morphological integration of traits, and the ranks of matricies, between central and marginal populations of three species-pairs of coral reef fishes.
Greater structural differences in P were observed between populations close to range margins and conspecific populations toward range centres, than between pairs of conspecific populations that were both more centrally located within their ranges. Approximately 80% of all pair-wise trait correlations within populations were greater in the north, but these differences were unrelated to the position of the sampled population with respect to the geographic range of the species.
Neither the degree of morphological integration, nor ranks of P, indicated greater evolutionary constraint at range edges. Characteristics of P observed here provide no support for constraint contributing to the formation of these species’ borders, but may instead reflect structural change in P caused by selection or drift, and their potential to evolve in the future.
Understanding how and why species’ range limits evolve [1–4], and the extent to which constraints on evolutionary responses are imposed by covariance among traits [5–10] are two important, but currently unresolved, issues in evolutionary biology. The theory of species’ borders evolution reviewed by  and evolutionary responses, where multiple co-varying traits are involved [5–10], are both considerably advanced, but empirical tests of these ideas are few [2, 4, 11]. Moreover, whether responses to selection imposed by multiple co-varying traits constrain evolution at range edges and leads to the evolution of species’ borders is largely unknown. There is some evidence that peripheral populations may be evolutionarily constrained [12–15], but the tendency of evolutionary biologists to study trade-offs between pairs of co-varying traits is unlikely to elucidate processes that depend on linkages between whole suites of traits [6, 9, 14, 16] as is potentially the case for the determinants of range limits.
Evolution where multiple traits co-vary can be studied using the multivariate response equation , where is the vector of mean trait responses, G is the additive genetic variance-covariance matrix, P is the phenotypic variance-covariance matrix, and S is the vector of selection differentials . Such multivariate approaches are now commonly used to understand how populations might respond to selection e.g. [7–11, 17–22]. A major obstacle, however, to studying multivariate trait selection and evolution is the accurate estimation of G. Estimating G requires large-scale, controlled, captive-breeding studies, or the collection of groups of relatives from the wild. Using either approach is unrealistic for all but a few species. P, however, may be a useful substitute for G in such analyses [11, 21, 24] where direct estimation of G is not feasible. While G and P are not strictly equivalent, P should reflect the structure of G, especially for traits with high heritabilities . Indeed, similarity between P and G has been supported by empirical studies [23–27] but see . Moreover, P is likely to be estimated with less error than G, and therefore, may represent G better than G estimated with large error [29, 30]. P also imposes an upper limit of dimensionality on G. Investigations of P, therefore, should provide some insight into the structure of G, and consequently, are beginning to gain greater currency in evolutionary research e.g. [11, 31–35].
As selection is blind to genotype, acting solely on phenotypic variation, the ability of species to evolve will be determined first by the phenotypic variation exposed to selection. It is well established that phenotypic traits in populations of the same species can vary among geographic locations  and citations therein. In contrast, comparatively little is known about how phenotypic traits co-vary over similar distances, but some evidence suggests that while P may not remain constant, it can show substantial stability even over large distances [26, 32]. Better knowledge of such stability, or otherwise, could then be used to infer selective regimes imposed on populations and species across space and how they may respond to selection in the future [27, 33–36]. For example, stability of P between centre and range edge populations, despite an expected shift in the selective landscape from stabilizing to directional selection , may infer evolutionary constraint. Alternatively, re-alignment of P, or changes in its shape could instead indicate responses to selection, or constraint, depending on the details of any such changes in P. For example, the reorientation of P between a range edge and centre may indicate a response to selection, if such a reorientation reflects a change in the direction of selection. Conversely, if P has lower rank or there is greater morphological integration in range edge populations, there would be less opportunity to respond to changes in the selective regime.
Our current lack of knowledge of how P varies among populations and species, and what knowledge of such variation might tell us about the operation of evolutionary processes, is exemplified by the study of the evolution of species’ geographic borders. In many species, no obvious limits to dispersal exist at their current range boundaries, and despite selective advantages associated with range expansion, range margins often appear to remain stable. Populations at, or toward, the edge of a species’ geographic range, however, may experience quite different selective landscapes, and possibly greater drift, than their more centrally located counterparts [1, 4]. Because of the complexity of processes that can operate on populations at range edges and the diversity of traits involved, taking a multivariate approach to the study of range edges should aid our understanding of their evolution and maintenance . If so, differences in P between centers and edges of species ranges may be informative about how these populations could respond to selection. Further limiting our current ability to draw inferences regarding the evolution of geographic ranges has been the tendency to investigate series of populations of a particular species at varying distances from a range edge. Such designs make it difficult to separate the effects of distance to range edge from geographic location per se; interspecific comparisons and contrasts between groups of species have been suggested as an alternate and potentially more powerful approach . That is, for a fixed set of resources, comparative approaches can increase the number of contrasts between centers and edges while controlling local environmental variation.
Understanding how geographically marginal populations might respond to selection is becoming increasingly urgent given the current threats of climate change, habitat fragmentation, and invasive species. With this, and the issues outlined above in mind, we adopted a comparative analytical approach that controls for geographic location and compares multiple phenotypic traits simultaneously through the analysis of P. Specifically, we investigated patterns of phenotypic covariance at species’ borders in reef fishes on Australia’s Great Barrier Reef (GBR). The GBR exists as a relatively contiguous habitat positioned along a predominately north–south gradient of approximately 2000 km. Many fish species inhabiting the GBR have distributions that extend well beyond both its northern and southern limits. Many others, however, have geographic range margins within, or toward the ends, of the GBR. Additionally, fish populations along the length of the GBR can be connected by gene flow over considerable distances during their larval phase, yet also exhibit detectable genetic structure over its length [37–39]. These population genetic patterns indicate that gene flow from central to marginal populations may be sufficient to disrupt local adaptation at range edges, but that gene flow is insufficient to render the local populations along the GBR effectively a single population. Across this geographic gradient there are also substantial biotic and abiotic gradients that may impose selection pressures on reef fishes of the GBR that could be important in determining their geographic range limits. For example, regional fish diversity is approximately 40%  and mean monthly maximum and minimum water temperatures 2 – 3°C greater (Source: data.aims.gov.au) in the north.
Range attributes of species compared: C, NB, and SB denote a population toward the centre, northern, or southern border of their geographic ranges, respectively
Distance to border
N-S (° lat.)
Summary of ecological traits for each species studied
Lagoon or outer reef, commensal with anemones
Planktonic copepods and algae
11 ± 0.3(s.d.)*
11.7 ± 0.3(s.d.)*
Upper reef slope
18.2 ± 0.4(s.d.)*
Zooplankton and algae
16.5 ± 3.9(s.d.)*
Lagoon or sub-tidal reef flat, burrows in sand or rubble
Small benthic invertebrates and algae
28.5 ± 1.1(s.d.)*
Lagoon or sub-tidal ref flat
30.5 ± 0.6(s.d.)*
Between these two distant locations, the two populations of each of the three control species, those that do not have a range margin along the length of the GBR, typically retained all axes of phenotypic variation (eigenvectors) in common and differed only in the amount of variation associated with these axes (eigenvalues) (Figure 2). The exceptions to this were the A. phalaena populations which when compared using the AIC method shared all but one of their eigenvectors, and the A. melanopus populations whose step-up analysis indicated only 4 out of 8 axes in common. For both these species, however, the alternate CPC method still indicated a full set of common axes. In contrast to this stability, comparisons of the three species whose populations over the same distance included a geographic margin indicated that in no case had these populations retained all axes of phenotypic variation in common (See Additional file 1 for full CPC results).
Nine-five percent confidence sets of models describing the similarity between the phenotypic covariance matrices from two populations for each of six reef fish species in three congeneric comparisons
Pair-wise comparisons of morphological traits
The number of stronger and weaker pair-wise correlations between morphological traits within a population was unrelated to whether the comparisons were between a central and a border population, or between two central populations. The number of significant differences in trait correlations was also unrelated to a population’s status as central or edge. In contrast, 80% of correlations between traits were stronger at the northern location (Additional file 2).
Potential for evolutionary constraint
Correlatedness of morphological traits and ranks of P within populations of reef fishes
No. of traits (N)
Sample size (M)
Substantial differences in phenotypic covariation were observed in populations of reef fishes at both northern (warm) and southern (cool) range margins compared to populations closer to their range centers. This instability of phenotypic covariation was greater than would be expected by geographic separation alone, and is in contrast to the stability of P seen both in the congeneric controls used here, and in previous matrix comparisons of some additional reef fish species at these locations . In the absence of a geographic margin, P typically retained all axes of variation in common, but differed in the amount of variation along these axes. This is suggestive of a considerable commonality of selective pressures encountered and evolutionary responses  by these populations. It also suggests that E either has little influence on P or has been canalized to reflect G in these species. The consistency of this result is good reason to believe that P may be informative of G for the populations studied here. Given the variety of life histories and morphologies represented by these species, and differences in environmental conditions experienced by these edge populations, the changes in P between central and marginal populations appear to be independent of these proximate factors, and are more likely the consequence of evolutionary processes operating in marginal populations.
The instability in patterns of morphological covariation in border populations was only observed in the second and lower order axes that primarily represent components of shape. Shape, however, is integral to the ecology of coral reef fishes , and shape in fishes can be closely tied to fitness and be selected . While it is tempting to try and link the differences in structure of P in marginal populations as revealed by these CPC results to the adaptive nature of the measured traits, there have been numerous issues raised about the biological interpretation of these orthogonal abstractions .
Indeed, the greater structural differences observed here in P in comparisons between centrally and marginally located populations relative to their congeners in the absence of a species’ border, was not reflected in the pair-wise correlations observed between traits. More frequently, trait correlations were stronger in the north irrespective of the positioning of those populations with respect to geographic limits. A similar pattern was reported for two species of grasshopper in which stronger covariances were observed where temperatures were greater . Given the observation of generally stronger correlations in the north in these fish populations, it is all the more remarkable that differences in the structure of P related to the position of populations relative to range edges were detected.
Differences in the structure of P between these central and marginal populations indicate that a unique subset of phenotypic space is accessible to selection in these marginal populations . Whether selection on these phenotypes has led to their adaptive evolution, or has been constrained as a result of these differences in P, is difficult to infer with certainty in the absence of estimates of selection on these traits. Some insight, however, into whether these populations have been constrained can be gleaned from the examination of the shapes of P. For example, unless selection happens to be oriented in the same direction as the axis of greatest variation, phenotypic covariance distributed more unevenly among axes, or among fewer axes, should be indicative of greater constraint  to the degree to which P reflects G. Neither the standard deviations of eigenvalues, nor the ranks of P, were related to the proximity of a species’ border. Therefore, these results more likely reflect responses to processes operating at geographic range margins other than phenotypic conservatism resulting from evolutionary constraint. Nevertheless, these edge populations would be expected to respond differently to the same selection pressures experienced by their centrally located relatives.
Direct estimation of multivariate selection in these populations is beyond the scope of this study. It is difficult, therefore, to move beyond speculation as to which processes may have shaped the observed differences in phenotypic covariation. The differences in P seen here are of the same magnitude as those reported previously as evidence of locally distinct selection regimes  and even morphological divergence between species . It is, however, also worth considering the effects of other processes such as differential phenotypic expression due to different environments, or demographic stochasticity, both of which could cause differences in P between central and marginal populations. We attempted to control the effects of environment by using a comparative analysis. It is possible, however, that selection, which may otherwise canalise the expression of environmental variation, is less effective in marginal populations as a consequence of gene swamping . Similarly, although the changes in P between central and marginal populations were greater than those typically associated with genetic drift where proportionality is used as a criterion , non-proportional changes as seen here may also result from the actions of drift and cannot be rejected out-of-hand until better diagnostics are developed .
Associated with the predictions of small population size and directional selection, is the expectation of reduced genetic variation in marginal populations . Although it is less clear how phenotypic variation will respond to the same processes, population genetics theory suggests that a decrease in phenotypic variation should also be evident , especially in the case of morphological traits . The lack of any obvious reduction here in phenotypic variation in marginal populations that selection could act on (i.e. reduced matrix ranks or greater trait integration estimated by SD(λ)), however, is not necessarily surprising. The loss of genetic variation in traits could be offset by increased expression of environmental variation in the phenotype. Alternatively, fluctuations in the direction of selection, quite possible in marginal populations exposed to changes in population densities , could increase phenotypic variation . As a result, it remains unclear exactly how the extent of phenotypic variation should evolve at range margins.
Irrespective of the exact processes contributing to this result, we have demonstrated that geographical marginality can be associated with substantial change in P. More work, both theoretical and empirical, is needed to assess the generality of this result in other taxa, and if it proves to be a common pattern, its causes and consequences for evolutionary rates and directions. In the meantime, it appears likely that for reef fishes at least, differences in P, and possibly G, can result from conditions encountered by wild populations living close to their range edges. As patterns of phenotypic variation can have a substantial influence over a population’s evolutionary trajectory [18, 54], such differences in phenotypic covariance are likely to have important consequences for evolution at range margins.
Given contemporary threats posed by climate change, invasive species, and landscape fragmentation, understanding the forces shaping species’ ranges is of critical importance to the long-term conservation of biodiversity. Attempts to predict future range migrations, or the longer-term persistence of populations in new locations, or with changing environmental conditions, while ignoring changes in phenotypic covariance at range edges may seriously undermine our predictions of the abilities of species to adapt, and thereby, our estimates of extinction risk. Acquiring a greater understanding of evolutionary potential in marginal populations should be accorded very high priority by evolutionary and conservation biologists alike.
Phenotypic covariation was greater between populations of reef fishes at both northern (warm) and southern (cool) range margins compared to populations closer to their range centers. Given the variety of life histories and morphologies represented by these species, and differences in environmental conditions experienced by these edge populations, the changes in P between central and marginal populations appear to be independent of these proximate factors, and are more likely the consequence of evolutionary processes operating in marginal populations. Neither the degree of morphological integration of the traits studied, nor the ranks of P, indicated greater evolutionary constraint at range edges. Instead, these differences in P may reflect structural change in P caused by selection or drift, and the potential to evolve in the future.
We studied Amblygobius rainfordi (Gobiidae) (since synonymised as Koumansetta rainfordi, a sister genus in the subfamily Gobiinea), Amphiprion akindynos (Pomacentridae), and Chrysiptera rollandi (Pomacentridae). Specimens of these species were collected in the vicinity of two locations, approximately 1200 km apart, on the GBR: Lizard Island (14°40’S, 145°28’E) in the north, and One Tree Island (23°25’S, 151°55’E) in the south (Figure 1). For two of these species, A. rainfordi and C. rollandi, the One Tree Island populations were within 50 kilometres of their southern distributional limit, whereas, both have been recorded a few thousand kilometres north of Lizard Island. A. akindynos, on the other hand, is regularly found over 1000 kilometres south of One Tree Island, but is rarely recorded more than a few hundred kilometres north of Lizard Island. These geographic distributions were estimated from publicly available databases (e.g. The Altas of Living Australia (http://www.ala.org.au), The Ocean Biogeographic Information System (http://www.iobis.org)) and are summarized in Table 1.
Theory predicts that populations across much of a species’ range may not be optimally adapted as a result of gene flow from the center to the periphery of ranges . Therefore, we are confident that the populations sampled here are sufficiently close to their range limits to sample the environmental conditions of their range margins. For our purposes here then, Lizard Island represents a sampling location for the northern border of A. akindynos, whereas One Tree Island represents a sampling location for the southern border of the other two species. These three species also encompass a diverse range of morphologies and life histories, including pelagic larval durations (PLD) that vary between 10 and 31 days [37, 42] (Table 2), and were chosen to maximize the generality of any patterns that emerged.
The morphology of ectotherms is sensitive to environmental conditions, particularly temperature , which differs between the northern and southern sampling locations used here. Also, as P is a function of G and E, where E is the matrix of environmental covariation , it is necessary to separate, as much as possible, the effects of environment from the effects of geographic marginality. To control the central/marginal comparisons for changes in P associated with environmental differences experienced by these fishes at different locations, and to provide a basis to compare changes in P across a geographic range in the absence of a geographic border, we adopted a comparative approach. For each of the species we examined that exhibits a range edge along the GBR, a congeneric species with similar life histories (Table 2), but whose distribution extends well beyond the northern and southern extremities of the GBR were included in this comparative analysis (Figure 1). The three congeneric species used were Amblygobius phalaena, Amphiprion melanopus, and Chrysiptera rex. All of these species are found a minimum of 10° latitude both north and south of the collection locations used here. Under this sampling design, differences in P between central and marginal populations compared to those seen between the populations of their paired species can be interpreted as indicative of processes operating in geographically marginal populations.
Specimens were collected and analysed using the methods described by Game and Caley . A total of 1040 fish were sampled including 113 A. rainfordi, 135 A. phalaena, 129 A. akindynos, 114 A. melanopus, 124 C. rollandi, and 156 C. rex.
In order to incorporate phenotypic variation among traits across different ontogenetic stages, individuals across the entire post-settlement size range of each species were sampled. Nine morphological traits: minimum caudal peduncle depth (CPD), dorsal fin length (DFL), nape length (NPL), head length (HDL), eye diameter (EYD), body depth at the back of the head (BDH), pectoral fin depth (PFD), inter pelvic/anal fin distance (IPA), and anal fin length (AFL), were estimated to the nearest 0.1 mm for each of the individuals used in this study. These nine traits were chosen to represent major morphological structures common to all these species, were distributed relatively evenly over the surface of each fish, and didn’t traverse multiple structures that may not co-vary isometrically. Two traits (i.e., NPL and HDL) were removed from the analysis of the Chrysiptera populations and three traits (i.e., HDL, EYD and PFD) from the analysis of Amblygobius populations because they could not be measured accurately (see  for further details). All traits used here were estimated by the same individual (EG) to eliminate inter-observer variation and % measurement error for all traits retained for analysis was estimated to be < 1% . Using these estimates of phenotypic traits, phenotypic variance-covariance matrices (P) were calculated for each population.
Covariance matrices can share a series of relationships between the extremes of equality and inequality . To determine the level of structural similarity between matrices, Phillips’ CPCA software  was used. This common principal component (CPC) analysis was run using both the step-up method, which fits within a traditional hypothesis testing framework, and the Akaike Information Criterion (AIC) method, which selects the best fitting model given the information available. Because AIC estimates the distance between two models, it is also possible to calculate a weight (w i ) for each model, interpreted as the probability that model i is the actual best model given the available set of models . Using these Akaike weights ninety-five percent confidence limits were estimated, in effect producing a 95% confidence set of models. This set of models will include the actual best model in 95% of cases and should help in interpreting the results in the context of the sampling variation likely for the sample sizes used here . For a more complete discussion of the techniques used here see Game and Caley .
Sources of structural differences between P matrices
where p(r ij | Data) is the posterior distribution of the difference in the correlation between One Tree Island and Lizard Island. If a particular trait correlation was greater/lesser at One Tree Island than at Lizard Island, p(r ij | Data) will be mainly greater/less than zero. Differences in trait correlations were considered significant if zero was contained in the 1st or 99th percentile of p(r ij | Data).
Potential for evolutionary constraint
The potential for evolutionary constraint given observed Ps was examined two ways. First, the degree of morphological integration of traits in each population was examined by estimating the standard deviation of the eigenvalues (SD(λ)) for each P, standardized for the number a traits measured and sample size . SD(λ) estimates the degree of co-variation among all traits represented in an estimate of P. Where SD(λ) is greater, changes in P should be relatively more constrained. We compared the SD(λ)s estimated for central populations with the SD(λ)s estimated for the border populations.
Ranks of P were also estimated and compared. The rank of a matrix equals its number of non-zero eigenvalues and describes its dimensionality. The lower the rank, the fewer the axes along which variation is distributed. Consequently, the lower the rank of P, the more constrained the response to selection in multi-trait space. Because P defines the upper bound of G, constraint imposed by G may be greater than that imposed by P e.g. . Therefore, P provides a conservative estimate of constraint.
Methods for estimating ranks of P have been developed based on the repeated measurement of individuals e.g. [28, 63]. Repeated measurements of the fish studied here were unavailable. Previously, however, we estimated percentage measurement error for these traits . We used these estimates of measurement error to simulate repeated measures using the method and code reported in Pavlicev et al. . For each estimated individual-by-trait combination, we simulated two, repeated measurements by adding and subtracting the percentage measurement error to and from the observed value, respectively.
This manuscript benefitted from input from M. Blows, S. Connolly, J. Endler, D. Houle, K. McGuigan, K. Mengersen, and M. Pavlicev. The fishes studied here were made available by K. Buchler. Funding was provided by the Hermon Slade and W. V. Scott Foundations, James Cook University, CSIRO, and the Australian Research Council.
- Hoffmann AA, Blows MW: Species borders: ecological and evolutionary perspectives. Trends Ecol Evol. 1994, 9: 223-227. 10.1016/0169-5347(94)90248-8.PubMedView ArticleGoogle Scholar
- Parmesan C, Gaines S, Gonzalez L, Kaufman DM, Kingsolver J, Peterson AT, Sagarin R: Empirical perspectives on species borders: from traditional biogeography to global change. Oikos. 2005, 108: 58-75. 10.1111/j.0030-1299.2005.13150.x.View ArticleGoogle Scholar
- Eckert CG, Samis KE, Lougheed SC: Genetic variation across species’ geographical ranges: the central–marginal hypothesis and beyond. Mol Ecol. 2008, 17: 1170-1188. 10.1111/j.1365-294X.2007.03659.x.PubMedView ArticleGoogle Scholar
- Sexton JP, McIntyre PJ, Angert AL, Rice KJ: Evolution and ecology of species range limits. Ann Rev Ecol Evol Syst. 2009, 40: 415-436. 10.1146/annurev.ecolsys.110308.120317.View ArticleGoogle Scholar
- Lande R: Quantitative genetic analysis of multivariate evolution applied to brain - body size allometry. Evolution. 1979, 33: 402-416. 10.2307/2407630.View ArticleGoogle Scholar
- Blows MW: A tale of two matrices: multivariate approaches in evolutionary biology. J Evol Biol. 2007, 20: 1-8. 10.1111/j.1420-9101.2006.01164.x.PubMedView ArticleGoogle Scholar
- Arnold SJ, Bürger R, Hohenlohe PA, Ajie BC, Jones AG: Understanding the evolution and stability of the G-matrix. Evolution. 2008, 62: 2451-2461. 10.1111/j.1558-5646.2008.00472.x.PubMed CentralPubMedView ArticleGoogle Scholar
- Kirkpatrick M: Patterns of quantitative genetic variation in multiple dimensions. Genetica. 2009, 136: 271-284. 10.1007/s10709-008-9302-6.PubMedView ArticleGoogle Scholar
- Walsh B, Blows MW: Abundant genetic variation + strong selection = multivariate genetic constraints: a geometric view of adaptation. Annu Rev Ecol Evol Syst. 2009, 40: 41-59. 10.1146/annurev.ecolsys.110308.120232.View ArticleGoogle Scholar
- Guillaume F: Migration-induced phenotypic divergence: the migration-selection balance of correlated traits. Evolution. 2011, 65: 1723-1738. 10.1111/j.1558-5646.2011.01248.x.PubMedView ArticleGoogle Scholar
- Agrawal AF, Stinchcombe JR: How much do genetic covariances alter the rate of adaptation?. Proc Roy Soc B: Biol Sci. 2009, 276: 1183-1191. 10.1098/rspb.2008.1671.View ArticleGoogle Scholar
- Blows MW, Hoffmann AA: The genetics of central and marginal populations of Drosophila serrata. 1. Genetic-variation for stress resistance and species borders. Evolution. 1993, 47: 1255-1270. 10.2307/2409990.View ArticleGoogle Scholar
- Stanton ML, Galen C: Life on the edge: Adaptation versus environmentally mediated gene flow in the snow buttercup, Ranunculus adoneus. Am Nat. 1997, 150: 143-178. 10.1086/286061.View ArticleGoogle Scholar
- Etterson JR, Shaw RG: Constraint to adaptive evolution in response to global warming. Science. 2001, 294: 151-154. 10.1126/science.1063656.PubMedView ArticleGoogle Scholar
- Magiafoglou A, Carew ME, Hoffmann AA: Shifting clinal patterns and microsatellite variation in Drosophila serrata populations: a comparison of populations near the southern border of the species range. J Evol Biol. 2002, 15: 763-774. 10.1046/j.1420-9101.2002.00439.x.View ArticleGoogle Scholar
- McGuigan K: Studying phenotypic evolution using multivariate quantitative genetics. Mol Ecol. 2006, 15: 883-896. 10.1111/j.1365-294X.2006.02809.x.PubMedView ArticleGoogle Scholar
- Via S, Lande R: Genotype-environment interaction and the evolution of phenotypic plasticity. Evolution. 1985, 39: 505-522. 10.2307/2408649.View ArticleGoogle Scholar
- Arnold SJ: Constraints on phenotypic evolution. Am Nat. 1992, 140: S85-S107. 10.1086/285398.PubMedView ArticleGoogle Scholar
- Björklund M: The importance of evolutionary constraints in ecological time scales. Evol Ecol. 1996, 10: 423-431. 10.1007/BF01237727.View ArticleGoogle Scholar
- Schluter D: Adaptive radiation along genetic lines of least resistance. Evolution. 1996, 50: 1766-1774. 10.2307/2410734.View ArticleGoogle Scholar
- Roff DA, Mousseau T: The evolution of the phenotypic covariance matrix: evidence for selection and drift in Melanoplus. J Evol Biol. 2005, 18: 1104-1114. 10.1111/j.1420-9101.2005.00862.x.PubMedView ArticleGoogle Scholar
- Gomulkiewicz R, Houle D: Demographic and genetic constraints on evolution. Am Nat. 2009, 174: E218-E229. 10.1086/645086.PubMedView ArticleGoogle Scholar
- Roff DA: Evolutionary quantitative genetics. 1997, New York: Chapman & HallView ArticleGoogle Scholar
- Lofsvold D: Quantitative genetics of morphological differentiation in Peromyscus. I. Tests of the homogeneity of genetic covariance structure among species and subspecies. Evolution. 1986, 40: 559-573. 10.2307/2408577.View ArticleGoogle Scholar
- Kohn LAP, Atchley WR: How similar are genetic correlation structures? Data from rats and mice. Evolution. 1988, 42: 467-481. 10.2307/2409032.View ArticleGoogle Scholar
- Roff DA: The estimation of genetic correlations from phenotypic correlations: a test of Cheverud’s conjecture. Heredity. 1995, 74: 481-490. 10.1038/hdy.1995.68.View ArticleGoogle Scholar
- Steppan SJ, Phillips PC, Houle D: Comparative quantitative genetics: evolution of the G matrix. Trends Ecol Evol. 2002, 17: 320-327. 10.1016/S0169-5347(02)02505-3.View ArticleGoogle Scholar
- McGuigan K, Blows MW: The phenotypic and genetic covariance structure of drosophilid wings. Evolution. 2007, 61: 902-911. 10.1111/j.1558-5646.2007.00078.x.PubMedView ArticleGoogle Scholar
- Cheverud JM: A comparison of genetic and phenotypic correlations. Evolution. 1988, 42: 958-968. 10.2307/2408911.View ArticleGoogle Scholar
- Cheverud JM: Quantitative genetic analysis of cranial morphology in the cotton-top (Saguinus oedipus) and saddle-back (S. fuscicollis) tamarins. J Evol Biol. 1996, 9: 5-42. 10.1046/j.1420-9101.1996.9010005.x.View ArticleGoogle Scholar
- Steppan SJ: Phylogenetic analysis of phenotypic covariance structure. 1. Contrasting results from matrix correlation and common principal component analyses. Evolution. 1997, 51: 571-586. 10.2307/2411129.View ArticleGoogle Scholar
- Game ET, Caley MJ: The stability of P in coral reef fishes. Evolution. 2006, 60: 814-823.PubMedView ArticleGoogle Scholar
- Eroukhmanoff F, Svensson EI: Phenotypic integration and conserved covariance structure in calopterygid damselflies. J Evol Biol. 2008, 21: 514-526. 10.1111/j.1420-9101.2007.01488.x.PubMedView ArticleGoogle Scholar
- Eroukhmanoff F, Outomuro D, Ocharan F, Svensson E: Patterns of phenotypic divergence in wing covariance structure of Calopterygid damselflies. Evol Biol. 2009, 36: 214-224. 10.1007/s11692-009-9057-8.View ArticleGoogle Scholar
- Kolbe JJ, Revell LJ, Szekely B, Brodie EB, Losos JB: Convergent evolution of phenotypic integration and its alignment with morphological diversification in Caribbean Anolis ecomorphs. Evolution. 2011, 65: 3608-3636. 10.1111/j.1558-5646.2011.01416.x.PubMedView ArticleGoogle Scholar
- Lande R, Arnold SJ: The measurement of selection on correlated characters. Evolution. 1983, 37: 1210-1226. 10.2307/2408842.View ArticleGoogle Scholar
- Bay LK, Buechler K, Gagliano M, Caley MJ: Intraspecific variation in the pelagic larval duration of tropical reef fishes. J Fish Biol. 2006, 68: 1206-1214. 10.1111/j.0022-1112.2006.01016.x.View ArticleGoogle Scholar
- Bay LK, Crozier RH, Caley MJ: The relationship between population genetic structure and pelagic larval duration in coral reef fishes on the Great Barrier Reef. Mar Biol. 2006, 149: 1247-1256. 10.1007/s00227-006-0276-6.View ArticleGoogle Scholar
- Bay LK, Caley MJ: Greater genetic diversity in spatially restricted coral-reef fishes suggests secondary contact among differentiated lineages. Diversity. 2011, 3: 483-502. 10.3390/d3030483.View ArticleGoogle Scholar
- Russell BC: Annotated checklist of the coral reef fishes in the Capricorn-Bunker group Great Barrier Reef. 1983, Townsville: Great Barrier Reef Marine Park AuthorityGoogle Scholar
- Froese R, Pauly D: 2012, http://www.fishbase.org,
- Victor BC: Duration of the planktonic larval stage of one hundred species of Pacific and Atlantic wrasses (family Labridae). Mar Biol. 1986, 90: 317-326. 10.1007/BF00428555.View ArticleGoogle Scholar
- Wainwright P, Bellwood DR: Ecomorphology of feeding in coral reef fishes. Coral Reef Fishes. Edited by: Sale PF. 2002, San Diego: Academic Press, 33-55.View ArticleGoogle Scholar
- McGuigan K, Franklin CE, Moritz C, Blows MB: Adaptation of rainbow fish to lake and stream habitats. Evolution. 2003, 57: 104-118.PubMedView ArticleGoogle Scholar
- Badyaev AV, Hill GE: The evolution of sexual dimorphism in the house finch. I. Population divergence in morphological covariance structure. Evolution. 2000, 54: 1784-1794.PubMedView ArticleGoogle Scholar
- Houle D, Mezey J, Galpern P: Interpretation of the results of common principal components analyses. Evolution. 2002, 56: 433-440.PubMedView ArticleGoogle Scholar
- Ackermann RR, Cheverud JM: Phenotypic covariance structure in tamarins (genus Saguinus): a comparison of variation patterns using matrix correlation and common principal component analysis. Am J Phys Anthropol. 2000, 111: 489-501. 10.1002/(SICI)1096-8644(200004)111:4<489::AID-AJPA5>3.0.CO;2-U.PubMedView ArticleGoogle Scholar
- Lenormand T: Gene flow and the limits to natural selection. Trends Ecol Evol. 2002, 17: 183-189. 10.1016/S0169-5347(02)02497-7.View ArticleGoogle Scholar
- Roff DA: The evolution of the G matrix: selection or drift?. Heredity. 2000, 84: 135-142. 10.1046/j.1365-2540.2000.00695.x.PubMedView ArticleGoogle Scholar
- Falconer DS, Mackay TCF: Introduction to Quantitative Genetics. 1996, Essex: LongmanGoogle Scholar
- Fowler K, Whitlock MC: The distribution of phenotypic variance with inbreeding. Evolution. 1999, 53: 1142-1156.View ArticleGoogle Scholar
- Caughley G, Grice D, Barker R, Brown B: The edge of the range. J Anim Ecol. 1988, 57: 771-785. 10.2307/5092.View ArticleGoogle Scholar
- Bull JJ: Evolution of phenotypic variance. Evolution. 1987, 41: 303-315. 10.2307/2409140.View ArticleGoogle Scholar
- Whitlock MC: Variance-induced peak shifts. Evolution. 1995, 49: 252-259. 10.2307/2410335.View ArticleGoogle Scholar
- Kirkpatrick M, Barton NH: Evolution of a species’ range. Am Nat. 1997, 150: 1-23. 10.1086/286054.PubMedView ArticleGoogle Scholar
- Atkinson D: Temperature and organism size - a biological law for ectotherms. Adv Ecol Res. 1994, 1992 (25): 1-58.View ArticleGoogle Scholar
- Lynch M, Walsh B: Genetics and analysis of quantitative traits. 1998, Sunderland: SinauerGoogle Scholar
- Flury BK: A hierarchy of relationships between covariance matrices. Advances in Multivariate Statistical Analysis. Edited by: Gupta AK. 1987, Boston: Reidel, 31-43.View ArticleGoogle Scholar
- Phillips PC: CPC: common principal components analysis. 1998, http://www.uoregon.edu/~pphil/software.html,Google Scholar
- Burnham KP, Anderson DR: Model selection and inference: a practical information theoretic approach. 1998, New York: SpringerView ArticleGoogle Scholar
- Gelman A, Carlin JB, Stern HS, Rubin DB: Bayesian Data Analysis. 2004, Boca Raton: Chapman and Hall/CRC, 2Google Scholar
- Pavlicev M, Cheverud JM, Wagner G: Measuring morphological integration using eigenvalue variance. Evol Biol. 2009, 36: 157-170. 10.1007/s11692-008-9042-7.View ArticleGoogle Scholar
- Pavlicev M, Wagner G, Cheverud JM: Measuring evolutionary constraints through the dimensionality of the phenotype: adjusted bootstrap method to estimate rank of phenotypic covariance matrices. Evol Biol. 2009, 36: 339-353. 10.1007/s11692-009-9066-7.View ArticleGoogle Scholar
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