Processes generating macroevolutionary patterns of ...webpages.icav.up.pt/PTDC/BIA-BEC/098414/2008/Bjorklund 1994.pdf · J. evol. Biol. I: 121 742 (1994) 1010 061X 94 060727 16 5

J. evol. Biol. I: 121 742 (1994) 1010 061X 94 060727 16 5 I.50 +0.x 0 t 1994 IbrkhAuser Vcrlag. Bascl

Processes generating macroevolutionary patterns of morphological variation in birds: a simulation study

Mats Bjiirklund

Key worht Macroevolution; microevolution; process; pattern; morphology; size allometry; birds; genetic correlations; correlated selection.

Abstract

Multivariate patterns of morphological variation in birds are analysed. In gen- eral, there are strong allometric patterns among characters such that most of the variation is confined to a major “size” axis. To analyse the possible evolutionary processes behind this pattern I employed a computer simulation of cladogenesis and anagenesis based on a genetic and a random walk model (drift). All runs started with one species and speciation occurred to generate 100 species. Three levels of correlations were allowed. The results from the simulations were compared with the pattern of variation in finches (Fringillidae).

The simulations showed two things. First, the univariate drift model was inap- propriate in terms of the level of variation: the observed level was lower than expected by drift. Univariate drift was also unable to create tight correlations among characters as observed in several taxa. Second. to create the pattern observed, either relatively strong genetic correlations (re z 0.5), or alternatively strong correlated selection, was needed. This suggests that morphological change in birds in genera1 consists of changes in growth such that species become larger or smaller than their ancestors but retain their ancestral shape. The results stress the importance of stabilising selection in shaping the macroevolutionary patterns of morphological variation in birds.

Introduction

Morphological variation in nature is patterned as a result of evolutionary processes, which through time have modified the already existing into novel ways of being. Numerous patterns of morphological variation have been described and a

727

728 Bjiirklund

plethora of processes has been suggested to account for the patterns observed (reviewed by Larson, 1989). The process inferred is, of course, conditional on the pattern observed (e.g. Eldredge and Cracraft, 1980), and there is no reason to assume that only one process has been operating over evolutionary time.

In the light of all models, is it possible to conclude that one particular process has been of predominant importance over time, or does the history of life consist of a complicated mixture of many kinds of processes? This question has been studied in dilt‘ercnt ways, using, for example, analysis of palcontological and neontological data (Turner, 1986; Larson, 19X9), and computer simulations (e.g. Raup et al., 1973; Raup and Gould, 1974; Lemen and Freeman, 1984, 1989; Maurer ct al., 1992). The obvious way would be to trace evolutionary trends and patterns of change through the chronicle of life (O’Hara, l988), and by using a well-corrobo- rated phylogeny infer the processes generating the patterns. However. at this point scarcity of sufficiently detailed phylogenetic information prevents us from doing this.

In this paper I will use computer simulations of microevolutionary models to analyse their ability to predict patterns of morphological variation in birds using the cardueline finches (Carduelinae: Fringillidae) as a model group. First, I will rcvicw literature data of morphological variation of different groups of birds. Second, I will briefly review the main features of the different microevolutionary models. Finally, I will implement the models in a computer simulation that utilises data gathered from museum specimens of cardueline finches (Bjiirklund, 1991). In contrast to previous simulations of the evolution of morphological variation (for example Raup and Gould, 1973; Lemen and Freeman, 1984, 1988; Maurer et al., 1992) my simulations will use an explicit quantitative genetic model involving genetic covariances among traits. Is it possible to regenerate the pattern observed in birds by using these microevolutionary models, or is it suficient to invoke simple univariate drift models?

Patterns of morphological variation in birds

To assess the pattern of morphological variation in different taxa of birds I performed a literature search. Several different taxonomic levels were used, namely, subspecies within species, species within genera and genera within Families, both passerincs and non-passerines, all chosen such that a wide spectrum of taxa was analysed. Furthermore, only taxa with data available for all members rather than various subsets were used. The measurements were taken from external morpholog- ical characters namely wing length, tarsus length. tail length, and bill length. Based on these data I analysed the variance of the eigenvalues of the among taxon correlation matrix (Wagner, 1984; Cheverud et al., 1989). There are as many cigcnvalues as there are rows (and columns) in the matrix. The variance of these cigenvalucs has shown to be a useful measure of the degree of correlational structure (Wagner, 1084; Cheverud et al., 1989) since if correlations were close to lero all eigenvalues will be about equal and hence the variance low. If there are very

Morphological variation 111 birds 129

high correlations, the first eigenvalue will be much larger than the remaining oncs, hence the variance will be high. I also calculated the among species variance for all traits combined (total variance) and will give also the variance for the most variable trait. To assess the significance of the variance of the cigcnvalucs I created random correlation matrices (with the appropriate number of characters involved) from randomly created data sets and calculated the variances of the eigenvalues. This was repeated IO 000 times to create a distribution of random variances. Observed variances were then compared against this random distribution.

Most taxa showed high variances of the eigenvalues (Tab. I), resulting from a dominant first eigenvaluc. The eigenvector associated with the leading cigenvalue without exception had loadings of the same sign for all characters indicating most of the variation to be limited to a general allomctric sire axis with only minor variations in shape (for an example see Fig. I ). Note that this holds regardless of taxonomic level, subspecies within species, species within genera. and genera within families all share the same pattern. This may to a certain extent reflect the classiffcation system used by earlier generations of taxonomists that may have grouped the species into taxa on the basis of subjective shape similarities. However. in birds many of the taxonomic delimitations are based on similarities in plumage,

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Sources: I) Forshaw. lY78. 2) Vaune. lYS3. 3) Miller. 1941. 4) Storer. IYXY. 5) Selander. 1964. 6) Fry.

19X4. 7) Williamson. lYh4. 8) Billiard, lY69. 9) Friedmann. IYSS. IO) Snow. 19X2. I I) Woodall. I99 I.

730 Bjiirklund

Fig. 1. An cxamplc of an allometric relationship within a taxon: bill depth and bill width in Carduelinac.

The c~~rretat~on cocficient in tlus case is 0.97.

and not shape (e.g. Cracraft, 1992), so it is likely that this is only a minor problem with regard to the present study.

In the carduelines five different traits were considered, namely wing length, tail length, tarsus length, bill depth, and bill width (Bjiirklund, 1991). The basic feature of the multivariate variation was the high positive correlations among traits, as rellccted in the highly uneven distribution of the eigenvalues. The first eigenvalue accounted for 83.6”% of all variation (based on the covariance matrix), while the second accounted for 11.6% (Tab. 2), and the variance of the eigenvalues of the correlation matrix was 2.83. The first eigenvector can be interpreted as a general allometric size vector (Bookstein, 1989), and the second vector as shape. The pattern of correlation among species can be plotted in a size-shape plane (Fig. 2).

Fig. 2. The pattern of SIX and qhapc variation in birds as uxcmplifed by the genus (‘~w~l~~~~/~.~

t(‘arducl~nae) adopted from Bjorklund and Merila (1993). Sile and shape dctcrmmed by principal

conlp~~nent\ ‘Inal>\‘\

Morphological variation III birds 731

Table 2. Desmption of Carduellne unlvariatc and multivariate morphology. a) Means. standard

dcwations and range expressed in units of standard devlatlona from thr man. PCA calculated on

covariance matrix and PCI and PC‘2 values correspond to loadings on the tirst and second elgenvector.

respectively. b) Among spccics correlation matrix.

a) Trait

Wing

Tail

Tarsus

Bill depth

Bill width

Eigenvaluc

%,

x3.93 14.1x - I .lY. 2.54 0.2Y2 0.21 I

Sl.Yl 12.00 --2 31, 2.52 0.377 0.655

17.12 3.23 - I .XY. 2.04 0.309 0. SOY

7.77 2.35 ~ I 55. 2.96 0 5XY - 0.395

6.30 I .Y4 I .50. 3.03 0.604 -0.333

0.243 0.034

83.6 I I.6

b) Trait Wing Tail Tarsus Bill depth BIII wdth

Wing I

Tail 0.77 I

Tarsus 0.75 0.88 I

Bill depth 0.77 0.62 0.66 I

Bill width 0.76 0.65 0.69 O.Y7 I

The variation along the size axis is far greater than the variation along the shape axis. Thus, the cardueline finches closely f.allow the pattern found in other taxa.

Models of evolutionary change

The simplest explanation for the pattern observed is random walk (Bookstein. 1987, 1988) as a result of drift due to the fact that each population acquires different mutations over time. That random walk models can create patterns is well known (Raup et al., 1973; Raup and Gould, 1974; Bookstein, 1987, 1988). Under the assumption of drift of effectively neutral characters it can be shown that the variance in the characters among 17 populations sharing a common ancestor is proportional to time and mutational input, i.e. Var(among) = 2t Var(- mut) (Lande, 1976; Turclli et al., 1988; Lynch, 1989). This can be extended to a multivariate case, so that, given long periods of independent evolution for each of the populations and random extinction and branching, the expected mean is the same as for the ancestor with the covariance matrix equal to 2tU where U is the matrix of mutational variances and covariances and r is time (Sawyer, 1976; Lande, 1979).

Microevolutionary changes in mean values of a set of morphological characters in each generation (AZ) are commonly described as a function of the genetic architecture of the species (G) and the selective pressures acting on it at a given time

AZ = G/I (1)

(Lande. 1979). where b is the selection gradient, i.e. the selection differentials after phenotypic correlations among characters have been partialled out ([j = P ‘s, where P is the henotypic variance-covariance matrix, and s is the selection differen- tial [Lande and Arnold, 19831). [I’ describes the change in character means as a result of the directional selection on each character taking into account selection on phenotypically correlated traits. Two extreme situations illuminate the importance of C, in predicting microevolutionary change. First, if genetic correlations are low (ofY-diagonal elements of G zero, or very close to zero) this results in nearly independent evolution of different parts of the phenotype, each responding to the local selective surface, i.e. AZ is strongly correlated with /I. Second, if the magnitude of the genetic correlations is great (close to 1 .O) the phenotype evolves more or less as a unit, commonly at the expense of local adaptiveness of each trait separately, i.e. AZ does not have a strong positive correlation with B. This leads to changes mainly in terms of overall (allometric) size, with only minor shape adjustments, the magnitude of which are determined by the strength of the genetic covariances. This model is strictly microevolutionary, as the level of genetic correlations can be shown to bc comparatively unimportant in the long run since they can be altered by selection and thus mainly affect only the rate at which populations move towards adaptive peaks (Felsenstein, 1979; Charlesworth et al., 1982; Lande, 1986; Zeng, 1988). Since long-term evolution depends on selection and to a much lesser degree on genetic parameters, the models used in the simulation, in effect, can be a description of the selection needed to generate certain patterns, rather than the effect of long-term transient genetic parameters. Hence, a correlation of 0.8 between characters will be taken to mean either a genetic correlation or correlated selection depending on the time scale adopted. In the short term (a few hundred generations) the genetic correlation interpretation is probably valid (Turelli, 1988), whereas in the long-term (millions of years) the correlated selection interpretation is more valid. This shows that the model adopted is very flexible and can be applied to many kinds of problems.

Methods

The simulations started with a seeding of the five characters, each with a value of 0.0, to an ancestral species. In each species and each time unit three things happened: first. a change in the mean values using one of the models given below,

Morphological variation in birds 733

second, speciation with probability S, and finally, extinction with probability E. The simulation ended after 500 time units, and each run was repeated 100 times. If the appropriate number of species had not yet arisen after this time period, the run was restarted. Since the approximate age of the carduclines is about 20 MYR (see Bjiirklund, 1991) one time unit corresponds to approximately 40 000 years. The whole clade was constrained to fall within the bounds delimiting the Carduelinae (Tab. 2).

A univariate random walk was simulated by adding or subtracting a value drawn from a normal distribution to each character with equal probability independent of the four other characters (i.e. a Brownian motion process). The basic model used in the simulations of selection was eq. (I). Obviously the structure of G will greatly affect the outcome of sclcction. Three different multivariate models will be used, diKering from each other with regard to the strength of genetic correlations. These will be low (rr = 0.2) intermediate (Y, = 0.5), and high (rc = 0.8). For all simula- tions it is assumed that the correlations are constant over time. I will also use a llexible correlation model where the strength of the correlations is determined, for each entry in the matrix and for each species and time unit, from a uniform random distribution ranging from 0.0 to 1 .O. In each generation the change in the multivari- ate models was set as in eq. ( I), where /i is a vector of random Gaussian deviates all with zero mean, and standard deviations fitted to yield an acceptable amount of change over the time span involved in the simulations (SD = 0.05). The choice of a Gaussian distribution is arbitrary.

There arc many ways to simulate cladogencsis (Raup. 1985). In this study I simulated the evolutionary history of the group in the following way. The model of cladogenesis by definition will be deterministic since I wanted to simulate the evolutionary history of an extant clade consisting of about 100 species. Therefore. speciation rate (S) was set higher than the extinction rate (E). Both S and E are unlikely to be constant over time and lineages. Thus, they were allowed to change by letting the probability of speciation or extinction equal .u:‘g, where x is fixed but different for extinction and speciation, and K a gamma deviate taken from a gamma distribution with the central mass centred around 3.0 to obtain probabilities for speciation and extinction for each species and time unit. The gamma distribution was used to make the process of speciation and extinction episodic rather than rate homogeneous. Two versions of the simulation were run. First. speciation and extinction were set to be independent of the actual number of species up to 100 species where spcciation could occur only after an extinction event (to be called the c/~~n.sit),-in~~~prnr/~Jnt model). This yields an exponential increase of number of species

134 Bliirklund

o\cr time, differing among runs mainly in terms of time to saturation (Fig. 3). Secondly, speciation and extinction were set to bc dependent on number of existing speck such that probabilily of speciation decreased and probability of extinction increased with increasing number of species (to be called the ck~nsi/~~-~k~pc~tt~lr~ttt model; Nee et al., 1992). This yields a smoother accumulation of species number (Fig. 3). Again, 100 specks were set as the limit. This corresponds to an adaptive radiation where after some time all available space is occupied and new species can arise only after extinction of an existing species. The new species formed was seeded

E‘ig. 3. Species build-up in the simulations by a) density-independent spcuation and extinction. and b)

dcmity-dependent spcciation and extinction. Maximum numb of species was set to 100. Each graph

jhows two randomly chosen runs 01‘ each model.

Morphological variation in birds 735

with the value of the parental species. Extinction was prohibited until 10 species had evolved. This restriction was set to avoid early extinction of the whole clade (i.e. the simulation would terminate too early).

A correlation matrix (5 times 5 characters) was calculated from the mean values of each species (100 species times 5 characters matrix) and eigenvalues and eigenvcctors extracted. The fit of the models to observed data was analysed by comparing the vector correlation of the first eigenvector of the simulated data matrix to the corresponding vector from the observed matrix from the carduelines and the level of integration, i.e. the variance of the cigenvalues to that found in the Cardueline.

Results

Neither in the univariate nor the multivariate random walk models were there any significant differences between the results obtained by the density-independent and the density-dependent models of cladogenesis. Therefore. in the following, only results from the runs involving density-dcpendencc will be shown (an arbitrary choice). The among-species variance in the finches was found to be in the order IO 1 to IO ’ (BjGrklund, 1991). The mutational input per population per genera- tion (assuming time since common ancestor as 2 x IO’ years) would have to be in the order of IO ‘I. This should be contrasted with the observed mutational variance in quantitative characters of approximately 10 3,, C’, (environmental variance; Lynch, 1988). Setting c’,. z 1/2V, (phenotypic variance) yields an estimate of IO 4 in the cast of carduelinc finches. Thus. the variation observed is orders of magnitude lower than that expected by drift alone. Either the estimate since the common ancestor is wrong by a factor of 105, which seems highly unlikely, or the estimates of the mutational variance are sevcrcly biased. There is no evidence for either of these possibilities (Lynch, 1988).

However, there is one assumption involved in these calculations that clearly is violated, namely independence of the lineages. The univariatc drift model assumes that each of the populations has evolved [ generations. Clearly. since evolution is a branching process. this is not the case. Therefore. I estimated the expected among- species variance under the same mutational input but using a branching tree rather than a star phylogeny. Using the very flexible model of cladogenesis described above the expected among-species variances were indeed lower than if we used a star phylogeny. but only with a factor of IO (based on 1000 runs). Thus, the estimates of necessary mutational input to create the observed among species variance by drift alone are still oft‘ by several orders of magnitude.

Moreover, the univariate random walk model was also unable to create the high level of integration found in the Carduelinae and other taxa (Tabs I and 3). The among species correlations obtained by the model were far too low to be compat- ible with the observed data. Furthermore, the correlations obtained also involved

Bj6rklund

negative correlations whereas in the real data sets, the correlations, virtually without exception, were strongly positive (see for example Carduelinae; Fig. 2). This overall pattern of correlations could not be produced by a model allowing characters to change randomly and independently of each other. To obtain such correlations mutations would have to have strong pleiotropic effects, all pointing in the same direction.

The vector correlation of the first eigenvector of simulated covariance matrices with the observed first eigenvector in the cardueline covariance matrix was similar across simulations (Tab. 3). In all cases the mean was between 0.3 and 0.4, with an upper 2.5 percentile around 0.87. This corresponds to the upper 5th percentile of the two random vector correlations, i.e. the similarity between the simulated data and the observed was not closer than that expected by chance.

On the other hand, there were clear patterns in the variance of the eigenvalues of the correlation matrix. Using rK = 0.2 the variance was much lower than predicted ( = found in the Carduelinae) and lower than for most other taxa analysed (Tabs I and 3) but substantially higher than for the univariate random walk model. At the other end of the spectrum, rx = 0.8 created too tight correlations with an average variance of the eigenvalues of 3.7, and with the lower 2.5 percentile higher than for all taxa analysed. The intermediate level, r, = 0.5, gave an excellent fit to the predicted values, with a mean of 2.79 (observed value = 2.83; Tab. 3). The mixed correlation model also gave acceptable results although the variances of the eigcnvalues were generally too low (Tab. 3). This is not surprising since the correlations were taken from a uniform distribution with end points 0.0 and I.0 which gives a mean value of 0.5. However, the variance of the mean is much higher in this model than in the fixed correlation model.

Table 3. Summary of the results from simulations with dill‘erent degrees of correlations among traits.

I:rom the left: mean vector correlatmns to the carduclinc first cigcnvector (Tab. 2; WI. 4) and in brackets 95’%1 conlidcnce limits. variance of the eigenvalues of the among species correlation matrix. and the

dilferencc between the observed (cardueline) and simulated variances in units of standard deviations 01

the simulated area.

Degree of correlation rc Difference

0.0 0.401 [0.015. 0.8711 0. I52 [O.OOO, 0.4591 -23.3

0.2 0.319 [O.Ol I, 0.X72] 0.X46 [0.230. I .674] --5.51

0.5 0.341 [0.020, 0.X64] 2.793 [X273, 3.2591 0.14

0.8 0.403 [0.027,0.857] 3.730 [3.570. 3.X46] + IS.3

MlXCd 0.356 [0.017,0.818] 2.005 [ 1.298, 2.7791 -2.39

Morphological variation in birds

Discussion

737

It is clear from the simulations that the univariate random walk model (drift) is unable to account for the patterns observed in the Carduelinac and other avian taxa. It failed in two important respects. First, the observed among-species variance was several orders of magnitude lowr than expected from drift models of neutral characters. This clearly rejects hypotheses of selective neutrality of these characters over time in favour of stabilising selection. The prevailing pattern in the taxa analysed is one of conservatism of a general phenotype over considerable time periods by means of selection for its preservation thus yielding stasis. This does not completely rule out drift. Suppose that each taxon occupies a specified adaptive peak, then movements around the peak may still occur as a result of drift, although their scope is delimited by the boundaries of the peak. In fact, this is the scenario suggested by genetic models of macroevolution, species can drift around a peak for considerable time periods (millions of years), especially if effective population sizes are large, and then a shift to a new peak will be relatively fast (thousands of years; Barton and Charlesworth, 1984; Lande, 1986, 1988). Data on selective neutrality of phenotypic morphological characters are rare (Endler, 1986) although Bjorklund and Linden ( 1993) provide an example from the great tit (Puru.r major). It was also found that the among-species variance between the great tit and its closest con- gener, the blue tit (Purus c~rru/~~u.s), were close to the expectations from a drift model. This indicates that rates of evolution may differ considerably among different taxa.

Second, although limits to diversification were imposed on the simulations by means of boundaries based upon those observed in the finches, these were not sufficient to create the patterns of among-species character correlations observed in the finches and other taxa by the univariate random walk model. In general, the real correlational patterns were tighter than those created by a univariate random walk, which also holds for the low-correlation model. This suggests two things. First, there may be long-term constancy of genetic correlations. Lande (1979) showed that if genetic correlations are constant over time. then an allometric pattern such as the one observed will arise. However, it is not possible to infer within species genetic correlation structures from among species allometric patterns, since any within species pattern can create a particular among species pattern (Zeng, 1988; Riska, 1989). On the other hand, if there is a strong within species correlational pattern, this will result in a strong among species allometric pattern (Zeng, 1988; Riska, 1989). If the among species allometric patterns are a result arising from strong within species genetic correlations then. for a given taxon, we would expect that the within group allometric pattern should be similar in orienta- tion to the among species allometric pattern. This has indeed been found in the cardueline genus Curthclis (Bjiirklund and Merila, 1993). as well as in a few other taxa (Sokal, 1978; Sokal et al., 1980; Sokal and Riska, 1981; Gibson et al., 1984; Voss et al., 1990; Armbruster, 1991; Lougheed and Handford, 1993). Second, since genetic correlation structures are subject to both selection and drift, they are likely to be unimportant on very large time scales (Felsenstein, 1979; Charlesworth et al.,

738 B~iirklund

1982; Lande, 1986; Zeng, 1988). Therefore, the patterns probably can also be interpreted as an effect of correlated selection for particular character combinations implying the range of possible multivariate phenotypes to be smaller than would be predicted from the boundaries of the combined univariate ranges. Again this suggests some kind of stabilising selection for a particular phenotype. Taken together, the univariate random walk model explored here was unable to account for the pattern observed which indicates that models of evolution based on assump- tions of univariate random walk (e.g. many Brownian motion models used in com- parative analyses; Harvey and Pagel, 1991) will in many cases be inappropriate.

Analyses of selection on character correlations have rarely been performed in any species of birds, although Bjorklund ( 1992) analysed possible selection on character combinations in a cardueline finch (the scarlet rosefinch, Curpoclucus erythrinzu). and indeed found that stabilising selection was affecting a certain combination of bill characters. In other taxa, such analyses have been scarce (but see Lande and Arnold. 1983; Arnold and Bennett, 1988; Moore, 1990; Mitchell-Olds and Bergel- son. lY90; Johnston, 1991; Brodie, 1992), and have generally been unsuccessful (Clark, IYXX: Rauscher and Simms, 1989; Arnold, 1988; Jordan, 1991). The results presented here strongly suggest that analysing sclcction on correlations in addition to selection on trait means and variances may be a highly profitable exercise in the future.

In the particular case of the finches, the prevalence of stabilising selection is probably related to their seed-eating habit, for which they possess several adapta- tions especially in the bill (Ziswiler, 1965; Newton, 1972). Only certain combina- tions of bill proportions work appropriately for the particular way of handling seed which is used by all finches. This may be a global feature for all members of this subfamily; in other words, the same kind of selection on correlations will operate regardless of other environmental selection pressures (Bjiirklund and Mcrihi, 19Y3). In birds that are mobile, it is probably the case that the species, by choosing its environment, is choosing its selection pressures in a conservative way, rather than Ictting the environment influence it (Lewontin, 1983; Bjorklund and Merila, 19Y3).

If characters are functionally coupled, an increase in phenotypic variance will decrease the rate of evolutionary change. In fact, if three or more characters are functionally coupled, the population will be unable to move beyond a certain limit (Burger. 1986; Wagner, 1986. 1988). Thus, too much phenotypic variability puts a limit on the amount of evolutionary change. The low level of variation among species within the subfamily Carduelinae with regard to shape (van den Elzen et al., 1987; Bjorklund, 1991; Bjiirklund and Merila, lY93) can thus be explained in terms of a large number of functionally coupled characters. This can also account for the patterns of variation observed in the cardueline genus Curchdi.s (Bjiirklund and Merila, 1993) where almost all variation among species in bill morphology consists of size differences.

The possibility of restricted multivariate phenotypic variance raises the question what really constitutes a character. Normally, dilferent traits such as wing length and tarsus length are analysed as if they were different and independent traits with a certain covariance. If there are strong positive genetic correlations between them,

Morphological variation ,n txrda 739

then they cannot be regarded as separate characters, but only as aspects of a more general unobserved size factor (Wright, 1968; Crespi and Bookstein, 1989). Viewed in this context. biologically more appropriate characters would be the eigenvectors of the genetic covariance matrix (e.g. Riska, 1989; Wagner, 1989). Thus. if all covariances are positive, this will give a first eigenvector to which all separate traits will bc positively correlated. If this is found to be the case, there are reasons to view this general si7c factor as a factor determining overall growth (McKinney and McNamara, 1991). Changes in growth rate or period will affect most aspects of the phenotype and hence will create positive covariances among traits. Changes in growth can occur at diff‘erent times in ontogeny. Early in ontogeny they will result in m:?jor size changes, while later they result in changes in the differentiated parts thus generating a change in shape. This has been proposed as an explanation for interspecilic allometry (Riska and Atchley, 1985; Riska, 1989). and may well apply to the patterns identified in the present study. This model is supported by the fact that in three species of finches the growth trajectories for different traits were highly correlated (Bjorklund. l993), and that there was phenotypic variation for only trajectory, namely one in which a high covariance prevailed among successive age stages in early ontogeny. These results indicate that the main way of growing is by increasing overall size (e.g. McKinney and McNamara, 1991).

It could be argued that the low among-species variances observed is a result of the taxa studied being dcpauperate and that it reflects the variance of a previously large and diverse and now declining group. This may be a valid explanation for a single taxon, but it is highly unlikely that all rcccnt avian taxa studied are only fragments of previously larger groups. Therefore, a more parsimonious explanation is stabilizing selection preserving a common phenotype.

In conclusion, both the simulation study and the comparison with other taxa showed that phenotypic variation is distinctly patterned. with strong correlations among traits. This suggests that evolutionary change in avian morphology primarily occurs in terms of minor size adjustments, while changes in shape are very rare.

Acknowledgements

I thank J. l~ndler. J. Mull& L. Olsson. T. Price. D. Schluter. S. (Jlf?tr,~nd and B. K’nlsh for ~aluahlc

u~mments and discussion around this paper. This work v.as financed b> the Swedlbh Natural Science Research (‘ouncil

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Rocleved 20 November 1993; accep~cd 25 March 1994. C‘orrcspondlng Editor: D. Haig