Complex clines: the predictivity of complicated patterns of geographic variation portrayed by multivariate analysis

The stability of complex patterns of geographic variation was investigated by assessing the congruence between multivariate ordinations derived from randomly chosen real characters. Two series of populations were analysed representing two situations with complex patterns of geographic variation. The first, a ‘Eurasian’ series of populations, showed a strongly structured hierarchical pattern, the second, an ‘eastern’ series of populations, showed a more subtle complex pattern of smooth clines and steps. The characters were selected from a total of 81 (Eurasian) or 61 (eastern) within-population independent characters from six different systems. The congruence between ordinations of the geographical populations was measured by the rotational fit statistic, R². Three procedures were used to compare ordinations based on from two to up to 80 characters randomly chosen to give: A, completely independent character sets; B, subsets compared to the total set; and C, potentially overlapping sets. All three procedures showed that congruence between the ordinations was asymptotic in relation to character number. This relationship was described by one of two mathematical models (procedure B did not result in a hyperbolic model as found with simple patterns of geographic variation). Generally speaking, once a sufficient number of characters are used, the complex patterns of geographic variation are stable, reliable and predictive and not substantially influenced by character choice. The strongly structured hierarchical pattern required 15 or so characters to achieve reliability whilst the more subtle patterns required 20 or so characters. However, the addition of further characters does improve reliability in both cases. The greater percentage of variance portrayed by three-dimensional ordinations compared to two-dimensional ordinations is achieved at the cost of lower congruence when a sufficient number of characters are used. If case studies of geographic variation were to adopt these procedures (preferably using completely independent character sets; procedure A) the reliability of their results would be indicated).     

Clines: character number and the multivariate analysis of simple patterns of geographic variation

The stability of a clinal pattern geographic variation in relation to character number was investigated by the random selection of real characters. The characters used were selected from a set of 18 significant characters, drawn from four different character systems, and had a low within-group correlation. Principal component/coordinate analysis was used to elucidate the main pattern of geographic variation and the first principal coordinate was plotted against a geographical transect to illustrate this pattern. The existence of 'clinal' or 'monotically clinal' variation was assessed by the rank correlation between geographic position and coordinate score and the congruence between patterns of geographic variation was assessed by the correlation between the first principal coordinates of the appropriate analyses.
Two procedural models were used: A, the congruence between completely independent character sets based on 1–9 characters, and B, congruence between the 'total' analysis and those analyses based on 1–16 characters. The frequency of the types of pattern of geographic variation shown by these Model B analyses was also determined. Congruence is asymptotic in relation to character number and is described by various mathematical models, depending upon parameter and procedure. A broad pattern of clinal variation occurred in all analyses based on six or more characters and appears to be a stable feature of the racial affinities that is unlikely to be influenced by character choice. The details of the clinal pattern cannot be shown to be stable and may be influenced by the choice of character. This study had several findings in common with a previous study of categorical variation, e.g. the approximately hyperbolic relationship between character number and congruence in Model B, which may prove to be generally true in comparable situations.     

Geographic variation in scalation of the lizard Gallotia stehlini within the island of Gran Canaria

The lacertid lizard ( Gallotia stehlini ), an endemic of Gran Canaria, shows no visually obvious geographic variation, yet all seven scalation characters that were examined exhibit significant geographic variation. The number of collar scales, scales along the ventral trunk and femoral pores are correlated with habitat type, while the number of femoral pores is correlated negatively with altitude. Mantel tests were used to compare simultaneously an observed pattern with three hypothesized patterns (habitat type, altitude and proximity). They indicate that, while several individual characters are significantly associated with the putative causal factors of habitat type and altitude, there is no association between an overall scalation distance matrix and habitat type, or altitude when the effect of proximity is removed. Consequently, one should consider the individual characters as well as the multivariate generalized distances. Some of the observed patterns of geographic variation in scalation are very similar to those of the small scincid lizard Chalcides sexlineatus on Gran Canaria and also parallel the altitudinal and latitudinal variation in the scalation of the Tenerife lacertid ( Galotia galloti ). The low level of congruence in patterns of geographic variation in individual characters (i.e. some vary with latitude, some with altitude and one varies with longitude) is consistent with the hypothesis that ecogenetically caused geographic variation may result in lower inter-character congruence than phylogenetically caused geographic variation.     

Within-island microgeographic variation in the colour pattern of the skink,Chalcides sexlineatus: Pattern and cause

The colour pattern of the Gran Canarian skink is described with eight independent colour pattern characters. Significant geographic variation occurs in each character. There are generally high levels of congruence between the patterns of geographic variation in each character although some differences exist. In canonical variate analyses, the first canonical variate expresses most of the among-locality variation in colour pattern, indicating a largely unidimensional pattern. Patterns of geographic variation in the colour pattern are portrayed by contouring. This reveals north-east/south-west clines for seven of the individual characters and the generalized pattern (CV1). Four causal hypotheses were erected which predicted four different unidimensional patterns of geographic variation. Mantel tests and partial correlation analyses were used to compare the observed patterns of microgeographic variation with the four hypothesized patterns. This method suggests differential selection occurring between ecotones as the cause of the microgeographic variation. Microgeographic variation in some aspects of the colour pattern can be explained by selection for different anti-predator strategies in the hot, arid southern areas vs the cooler, lusher northern areas.     

Congruence between independent character systems across a hybrid zone: patterns in geographic space

The hybrid zone between eastern and western grass snakes, which has been independently hypothesized to be due to secondary contact, is investigated using univariate and multivariate analysis of a large number of independent, quantitative characters. Investigation of the patterns of geographic variation show that 5 out of 6 character systems show a congruent pattern of “stepped clinal” change across the zone. Insofar as this case is concerned, secondary contact ‘hybrid’ zones are associated with concordant changes in many character systems and “speciation” involves the origin of a large number of small differences in most character systems rather than the major reorganisation of a single system.     

Geographic variation in Pemphigus populicaulis (Insecta: Aphididae) in Eastern North America*,†

The geographic variation of 33 morphological characters of the gall-forming aphid Pemphigus populicaulis is studied for 118 localities east of 100^oW longitude. Variation can be partitioned into within-gall, among-gall and among-locality components. Among localities variation ranges from 26 to 54%, being significant for all characters. Variation among galls within localities ranges from 24 to. 56%, that within-galls from 8 to 4796. The design of the study permits computation of character correlation matrices within and among localities. Gall size is correlated with tnorphometric characters only on an interlocality but not on an intralocality basis. Interlocalily correlations are a function of intralocality correlations, confirming earlier predictions. There is little correlation between characters of stem mother and alate morphotypes within localities, whereas among localities such correlation is appreciable. This phenomenon may be caused by aspects ol the environment that vary among localities but remain reasonably constant through the earlv life cycle of the aphid. When subjected to factor analysis both correlation matrices yield four factors. Multiple discriminant analysis of the data set results in five interpretable significant axes. Maps are furnished for characters representing the independent dimensions of variation and for discriminant function scores. The patterns of variation can be shown to be significantly nonrandom by Mantel's test and by spatial autocorrelation analysis. All variables are significantly positively autocorrelated at 200 km, many at 400 km and a few at 600 km; few general statements can be made about significant autocorrelations at higher distances. The positive autocorrelation at relatively short distances may be related to the pool of clones from which the genotypes of any one locality sample are taken. There are three correlogram patterns that can be associated with four clusters of variation patterns of characters. The separate patterns presumably cannot be explained by a single microevolutionary process.     

Morphological and molecular variation in tiger beetles of the Cicindela hybrida complex: is an ‘integrative taxonomy’ possible?

Current taxon assignments at the species level are frequently discordant with DNA-based analyses. Recent studies on tiger beetles in the Cicindela hybrida complex identified discordance between mtDNA patterns and the entities currently defined by the taxonomic literature. To test the accuracy of morphologically delimited groups, five named taxa (species) from 24 representative sampling sites across Europe were scored for 41 external morphological characters. Three of the named taxa were 'diagnosable', that is, defined by between one and three characters unique to each group. Newly sequenced ITS1 and existing mitochondrial cox1 markers established 20 and 22 different haplotypes, respectively, but only cox1 produced (four) diagnosable units. Phylogenetic analysis and statistical parsimony networks showed poor congruence of character variation with the taxonomic entities (and each other). Variation in morphological characters was therefore tested directly for association with DNA-based nesting groups at various hierarchical levels using permutational contingency analysis. Significant statistical associations of 11 (of 13 variable) morphological characters were observed with nesting groups from ITS1 and mitochondrial DNA markers, predominantly at the 4-step level. The analysis demonstrates the need for formal tests of congruence with morphological variation at the level of individual characters, a step that is omitted from recent studies of 'integrative taxonomy'. In addition, statistical correlation of particular morphological characters with DNA-based nesting groups can identify the lowest hierarchical level at which various character sets show congruence, as a means to define evolutionarily separated entities supported by diverse data sources.     

Ecotypes and genetic structure of Rhinanthus alectorolophus (Orobanchaceae) in southwestern Germany

European annual species of the genus Rhinanthus often exhibit seasonal ecotypic variation, a phenomenon also known from related genera of hemiparasitic Orobanchaceae. Populations with different flowering times exist, correlated with differences in a number of morphological characters. The present study evaluates the correlation of morphological characters and genetic differentiation of populations of Rhinanthus alectorolophus. Thirty-nine populations of three different subspecies from southwestern Germany were sampled. A total of 798 individuals were used for morphological analyses and 187 of these for AFLP analyses. Principal component analysis showed that morphological variation is mostly continuous. In a discriminant analysis based on morphological characters, only 89.7 % of all individuals were correctly assigned to their previously determined subspecies, indicating that subspecies identification is ambiguous for some populations. Using AFLP data and Bayesian assignment analysis, the sampled individuals could be grouped in three genetic clusters which do not correspond to the three subspecies. Instead, the clustering shows a clear geographic pattern and a Mantel test likewise revealed a significant correlation between genetic and geographic distances. Correlations of genetic distances with differences in morphological characters were weak and mostly insignificant. The results indicate that the subspecies of R. alectorolophus do not form discrete entities and that the character combinations distinguishing them are homoplastic.     

BIOMETRIC ANALYSIS OF GEOGRAPHIC VARIATION AND RACIAL AFFINITIES

1. The study of geographic variation and the racial affinities between populations is of central importance to systematics and evolutionary theory. When using phenotypic variation to measure the similarity between the populations of a species one should analyse the variation in several characters simultaneously. This is a statistical procedure and is known as multivariate analysis. Multivariate analysis of phenotypic variation, unlike some other methods, has the advantage of not being dependent on living specimens. 2. To obtain an adequate sample at each locality, and an adequate distribution of localities within a given geographic area, can be a major problem. The pooling of data from adjacent localities is discussed. 3. There are several sources of phenotypic variation within a species, e.g. sexual and ontogenetic variation. Failure to eliminate the non-geographic sources of variation can confuse the assessment of the similarity between populations. 4. Correlation between characters can reflect similar genetic control and/or similar patterns of geographic variation, the biological interpretation being influenced by whether the data come from one locality or many. 5. The influences of environmental induction and genetic control cannot easily be separated. Also, some characters may not be entirely homologous throughout the range of the species. 6. Most studies rely on far too few characters of a too restricted type to give an ‘overall’ assessment of the phenotypic similarity. This is one of the most neglected aspects of the study of geographic variation. 7. The various forms of clinal and categorical variation, the precise nature and position of sharp transition (hybrid) zones, the relationship between non-adjacent as well as adjacent populations and the phenotypic divergence between island populations, etc., all come under the heading of geographic variation. The ideal technique should be able to elucidate all types of geographic variation but some techniques can only be used effectively with a few of them. Moreover, techniques may be limited in their application because they require the data to conform to certain models, e.g. normal distribution. 8. The degree of phenotypic similarity between populations can be measured by a wide range of similarity coefficients. Comparison between even a small series of populations produces a large set (or matrix) of similarity coefficients that is difficult to interpret. However, the relationships between populations can be summarized in several ways and these may be loosely grouped into four categories; (i) network diagrams, (ii) contours and isometric plots, (iii) hierarchical clusters, and (iv) ordination methods. These methods are explained and their advantages and limitations discussed. 9. The hierarchical (dendritic) model of cluster analysis is unsuitable for analysing all but a few types of geographic variation. 10. There are several types of ordination technique. They all aim to summarize the variation of many characters in a reduced number of axes. One can either emphasize the biological interpretation of each separate axis, or treat the analysis as a classifying technique and assess the grouping of the populations in the space defined by the axes. Considerable care is needed in interpreting the results of both of these approaches. If correctly applied, ordination techniques generally can be used to analyse all the forms of geographical variation and are therefore recommended. Contrary to current practice they can be used with a large number of characters. The advantages and limitations of the various ordination techniques are discussed. 11. Contours and their three-dimensional isometric plots can be used to portray geographic variations in the information obtained from a multivariate analysis. However, contours and isometric plots are limited in their applicability and the amount of information they can convey. 12. The sophistication of some multivariate methods should not be allowed to cloak the scientific inadequacies of a study. The use of more than one technique and variety in the choice of pertinent parameters may be of value in indicating the reliability of the results.     

Function and the Evolution of Phenotypic Stability: Connecting Pattern to Process

Phenotypes manifest a balance between the inherited tendencyto remain the same (phenotypic stability) and the tendency tochange in response to current environmental conditions (adaptation).This paper explores the role of functional integration and functionaltrade-offs in generating phenotypic stability by limiting theresponses of individual characters to environmental selection.Evolutionarily stable configurations (ESCs) are systems of functionallyinteracting characters within which characters are "judged"by their contribution to system-level functionality. This "internal"component of selection differs from traditional "external" selectionin that it travels with the organism wherever it goes and ismaintained across a wide range of environments. External selection,in contrast, is by definition environment-dependent. The temporaland geographic constancy of internal selection therefore actsto maintain phenotypic stability even as environments change.Functional trade-offs occur when one character participatesin more than one function, but can only be optimized for one.Participation of certain ("keystone") characters in a trade-offpotentially causes stabilization of an entire system owing toa cascade of functional dependencies on that character. Phylogeneticcharacter analysis is an essential part of elucidating theseprocesses, but patterns cannot be used as prima facie evidenceof particular processes.     

Analysis of asymmetries in the African fruit bats Eidolon helvum and Rousettus egyptiacus (Mammalia: Megachiroptera) from the islands of the Gulf of Guinea. I. Variance and size components of bilateral variation

A set of cranial characters was examined in the fruit bats Rousettus egyptiacus and Eidolon helvum to compare trends and relative importance of major components of bilateral morphometric variation, and their relationship with character size. Using two‐way, sides‐by‐individuals ANOVA , four components of variation were estimated for each bilateral variable: individual variation (I), directional asymmetry (DA), non‐directional asymmetry (NDA) and measurement error (E). Both species exhibit similar major trends of variation in asymmetry across characters, as shown by principal component analysis, using variance components as variables. Degree of interspecific congruence among characters was confirmed by a two‐way ANOVA with species and variance components as fixed factors. Congruence of asymmetry patterns between species suggests that the concept of population asymmetry parameter (PAP) could be extended to higher hierarchies. PAPs above the species level may result from common mechanisms or similar developmental constraints acting on species’ buffering capacities and morphological integration processes.     

Morphometric analysis of the Bersama abyssinica Fresen. complex (Melianthaceae) in East Africa

 The morphological variation of the Bersama abyssinica complex in East Africa is analysed. A wide range of characters was examined both on specimens collected for this study and on a selection of type material. The character distribution of each character was examined individually. The ratios of some of the characters were calculated, and selected characters were plotted in pairwise combinations. Non-metric multidimensional scaling and principal component analysis were employed in the multivariate analyses. On the basis of the patterns observed in the numerical analyses as well as those in the field, a new combination, Bersama abyssinica Fresen. ssp. rosea (Hoyle) Mikkelsen is proposed. The presence of the two flower types described by White: (a) male flowers, with long stamens and short gynoecium and (b) female flowers, with short, abortive stamens and long gynoecium is confirmed, but found to be taxonomically insignificant. Received May 12, 2000 Accepted February 13, 2001     

长白落叶松种群地理变异研究

根据17年生长白落叶松种源试验资料,从生态遗传学的观点出发,采用典型相关分析等方法,揭示了长白落叶松地理变异规律可以认为,以海拔垂直梯度为主、纬向渐变为辅的连续型变异;低海拔、低等效纬度的小北湖种源是长白落叶松优良基因资源中心,生长较快、生长期较长;水热因子的综合选择作用是长白落叶松地理变异的重要因素,其中温度是主导因子;在地理种群的遗传分化中,生长性状的分化最为明显,可以作为种源区区划的主要性状;从长白落叶松分布的低等效纬度地区向高等效纬度地区调种(一般不超过2个等效纬度),可望获得较大的遗传增益.     

The adaptedness of the floral phenotype in a relict endemic, hawkmoth-pollinated violet. 2. Patterns of variation among disjunct populations

This study examines patterns of variation in quantitative floral traits among 18 disjunct populations of Viola cazorlensis (Violaceae), a relict endemic violet of south-eastern Spain. At all sites, the species is almost exclusively pollinated by a single species of day-flying hawkmoth. Differences between populations were significant for all traits examined, and population means exhibit a broad range of variation. When all characters are considered together, each population displays a unique combination of characters. Despite interpopulation differences in character means, local populations retain most of the variability of the entire species. Floral traits do not vary in unison among flowers, and at least four different subsets of independently varying traits are identifiable. Floral similarity between populations of V. cazorlensis was largely unrelated to geographic proximity, as revealed by analyses at both large and small geographic scales. The geographic pattern of floral variation among populations represents a random patchwork, with unique combinations of character means occurring randomly across the study region. Marked population differences in quantitative floral traits in spite of spatial constancy in the identity of pollinators, a disintegrated floral phenotype, and prevailingly random geographic variation among populations, suggest low adaptedness of the floral phenotype of V. cazorlensis to its current hawkmoth pollinators.     

QUANTITATIVE CHARACTERS IN PHYLOGENETIC ANALYSIS

Abstract— When analysing phylogcnetic relationships at low laxonomic levels it is often the ease that many of the features that can be used to separate taxa show continuous variation. The theoretical and practical problems for the use of such quantitative characters in phylogenetic analysis arc examined. Three methods of coding continuous data into discrete characters are assessed in detail: simple gap-coding, generalised gap-coding and segment-coding, a form of range-coding. The methods are applied to a data set gathered for Eucatyptus L'Hérit. informal subgenus Symphyomyrtus section Maidenana (Myrtaceae). Each method is capable of distorting relative differences between taxa, but segment-coding produces the least amount of distortion, provided the range of variation of the character is divided into a sufficient number of character states.
Continuous quantitative characters provide data for phylogenetic analysis that arc more noisy than those provided by discrete qualitative characters and should, therefore, only be used when the number of qualitative characters is insufficient for resolution of relationships. The results of such analyses should be recognised as provisional pending the discovery of more readily informative characters.     

Convergence and parallelism: is a new life ahead of old concepts?

In comparative biology, character observations initially separate similar and dissimilar characters. Only similar characters are considered for phylogeny reconstruction; their homology is attested in a two‐step process, firstly a priori of phylogeny reconstruction by accurate similarity statements, and secondly a posteriori of phylogeny analysis by congruence with other characters. Any pattern of non‐homology is then a homoplasy, commonly, but vaguely, associated with “convergence”. In this logical scheme, there is no way to analyze characters which look similar, but cannot meet usual criteria for homology statements, i.e., false similarity detected a priori of phylogenetic analysis, even though such characters may represent evolutionarily significant patterns of character transformations. Because phylogenies are not only patterns of taxa relationships but also references for evolutionary studies, we propose to redefine the traditional concepts of parallelism and convergence to associate patterns of non‐homology with explicit theoretical contexts: homoplasy is restricted to non‐similarity detected a posteriori of phylogeny analysis and related to parallelism; non‐similarity detected a priori of phylogenetic analysis and necessarily described by different characters would then correspond to a convergence event s. str. We propose to characterize these characters as heterologous (heterology). Heterology and homoplasy correspond to different non‐similarity patterns and processes; they are also associated with different patterns of taxa relationships: homoplasy can occur only in non‐sister group taxa; no such limit exists for heterology. The usefulness of these terms and concepts is illustrated with patterns of acoustic evolution in ensiferan insects. © The Willi Hennig Society 2005.     

CHARACTER DISCRIMINATORY POWER,CHARACTER-SET CONGRUENCE,AND THE CLASSIFICATION OF INDIVIDUALS FROM HYBRID ZONES: AN EXAMPLE USING STONE CRABS (MENIPPE)

Many investigators categorize individuals from hybrid zones to facilitate comparisons among genotypic classes (e.g., parental, F₁, backcross) for comparative studies in which components of fitness or geographic variation are being analyzed. Frequently, multiple character sets representing genetically independent traits are used to classify these individuals and various methodologies are employed to combine the classifications obtained from the different character sets. We adapted the principles of total evidence and taxonomic congruence (two formalized approaches used by systematists in formulating phylogenetic hypotheses) to address the problem of discriminating hybridizing species and classifying individuals from hybrid zones. As our model, we used two morphological (coloration and morphometric) and two molecular (allozyme and mitochondrial DNA restriction-fragment-length polymorphism) character sets that differentiate two stone crab species (Menippe adina and M. mercenaria). Using principal-components analysis, we determined that combining character sets and eliminating characters or character sets that did not have large eigenvector coefficients for the principal component that best separated the two species yielded the highest level of discrimination between species and allowed us to classify a broad range of morpho-genotypes as hybrids. For the stone crabs, three diagnostic allozyme loci and five diagnostic coloration characters best separated the species. The two character sets were not completely congruent, but they agreed in their classification of 50% of the individuals from the hybrid zone and rarely strongly disagreed in their classifications. Classification discrepancies between the two character sets probably represent variation between traits in interspecific gene flow rather than intraspecific, ecologically mediated variation. Our results support the assertions of previous investigators who espoused the benefits associated with using multiple character sets to classify individuals from hybrid zones and demonstrate that, if character sets are reasonably congruent and numerically balanced, combining diagnostic characters from multiple character sets (a total-evidence approach) can enhance discriminatory power between species and facilitate the assignment of hybrid-zone individuals to genotypic classes. On the contrary, classifying hybrid-zone individuals using character sets separately (a taxonomic-congruence approach) provides the opportunity to compare levels of introgression between species and to assess reasons for discordance among the data sets.     

Sequence length variation, indel costs, and congruence in sensitivity analysis

The behavior of two topological and four character‐based congruence measures was explored using different indel treatments in three empirical data sets, each with different alignment difficulties. The analyses were done using direct optimization within a sensitivity analysis framework in which the cost of indels was varied. Indels were treated either as a fifth character state, or strings of contiguous gaps were considered single events by using linear affine gap cost. Congruence consistently improved when indels were treated as single events, but no congruence measure appeared as the obviously preferable one. However, when combining enough data, all congruence measures clearly tended to select the same alignment cost set as the optimal one. Disagreement among congruence measures was mostly caused by a dominant fragment or a data partition that included all or most of the length variation in the data set. Dominance was easily detected, as the character‐based congruence measures approached their optimal value when indel costs were incremented. Dominance of a fragment or data partition was overwhelmed when new sequence length‐variable fragments or data partitions were added. © The Willi Hennig Society 2005.