Printer Friendly

Morphological evolution of the Drosophila virilis species group as assessed by rate tests for natural selection on quantitative characters.

The causes and mechanisms of morphological change and stasis have become controversial topics among evolutionary biologists. The motivation for much of the recent discussion comes from the theory of punctuated equilibria, which states that species remain morphologically unchanged for most of their existence but change suddenly during rapid speciation events (Eldredge and Gould 1972; Gould and Eldredge 1977). The reason for the discussion regarding the biological basis for change and stasis is that it has been suggested that both the rapid change and lack of morphological change seen in the fossil record cannot be explained by the microevolutionary mechanisms that are usually invoked to explain these phenomena (Stanley 1979; Gould 1980).

The traditional neo-Darwinian theory, which suggests that macroevolution is largely an extension of microevolution, proposes that it is primarily natural selection that shapes phenotypic characters (Simpson 1944, 1953; Charlesworth et al. 1982). This theory has been deduced from the observation that there is much heritable variation found in phenotypic characters that readily responds to selection (Falconer 1981), and that, in addition, studies on wild populations have revealed that natural selection appears to be a common phenomenon (Endler 1986). The obvious alternative to this theory is that morphological characters are largely neutral. Haldane (1949) suggested that if the polygenic mutation rate for morphological characters was high (which it has subsequently proven to be), this would constitute a significant evolutionary force and would have to be taken into account. This theory does not deny that natural selection is important for creating morphological adaptations, but only that much of the variation in morphological characters can be explained simply by mutation pressure or neutral drift (Nei 1987; Wilkens 1988).

Several other theories have also emerged to explain morphological diversity and stasis. One theory invokes developmental constraints that limit the amount of evolution that can occur. These constraints are therefore responsible for morphological stasis (Alberch 1980; Gould 1980, 1989; Williamson 1981). Another theory suggests that macromutations are responsible for creating morphological diversity and are responsible for the rapid changes seen in the fossil record (Stanley 1979; Gould 1980; Rachootin and Thomson 1981). The idea that stasis is the result of constraints comes from the paleontological observation that many taxa remain morphologically uniform over millions of years, even in the face of apparent environmental change (Stanley 1979; Gould 1980). The biological evidence for this theory comes from the observation that many characters are largely uniform over the entire range of a species but differ between species, thus, some genetic constraint that prevents characters from changing is hypothesized (Mayr 1963; Williamson 1987). The theory regarding macromutations will not be discussed further.

Recently, several tests have been proposed to help answer the question about the relative importance of natural selection and neutral drift on phenotypic traits. The first series of tests are considered pattern tests, and are based on the observation of random walks in nature (Raup and Crick 1981; Charlesworth 1984; Bookstein 1987, 1988). These statistical tests are designed to test for the existence of variation in evolutionary rates over time, which restricts the tests' use to fossil evidence. The other set of tests are based on quantitative genetic theory. These statistical tests are designed to examine comparisons between populations or species for the purpose of discriminating either stabilizing or directional selection against the null hypothesis of neutral evolution. Unfortunately, these tests have been used relatively little so far. Previous examples have concerned either fossil lineages (Lande 1976; Reyment 1982, 1983; Turelli et al. 1988) or experimental populations of Drosophila (Lande 1977; Turelli et al. 1988), although several species comparisons concerning living mammals (Lynch 1991a) and birds (Bjorklund 1991; Savalli 1993) have been performed.

However, there is a potential problem with the previous formulations of these tests in that phylogeny has not been explicitly considered. In some circumstances, this is not a problem; for example, when examining a fossil lineage. However, when comparing living species or populations, the evolutionary history of the organisms must be considered. I present several ways to account for the phylogeny when applying these tests and compare these phylogenetic techniques as to how they affect the rate tests. As an example of how to integrate phylogeny into the rate tests, I examine the morphological evolution of several species of the Drosophila virilis species group.

The morphological similarity among Drosophila species has long been recognized (Mather and Dobzhansky 1939; Reed and Reed 1948; Burla et al. 1949; Rizki 1951; Townsend 1954; Spassky 1957). This observed phenotypic similarity both within (Stalker and Carson 1947, 1949) and between Drosophila species (Reed and Reed 1948) has generally been attributed to the effects of stabilizing selection, although the adaptive significance of interspecific differences has been questioned (Pasteur 1970). However, no quantitative tests have ever been performed to distinguish whether this similarity is caused by adaptation, chance, or constraint. I have examined this problem by comparing several phenotypic traits among species in the D. virilis species group and some more distantly related taxa to test for the effects of natural selection by using rate tests. Although this species group has some distinctive phenotypic differences (Spicer 1991a), like many other Drosophila groups, it is noted for its morphological similarity (Spicer 1992).

Models and Statistical Tests

Two different models based on quantitative genetic theory have been proposed. Both can serve as a basis for statistical rate tests to test for natural selection: the constant-heritability (CH) model of Lande (1976, 1977) and the mutation-drift-equilibrium (MDE) model of Turelli et al. (1988). A simple test for neutral rates has also been developed by Lynch (1991a), which is very similar to that under the MDE model. The object of these tests is to determine whether morphological change has occurred either too fast or too slow to be explained by neutral drift. When change has proceeded faster than the neutral expectation, this suggests directional selection, but if it has occurred slower, then stabilizing selection can be inferred.

The phenotypic differences for a single lineage are calculated for both models in the following way:

|Mathematical Expression Omitted~,

where |Mathematical Expression Omitted~ is the character mean at time t, and |Mathematical Expression Omitted~ is the initial mean value. When z is calculated for the branch of a phylogeny, the initial |Mathematical Expression Omitted~ is an estimated value.

When two or more populations or species are being compared an among-taxa mean square is calculated for both models as

|Mathematical Expression Omitted~,

with

|Mathematical Expression Omitted~.

This calculation can be used when several populations or species are being compared simultaneously, for example, in the case of a polychotomy when the phylogeny is unresolved because of an assumed adaptive radiation or multiple speciation event (Maddison 1989).

The constant heritability (CH) model is

|Mathematical Expression Omitted~.

Where |Mathematical Expression Omitted~ is the character mean, ||Sigma~.sup.2~ is the variance of the character (weighted average if two or more samples are involved), |h.sup.2~ is the narrow sense heritability, t is the number of generations, and |N.sub.e~ is the effective population size. For the derivation of this model and the following statistical tests, see Lande (1976, 1977).

The CH statistic for a single lineage that can be interpreted as a test for directional selection is

F = |z.sup.2~/||Sigma~.sup.2~|h.sup.2~t/|N.sub.e~. (2)

The CH statistic for a comparison of two or more taxa using the mean-square technique that can be interpreted as a test for directional selection is

|Mathematical Expression Omitted~.

The CH statistic for a single lineage that can be interpreted as a test for stabilizing selection is

F = ||Sigma~.sup.2~|h.sup.2~t/|N.sub.e~/|z.sup.2~. (4)

The CH statistic for a comparison of two or more taxa using the mean-square technique that can be interpreted as a test for stabilizing selection is

|Mathematical Expression Omitted~.

The mutation-drift-equilibrium (MDE) model is

|Mathematical Expression Omitted~,

where |Mathematical Expression Omitted~ is the character mean, t is the number of generations, and |Mathematical Expression Omitted~ is the mutational variance. For the derivation of this model and the following statistical tests see Turelli et al. (1988). Although the MDE model (6) is based on the |Mathematical Expression Omitted~, for practical reasons described below these tests will be performed by using the mutational variance as a proportion of the phenotypic variance (|Mathematical Expression Omitted~).

The MDE statistic for a single lineage that can be interpreted as a test for directional selection is

|Mathematical Expression Omitted~.

The MDE statistic for a comparison of two or more taxa using the mean-square technique that can be interpreted as a test for directional selection is

|Mathematical Expression Omitted~.

The MDE statistic for a single lineage that can be interpreted as a test for stabilizing selection is

|Mathematical Expression Omitted~.

The MDE statistic for a comparison of two or more taxa using the mean-square technique that can be interpreted as a test for stabilizing selection is

|Mathematical Expression Omitted~.

The CH and MDE statistics that can be interpreted as tests for directional selection have an approximate F distribution with (n - 1) degrees of freedom (where n is the number of lineages) in the numerator and infinite degrees of freedom in the denominator. The 0.05 critical value in an F table for one degree of freedom is 3.84 for these tests. The CH and MDE statistics that can be interpreted as tests for stabilizing selection also have an approximate F distribution, but with infinite degrees of freedom in the numerator and (n - 1) degrees of freedom (where n is the number of lineages) in the denominator. The 0.05 critical value in an F table for one degree of freedom is 254.3 for these tests.

Model and Test Differences

There are several differences between these models including the parameters to be estimated and the underlying assumptions. These need to be considered before determining which model is the most appropriate for the particular case being examined. However, as Turelli et al. (1988) indicated, sometimes neither model fits the requirements, and no test is possible. The primary difference between the models concerns the mutation-drift equilibrium. The CH tests are designed to deal with populations that are not in equilibrium, whereas the MDE tests rely on the organisms to be at an equilibrium for additive genetic variance. The precise conditions for which test to use depends on the effective population size (|N.sub.e~) and the number of generations since they separated (t). If t is less than |N.sub.e~/5, then the CH model is the most appropriate, but if t is greater than 4|N.sub.e~, then the MDE model is more appropriate. For t values that fall between |N.sub.e~/5 and 4|N.sub.e~, Turelli et al. (1988) suggest that in many instances the MDE model will still work if one can assume that the organisms are near their equilibrium value for additive genetic variance. Unfortunately, determining whether the populations or species involved are near their equilibrium value is virtually impossible, but it is likely that many organisms can be considered to be in an equilibrium state for their additive genetic variance. However, for some organisms that have experienced relatively recent dramatic population changes, this usual assessment may be incorrect. In general, the CH tests would be the one of choice for populations that have recently diverged, but when examining species that have been separated for a long time, the MDE tests are more appropriate.

Estimating Parameters

The utility of these tests relies largely on the ability to estimate the appropriate parameters that go into the models. Given that we are testing historical processes that do not permit any retrospective analysis, these tests should be considered as only qualitative tests of the hypothesis and should not be considered true statistical tests, because many of the parameters have sampling errors that are effectively unestimatable (Turelli et al. 1988).

The effective populations size (|N.sub.e~) is an important parameter for the CH test, and as mentioned above can also be useful for evaluation which test to use. Unfortunately, the estimation of effective population size is very difficult. Nei and Graur (1984) presented a list of organisms and estimates of their population sizes (N), which can be consulted to obtain an initial assessment of effective population size for many different organisms. However, the population size is usually greater than the effective population size, because the effective population size tends to be closer to the smallest population size that the species has experienced (Wright 1938). The few studies that have been conducted suggest that the ratio of |N.sub.e~/N ranges from about 0.48 to 0.96 (Wright 1977). By using a low value for |N.sub.e~/N of 0.5 as a correction factor, because of fluctuations in population size that probably occur in a species lifetime, average values of |N.sub.e~ seem to range from about |10.sup.5~ to |10.sup.8~ for widespread species (Nei and Graur 1984). But these values do not take into account bottlenecks, and although little is known concerning the importance of bottlenecks in nature some think they are a common occurrence (Nei and Graur 1984; Nei 1987). If this is the case, then the long-term effective population sizes would be much smaller than those given above. Although there are inherent problems with estimating |N.sub.e~ by population size, this is currently the best way. Other techniques are also available, but these tend to be much more difficult. For example, lethal allelism data has been used very effectively to estimate |N.sub.e~ at the population level (Mukai and Yamaguchi 1974), but these data are very difficult to collect for most organisms. Also, biochemical techniques that measure heterozygosity have been suggested for estimating |N.sub.e~ (Nei 1987), but much controversy exists about the maintenance of genetic diversity, and if it is not neutral, then these estimates would be false. With the advent of rapid DNA sequencing and restriction mapping, molecular techniques that estimate |N.sub.e~ by linkage disequilibrium and coalescent processes many become very important and easy to use (Hudson 1987, 1990; Avise et al. 1988; Avise 1992; Felsenstein 1992).

Heritability is a parameter that is necessary for the CH rate test and helpful for the MDE test as well, because the value for |Mathematical Expression Omitted~ depends on the heritability of the character. The narrow sense heritability (|h.sup.2~) is a measure of the additive genetic component (Falconer 1981). This parameter is most commonly estimated by the regression of offspring on parents, although other estimation techniques are available (Falconer 1981). However, it will often not be necessary to actually measure this parameter for use in the rate tests, because extensive information regarding heritability already exists. Roff and Mousseau (1987) and Mousseau and Roff (1987) have compiled a list of heritability values from a wide variety of organisms and different characters. For many comparisons among different species it will probably be possible to find a heritability value that is representative for a given character.

The mutational variance proportional to the phenotypic variance (|Mathematical Expression Omitted~) is an important parameter for the MDE rate test. The ideal method for estimating this parameter is to measure the accumulation of mutational variance over many generations for an inbred organism. This information can be used to estimate the mutational rate of input of genetic variance (|Mathematical Expression Omitted~), which is usually scaled to a dimensionless value by dividing |Mathematical Expression Omitted~ by the environmental variance (|Mathematical Expression Omitted~). Although the mutational heritability |Mathematical Expression Omitted~ is a difficult parameter to estimate, it is possible to take values from the literature. Lynch (1988) has extensively reviewed the literature regarding polygenic mutation rates and has compiled a list of rates for a wide variety of organisms and traits, including Drosophila, Tribolium, rodents, and several crop plant species. All of the studies to date, including the more recent estimates (Enfield and Braskerund 1989; Keightley and Hill 1990; Weber and Diggins 1990; Caballero et al. 1991; Mackay et al. 1992; Santiago et al. 1992), give very similar values for the polygenic mutation rate. Values for |Mathematical Expression Omitted~ are typically on the order of 0.001 (Lande 1975), with a range of 0.05 to 0.0001 per generation (Lynch 1991a). Given the usual estimates normally measured for |Mathematical Expression Omitted~ (Lynch, 1988, 1991a), the |Mathematical Expression Omitted~ values can be considered equivalent to the |Mathematical Expression Omitted~ parameter. However, when |h.sup.2~ is unusually high, the polygenic mutation rate will be inflated, and conversely, when |Mathematical Expression Omitted~ is very large, the polygenic mutation rate values will be deflated. The way this affects the tests will depend on which tests are being performed. The stabilizing selection tests will be conservative when |h.sup.2~ is large but may be unreliable when |Mathematical Expression Omitted~ is unusually high. The effects of these parameters on the directional selection tests will be just the opposite of those described for the stabilizing tests. However, as Turelli et al. (1988) indicate, for most typical heritability values the polygenic mutation rates given by Lynch (1988) will be appropriate. In general, given the qualitative nature of these tests, these problems will have little effect on the significance levels, particularly when conservative estimates of |Mathematical Expression Omitted~ are used.

The number of generations since divergence (t) is needed for both the CH and MDE rate tests is best estimated by determining the absolute time of divergence and then estimating the average number of generations per year based on demographic information. Lande (1976), Reyment (1983), and Turelli et al. (1988) have used times of divergence based on fossil evidence and then estimated generation times from living organisms. Most researchers working with contemporary species will be unable to estimate absolute divergence time directly from fossil evidence, thus other estimation techniques may need to be employed. The simplest way to obtain a rough approximation of the absolute divergence time is by using a molecular evolutionary clock. Although often difficult and problematic, it will probably be a viable solution in many instances. The best way to estimate generation time, as with the fossil evidence, is by examining the most closely related living members of the species of interest.

The phenotypic variance of the characters (||Sigma~.sup.2~) needs to be estimated for both the CH and MDE rate tests. Because these tests depend on the normal distribution, it is necessary for the phenotypes to be normally distributed and for the means and variances to be uncorrelated. This is often not the case, but it is possible to convert many distributions which are not normal to a normal distribution and to uncorrelate the means and variances simply by changing the scale of measurement. A common transformation that will often eliminate both these problems is the |log.sub.e~-transformation (Lande 1976). Wright (1968) and Falconer (1981) provided examples of other transformations. In theory, the variances need to remain constant during the evolution of the taxa (Lande 1976), but this will often not be the case. A related problem is that samples should not be pooled because these are intra population sample tests, but once again this is unavoidable in many instances, particularly when making comparisons among different species. The effect of both of these problems results in the inflation of the estimated variances, but this effect will probably be negligible in most instances (Lynch 1991a).

Phylogenetic Considerations

The estimation of the mean differences among populations or species is required for both the CH and MDE rate tests and is discussed in the Models and Statistical Tests section. Previous formulations of these tests have ignored the phylogenetic aspects when estimating mean differences, but this was appropriate, because they were testing either fossil lineages or recently diverged populations that were all equally related. However, if natural populations or species are being compared, then the evolutionary history of the organisms can be an important element (Ridley 1983; Felsenstein 1985; Huey 1987; Pagel and Harvey 1988; Brooks and McLennan 1991; Harvey and Pagel 1991). In the context of rate tests, the greatest problem is the underestimation of mean differences, which will bias the tests (Bookstein 1989). The techniques discussed below somewhat alleviate this problem by estimating ancestral states that can then be used in the estimation of phenotypic difference.

The first requirement is that a phylogeny be available to estimate the ancestral character states such that the rate tests can be applied. I will not discuss the topic of phylogeny estimation, because this is a large and complicated issue, but some excellent reviews are provided by Wiley (1981), Felsenstein (1982, 1983, 1988a,b) and Swofford and Olsen (1990). All further discussion concerning rate tests and phylogeny will assume that once a phylogeny has been obtained it is then taken as a given. If different phylogenies have been proposed for a group of organisms then this can be accounted for to some extent by calculating the statistics for all the competing phylogenies. If the outcome of the tests are the same, then this can be considered a robust conclusion.

There are three basic approaches that I will consider to account for phylogeny by estimating ancestral states: simple pairwise comparisons that ignore the estimated phylogeny but make explicit assumptions about the phylogeny; a Brownian motion model (Felsenstein 1973, 1985): and the parsimony approach (Swofford and Maddison 1987). Another recent technique that may be appropriate is that of Lynch (1991b), although it is not considered here. Other methods exist and may ultimately be considered more realistic models, but at the moment these do not appear to be viable approaches (see Felsenstein 1988a).

Pairwise Comparisons. -- With this technique, the phenotypic differences either between or among taxa are estimated, and the |Mathematical Expression Omitted~ value is calculated as in the Models and Statistical Tests section (Lynch 1991a). This is the simplest test that can be made, but it ignores the phylogeny of the organisms, because no estimate regarding intermediate states is considered. Consequently, it may be an inappropriate test, with the exception of when only a single comparison is made between or among sister taxa. Although this model does not take into account any information from an estimated phylogeny, it is based on an explicit evolutionary mode, which is equivalent to the Brownian-motion model considered below (Felsenstein 1985). The calculation of any pair-wise comparison assumes that the ancestral population or species was exactly intermediate among the contemporaneous taxa. The problem with this approach is that it may greatly underestimate the amount of change that has actually occurred, because it ignores any information concerning possible ancestral states. Another related model that can be used, but which is much more restrictive in its assumptions, is to calculate the single lineage formula for the pair-wise comparisons. It is possible to calculate the pairwise statistic by using only z, if one assumes that one of the populations or species (|Mathematical Expression Omitted~) represents the ancestral condition and has not changed, such that the other population or species (|Mathematical Expression Omitted~) is the only one evolving. A much more conservative estimate is found when using the stabilizing selection test, because it maximizes the amount of change. However, it has the opposite effect when testing for directional selection, because it assumes much more change has occurred.

Brownian Motion Model. -- The use of this model for quantitative characters has been extensively reviewed by Felsenstein (1973, 1981, 1985, 1988a). This model is now widely employed as part of a procedure to generate phylogenetically independent constrasts for the statistical evaluation of comparative data sets in evolutionary biology (Felsenstein 1985; Grafen 1989; Martins and Garland 1991; Garland 1992; Garland et al. 1992). Basically, the model describes morphological change by what would be expected under the conditions of genetic drift. This neutral model permits the estimation of ancestral states by a relatively simple calculation, which has been elaborately discussed by Felsenstein (1973, 1985).

Parsimony Approach. -- The maximum parsimony procedure determines ancestral states by minimizing the amount of evolutionary change that has occurred (Swofford and Maddison 1987). Although this technique has probably become the most widely used method for accounting for phylogeny in comparative studies (Ridley 1983; Pagel and Harvey 1988; Brooks and McLennan 1991), it is somewhat unrealistic for quantitative traits. The difficulty with the parsimony approach is that it permits only discrete ancestral character state estimates, and continuous characters are probably best considered as continuous characters and not as discrete (Felsenstein 1988a). However, this difficulty can partially be remedied by using the approach suggested by Maddison and Slatkin (1990). They show that continuous characters can be coded into discrete ordered character states without changing the parsimonious arrangement. This means that the standard parsimony computer packages, such as Swofford (1993), Maddison and Maddison (1992), and Felsenstein (1993), can estimate continuous character transformation series. Another potential problem concerns unresolved phylogenies, but Maddison (1989) has shown how parsimonious character transformations can be obtained from polychotomous branchings. It is also known that ambiguous character state assignments are possible even with the most parsimonious reconstruction, but Swofford and Maddison (1987) have shown how to deal with these ambiguities.

The exact calculation of F-values can be performed once the ancestral character states have been obtained. For the pair-wise mean square comparisons, this is simply the summation of all the mean differences along the nodes separating the taxa being examined back to their common ancestral node. For the Brownian motion models and parsimony approach, an additional advantage is that by using the single lineage calculation it is possible to locate internal branches on the phylogeny where interesting changes have occurred, because the statistic can be calculated for each internode. Nevertheless, accounting for the phylogenetic component of quantitative traits is fraught with difficulty, and is very model and data dependent (Felsenstein 1985, 1988a).

Given that we do not know how accurately to model morphological change over the evolutionary time scale (Felsenstein 1988a), probably the best approach for taking phylogeny into account is to use all of the above techniques. By examining the statistical outcome of the rate tests with several different methods of evolutionary change, it should be possible to obtain an idea of how much variation the phylogeny models introduce into the tests. Consequently, only statistically significant results that are based on several different phylogeny models should be considered robust conclusions.

Materials and Methods

The flies were maintained in half-pint glass bottles on a 4:1 (by volume) mixture of Carolina Biological's Drosophila instant media and corn starch with about 0.5 g of live baker's yeast added. The incubator was on a 12:12 h light-dark cycle and kept at approximately 24 |degrees~ C. Flies were raised in as uniform an environment as possible. Adult flies were permitted to lay eggs for 2 d in a half-pint glass bottle. Eggs were then removed from the old bottle and placed in a new bottle. The flies from the new bottle were raised and the characters were measured. Only flies from bottles that produced between 50-100 flies were used.

The strains that were used and their corresponding National Drosophila Species Resource Center stock numbers are as follows: Drosophila americana (15010-0951.7), Oakdale, Nebraska; (15010-0951.9), Myrtle Beach State Park, South Carolina; Independence, Missouri; D. littoralis (15010-1001), Mellingen, Switzerland; (15010-1001.6), Pokouke, Russia; D. lummei (15010-1011), Finland; (15010-1011.1), Moscow, Russia; (15010-1011.3), Ghazvin, Iran; D. montana (15010-1021), Moosonee, Ontario, Canada; (15010-1021.6), Blacksands, Ontario, Canada; (15010-1021.15), Salmon River, Idaho; (15010-1021.16), Grand Teton National Park, Wyoming; (15010-1021.19), Mount Hood National Forest, Oregon; D. novamexicana (15010-1031), Grand Junction, Colorado; (15010-1031.5), Moab, Utah; (15010-1031.8), San Antonio, New Mexico: D. texana (15010-1041.23), Morrilton, Arkansas; (15010-1041.25), Swift Creek, South Richmond, Virginia; (15010-1041.29), Jamestown, South Carolina; St. Francisville, Louisiana, September 3. 1974, isofemale # 6: D. virilis (15101-1051). Pasadena, California: (15101-1051.47), Hangchow, China; (15101-1051.83), autosomal marker stock; Whiteshell Provincial Park, Manitoba, Canada, August 2, 1974: 16--Sapporo, Hokkaido, Japan, from Wheeler 1971; D. robusta (15020-1111), Tombigbee River, Alabama; (15020-1111.2), Blue Mountain Lake, New York: (15020-1111.3), Crystal Lake, Hastings, Nebraska; (15020-1111.7), Austin, Texas; D. funebris (15120-1911), Sturgis, Kentucky; (15120-1911.1), Mexico City, Mexico; (15120-1911.2), Minneapolis, Minnesota; (15120-1911.6), Big Lake, Alaska.

The specific measurements that were taken and the abbreviations used are given in figure 1 and table 1, respectively. All the head and thorax measurements of the flies were taken by using an ocular micrometer at 42 x magnification. The wing measurements were made by using a Ken-a-vision model X 1000-1 microprojector at approximately 80 x magnification. Ten male flies from each strain were measured.

The mutation-drift-equilibrium model (MDE) rate test for stabilizing selection was used to test for natural selection. This test was selected because the time since divergence is very large, thus these flies can be considered to be in mutation-drift equilibrium. No directional test was performed because the Z values were so small relative to the number of generations that this test would not attain statistical significance. The MDE test requires the estimation of four parameters: t (the number of generations since divergence), z (the character mean), ||Sigma~.sup.2~ (the variance of the character; weighted average if two or more samples are involved), and |Mathematical Expression Omitted~ (the mutational variance proportional to the phenotypic variance). The phylogeny and the divergence times that were used come from the two-dimensional electrophoretic data sets of Spicer (1988; fig. 5), Spicer (1991b; fig 6), and Spicer (1992). The estimation of t was based on molecular clock estimates. I have taken a conservative approach by assuming three generations per year for all the Drosophila species examined. Three generations per year are probably fewer than for most species. However, Baker (1975) suggests that some alpine populations of D. montana have only one generation per year. But for the other species, which live in a warmer environment, several generations per year would certainly be normal. For the reconstruction of ancestral states by the parsimony approach, I have used the technique of Maddison and Slatkin (1990) and the PAUP computer package of Swofford (1990). The minimum f-value optimization was invoked. The means (z) and variances (||Sigma~.sup.2~) for each character were measured as above. The variances used in the tests were the weighted average among all species for each character. All the measurements were |log.sub.e~-transformed. Although the average value of |Mathematical Expression Omitted~ is usually taken as 0.001 (Lande 1975), the much more conservative value of |Mathematical Expression Omitted~ was used for all the tests (Lynch 1988).
TABLE 1. Abbreviations and landmarks for the morphological characters.

BEW      width between the eyes

HW       width of the head

CL       length of the cheek

TL       length of the thorax from anterior most part
         of the thorax to the posterior part of the
         scutellum

TW       width between the interior postalar setae

BW       width between the anterior scutellar setae

V3       length of wing vein 3

V2-5     distance between the distal end of wing vein
         2 to the distal end of wing vein 5


RESULTS

The means and variances for all the characters are presented in table 2 and the |log.sub.e~-transformed means and variances are presented in table 3. None of the means and variances are correlated, although the variances for each character are different. To test for homogenity of variances among strains within species, the |F.sub.max~-test was employed (Sokal and Rohlf 1981), which revealed that of the 81 distributions tested, 25 were found to be heterogeneous; and to test for normality of the distributions among strains within species, the Shapiro-Wilk W-test was employed (JMP 1989), which revealed that of the 81 distributions tested, 45 were found to be non-normal. However, as discussed previously, nonhomogeneous and non-normal variances probably have a relatively insignificant effect on the outcome of these tests (Lynch 1991a). The distributions of probability values obtained from the F-tests for each of the phylogeny accounting procedures are presented in figure 3. However, as mentioned above, some caution needs to be exercised in evaluating these probability values, because as Turelli et al. (1988) indicate these are not rigorous statistical tests because of the inability to adequately assess sampling errors for several of the parameters.

Figure 2 shows the amount of phenotypic change (in standard deviations) that would have to occur to reject stabilizing selection using the MDE rate test. Values are presented for both the conservative parameter value of |Mathematical Expression Omitted~, which was actually used in the rate tests, and the more realistic parameter value of |Mathematical Expression Omitted~. To give an idea of how much morphological change has actually occurred, the largest difference measured between any two species among all the characters is a 5.9 SD change between D. littoralis and D. funebris for the TL character. The average amount of the largest phenotypic change between species considered for each character is 4.4 SD, with a range of 2.1 to the largest value of 5.9 SD. Figure 2 shows that these values are well within the significant range for most of the comparisons even when considering only the more recently evolved species.

All the phylogeny adjusting techniques produced a statistically significant result that suggests the action of stabilizing selection, even though there are differences among these methods. This can most easily be seen by examining the average P values from the F-tests, and even though this average P value is formally incorrect (because the comparisons do not take into account the phylogeny, thus they are not statistically independent), it does give an idea about the over level of significance. The mean level of significance for the nine characters over all the 324 comparisons for the pairwise |Mathematical Expression Omitted~ technique is P = 0.0077, but for the pairwise Z-test the mean was only P = 0.0109. When the techniques to account for the phylogenetic component were used, the values changed even more significantly. The parsimony method has an overall P = 0.0115, and the Brownian motion model produced the largest overall probability value with P = 0.0129. Another way to compare these tests is by examining the largest observed test value. Of the 324 comparisons the largest P-value for any of the characters with the pairwise |Mathematical Expression Omitted~ test (in this case the EL character comparison between D. texana and D. novamexicana) is P = 0.0270. Even when the phylogeny techniques are used the probability values are still very significant. Once again the largest probability value obtained was for the EL character comparison between D. texana and D. novamexicana; both the single lineage pairwise Z-test and parsimony method produced the same value of P = 0.0383. Consequently, all the comparisons can be considered as significant even when using a conservatively low polygenic mutation rate. It can also be concluded that the phylogeny adjusting techniques can make a difference when using rate tests and need to be considered when performing these tests.

DISCUSSION

The conclusion from these tests suggests that there has been significant stabilizing selection for all the characters examined. This result is found with all the techniques used to account for phylogeny and all the parameters conservatively estimated, thus it is very unlikely that a type I statistical error has been committed. Consequently, this can be considered a robust result that rejects the neutral hypothesis of morphological character evolution.

These results imply that most of the morphological characters of a Drosophila are shaped by natural selection, but there are some potential problems with this analysis. One possible difficulty with this study is that the characters may have virtually no mutational variance. But given TABULAR DATA OMITTED TABULAR DATA OMITTED the nearly universal observation of a large polygenic mutation rate, and that some morphological characters of Drosophila have been shown to have a large mutational variance (Lande 1975; Lynch 1988; Mackay et al. 1992; Santiago et al. 1992), it seems unlikely that this is a problem. However, in an effort to take this into account. I have used a conservatively small estimate for the mutation parameter in the rate tests. An obvious concern is that laboratory measurements ere used that might reduce the amount of estimated variation that would be observed in nature (Coyne and Beecham 1987; Prout 1958; Riska et al. 1989). When using the MDE model to test for stabilizing selection, reducing the phenotypic variance just makes it more difficult to reject the null model of too little change. Hence, this makes the test more conservative in the present circumstance. Another possible difficulty with this analysis is that the correlation among characters has not been taken into account, such that natural selection on any particular character may be the result of correlated natural selection on another character (Lande and Arnold 1983). It is apparent that phenotypic correlations do exist among the characters, and some of them are relatively high. However, not all the characters have large correlations, such that even though any given character may not be under direct selection, it is unlikely that the overall picture of natural selection would be incorrect. Correlation is also unlikely to be a problem from the genetic viewpoint, because the genetic evidence indicates that correlations are subject to genetic change and evolution (Cock 1966; Atchley and Rutledge 1980; Lofsvold 1986). This suggests that mutations are constantly occurring that uncouple character correlations, but because of natural selection these correlations persist. Unfortunately, little information on the effects of the polygenic mutation rate on correlations among characters exists to answer this question fully (Barton 1990; Santiago et al. 1992).

The result presented here cannot refute the arguments based on the developmental constraint hypothesis. Maynard Smith et al. (1985) suggest four ways to distinguish developmental constraints from the effects of natural selection. These include a priori adaptational predictions concerning the character, the measurement of genetic variability or heritability for the character, the measurement of natural selection on the character, and the comparative method. Unfortunately, the constraint hypothesis cannot be tested using the methodology employed in this paper (Maynard Smith 1983; Maynard Smith et al. 1985). However, it should be mentioned that several Drosophila species have been shown to have many morphological characters that exhibit heritable variation in both the laboratory (Roff and Mousseau 1987) and nature (Coyne and Beecham 1987; Riska et al. 1989), thus it seems unlikely that developmental constraints are preventing these characters from evolving.

Although the present study can show only the possible importance of stabilizing selection, I suggest that it also has some implications for directional selection. Given that stabilizing selection is apparently shaping the morphology of these flies, it would seem that any dramatic changes that occur are probably mediated by directional selection. The rationale for this suggestion is that it seems unlikely that characters that are maintained by natural selection would change in a process not governed by selection. The alternative view would be that although the characters are controlled by strict stabilizing selection, under certain conditions this selection is relaxed and the population is permitted to drift to a new optimum, where upon stabilizing selection TABULAR DATA OMITTED resumes. This is a difficult hypothesis to reject using the current models, although it is certainly a plausible way for the quantitative characters to evolve (Lande 1985).

To resolve these problems, one could examine the fossil record and see if directional selection appears to be an important factor in evolution. This is a difficult task for Drosophila, because so few fossil species are known, and it is unlikely that any extensive sequences of Drosophila lineages will be discovered. However, it may be possible to make generalizations from the fossil records of other organisms that have extensive fossil records. This has been done to a small extent, and the tentative results are that the tests have had difficulty rejecting the importance of neutral drift as a major factor. None of the characters that Lande examined using the CH test based on fossil evidence could conclusively be determined to have occurred by natural selection. In another study, Reyment (1982) examined the morphological change in a variety of microfossils and determined that most were the result of directional selection. However, Turelli et al. (1988) reexamined one of his examples using the more appropriate MDE test for directional selection and concluded that the evidence could not reject the neutral model. Consequently, the evidence from the fossil data by using these tests has yet to determine that natural selection is the primary cause of morphological change. But a qualification is that all these cases involve tests for directional selection, which is clearly the most difficult form of selection to accept using these tests.

It appears that rate tests for natural selection can be useful for evolutionary studies, particularly systematic studies that routinely examine morphological traits among populations and species. The CH and MDE quantitative models provide a framework to test for natural selection on the macroevolutionary scale and another avenue for testing adaptational hypotheses, which are not permissible by the usual population studies (e.g., Manly 1985; Endler 1986). Unfortunately, there are difficulties in the estimation of some of the necessary parameters, in addition to some of the simplifying assumptions that must be made when performing these rate tests. There is also the concern for adjusting for phylogeny effects, which has difficulties of its own. Nevertheless, the ability to test for natural selection on the macroevolutionary scale seems to far outweigh the previous alternative of adaptational explanations.

ACKNOWLEDGMENTS

I am most grateful to my wife, C. Spicer, for her assistance in maintaining the Drosophila stocks and measuring the flies in this study. I would like to thank J. Arnold, B. Charlesworth, J. Coyne, R. Lande, S. Lanyon, S. Lawson, and J. Spofford for their useful comments. I would also like to thank R. Lande and M.

Turelli for their invaluable discussions concerning rate tests and W. Maddison and D. Swofford for their helpful discussions concerning the phylogenetic reconstruction of characters states, and M. Willig for performing some of the statistics. I thank M. Lynch for providing me with a preprint of his paper. This study was supported in part by the U.S. Public Health Service Training Grant in Genetics administered through the University of Chicago.

LITERATURE CITED

Alberch, P. 1980. Ontogenesis and morphological diversification. American Zoologist 20:653-667.

Atchley, W. R., and J. J. Rutledge. 1980. Genetic components of size and shape. I. Dynamic components of phenotypic variability and covariability during ontogeny in the laboratory rat. Evolution 34: 1161-1173.

Avise, J. C. 1992. Molecular population structure and the biogeographic history of a regional fauna: a case history with lessons for conservation biology. Oikos 63:62-76.

Avise, J. C., R. M. Ball, and J. Arnold. 1988. Current versus historical population sizes in vertebrate species with high gene flow: A comparison based on mitochondrial DNA lineages and inbreeding theory for neutral mutations. Molecular Biology and Evolution 5:331-344.

Baker, W. K. 1975. Linkage disequilibrium over space and time in natural populations of Drosophila montana. Proceedings of the National Academy of Sciences. USA 72:4095-4099.

Barton, N. H. 1990. Pleiotropic models of quantitative variation. Genetics 124:773-782.

Bjorklund, M. 1991. Evolution, phylogeny, sexual dimorphism and mating system in the grackles (Quiscalus spp.: Icterinae). Evolution 45:608-621.

Bookstein, F. L. 1987. Random walk and the existence of evolutionary rates. Paleobiology 13:446-464.

-----. 1988. Random walk and the biometrics of morphological characters. Evolutionary Biology 23: 369-398.

-----. 1989. Comment on a rate test. Evolution 43: 1569-1570.

Brooks, D. R., and D. A. McLennan. 1991. Phylogeny, ecology, and behavior. University of Chicago Press, Chicago.

Burla, H., A. Brito da Cunha, A. R. Cordeiro, T. Dobzhansky, C. Malogolowkin, and C. Pavin. 1949. The willistoni group of sibling species of Drosophila. Evolution 3:300-314.

Caballero. A., M. A. Toro, and C. Lopez-Fanjul. 1991. The response to artificial selection from new mutations in Drosophila melanogaster. Genetics 127: 89-102.

Charlesworth, B. 1984. Some quantitative methods for studying evolutionary patterns in single characters. Paleobiology 10:308-318.

Charlesworth, B., R. Lande, and M. Slatkin. 1982. A neo-Darwinian commentary on macroevolution. Evolution 36:474-498.

Cock, A. G. 1966. Genetical aspects of metrical growth and form in animals. Quarterly Review of Biology 41:131-190.

Coyne, J. A., and E. Beecham. 1987. Heritability of two morphological characters within and among natural populations of Drosophila melanogaster. Genetics 117:727-737.

Eldredge, N., and S. J. Gould. 1972. Punctuated equilibria: An alternative to phyletic gradualism. Pp. 82-115 in T.J.M. Schopf, ed. Models in paleobiology. Freeman, Cooper and Co., San Francisco.

Endler, J. A. 1986. Natural selection in the wild. Princeton University Press, Princeton. N.J.

Enfield, F. D., and O. Braskerund. 1989. Mutational variance for pupa weight in Tribolium castaneum. Theoretical and Applied Genetics 77:416-420.

Falconer, D. S. 1981. Introduction to quantitative genetics. Longman, London.

Felsenstein, J. 1973. Maximum-likelihood estimation of evolutionary trees from continuous characters. American Journal of Human Genetics 25:471-492.

-----. 1981. Evolutionary trees from gene frequencies and quantitative characters: finding maximum likelihood estimates. Evolution 35:1229-1242.

-----. 1982. Numerical methods for inferring evolutionary trees. Quarterly Review of Biology 57:379-404.

-----. 1983. Parsimony in systematics: biological and statistical issues. Annual Review of Ecology and Systematics 14:313-333.

-----. 1985. Phylogenies and the comparative method. American Naturalist 125:1-15.

-----. 1988a. Phylogenies and quantitative characters. Annual Review of Ecology and Systematics 19:445-471.

-----. 1988b. Phylogenies from molecular sequences: Inferences and reliability. Annual Review of Genetics 22:521-565.

-----. 1992. Estimating effective population size from samples of sequences: inefficiency of pairwise and segregating sites as compared to phylogenetic estimates. Genetical Research 59:139-147.

-----. 1993. PHYLIP. Phylogeny inference package (ver. 3.5). University of Washington, Seattle, Washington.

Garland, T. 1992. Rate tests for phenotypic evolution using phylogenetically independent contrasts. American Naturalist 140:509-519.

Garland, T., P. H. Harvey, and A. R. Ives. 1992. Procedures for the analysis of comparative data using phylogenetically independent contrasts. Systematic Biology 41:18-32.

Gould, S. J. 1980. Is a new and general theory of evolution emerging? Paleobiology 6:119-130.

-----. 1989. A developmental constraint in Cerion, with comments on the definition and interpretation of constraint in evolution. Evolution 43:516-539.

Gould, S. J., and N. Eldredge. 1977. Punctuated equilibria: the tempo and mode of evolution reconsidered. Paleobiology 3:115-151.

Grafen, A. 1989. The phylogenetic regression. Philosophical Transactions of the Royal Society of London B Biological Sciences 326:119-157.

Haldane, J.B.S. 1949. Suggestions as to quantitative measurement of rates of evolution. Evolution 3:51-56.

Harvey, P. H., and M. D. Pagel. 1991. The comparative method in evolutionary biology. Oxford University Press, Oxford.

Hudson, R. R. 1987. Estimating the recombination parameter of a finite population model without selection. Genetical Research 50:245-250.

-----. 1990. Gene genealogies and the coalescent process. Oxford Survey of Evolutionary Biology 7:1-44.

Huey, R. B. 1987. Phylogeny, history, and the comparative method. Pp. 76-98 in M. E. Feder et al., eds. New directions in ecological physiology. Cambridge University Press, Cambridge.

JMP. 1989. User's guide, vet. 2. SAS Institute, Carey, N.C.

Keightley, P. D., and W. G. Hill. 1990. Estimating new mutational variation in growth rate of mice. Proceedings of the 4th World Congress of Genetics Applied and Livestock Production 13:325-328.

Lande, R. 1975. The maintenance of genetic variability by mutation in a polygenic character with linked loci. Genetical Research 26:221-235.

-----. 1976. Natural selection and random genetic drift in phenotypic evolution. Evolution 30:314-334.

-----. 1977. Statistical tests for natural selection on quantitative characters. Evolution 31:314-334.

-----. 1985. Expected time for random genetic drift of a population between stable phenotypic states. Proceedings of the National Academy of Sciences, USA 82:7641-7645.

Lande, R., and S. J. Arnold. 1983. The measurement of selection on correlated characters. Evolution 37:1210-1226.

Lofsvold, D. 1986. Quantitative genetics of morphological differentiation in Peromyscus. I. Tests of the homogeneity of genetic covariance structure among species and subspecies. Evolution 40:559-573.

Lynch, M. 1988. The rate of polygenic mutation. Genetical Research 51:137-148.

-----. 1991a. The rate of morphological evolution in mammals from the standpoint of the neutral expectation. American Naturalist 136:727-741.

-----. 1991b. Methods for the analysis of comparative data in evolutionary biology. Evolution 45:1065-1080.

Mackay, T.F.C., R. F. Lyman, M. S. Jackson, C. Terzian, and W. G. Hill. 1992. Polygeneic mutation in Drosophila melanogaster: Estimates from divergence among inbred strains. Evolution 46:300-316.

Maddison, W. P. 1989. Reconstructing character evolution on polytomous cladograms. Cladistics 5:365-377.

Maddison, W. P., and D. R. Maddison. 1992. MacClade. Analysis of phylogeny and character evolution (ver. 3.01). Sinauer, Sunderland, Mass.

Maddison, W, P., and M. Slatkin. 1990. Parsimony reconstructions of ancestral states do not depend on the relative distances between linearly-ordered character states. Systematic Zoology 39:175-178.

Manly, B.F.J. 1985. The statistics of natural selection. Chapman and Hall, London.

Martins, E. P., and T. Garland. 1991. Phylogenetic analyses of the correlated evolution of continuous characters: a simulation study. Evolution 45:534-557.

Mather, K., and T. Dobzhansky. 1939. Morphological differences between the "races" of Drosophila pseudoobscura. American Naturalist 73:5-25.

Maynard Smith, J. 1983. The genetics of stasis and punctuation. Annual Review of Genetics 17:11-25.

Maynard Smith, J., R. Burian, S. Kauffman, P. Alberch, J. Campbell, B. Goodwin, R. Lande, D. Raup, and L. Wolpert. 1985. Developmental constraints and evolution. Quarterly Review of Biology 60:265-287.

Mayr, E. 1963. Animal species and evolution. Harvard University Press, Cambridge, Massachusetts.

Mousseau, T. A., and D. A. Roff. 1987. Natural selection and the heritibility of fitness components. Heredity 59:181-197.

Mukai, T., and O. Yamaguchi. 1974. The genetic structure of natural populations of Drosophila melanogaster. XI. Genetic variability in a local population. Genetics 76:339-366.

Nei, M. 1987. Molecular evolutionary genetics. Columbia University Press, New York.

Nei, M., and D. Graur. 1984. Extent of protein polymorphism and the neutral mutation theory. Evolutionary Biology 17:73-118.

Pagel, M. D., and P. H. Harvey. 1988. Recent developments in the analysis of comparative data. Quarterly Review of Biology 63:413-440.

Pasteur, G. 1970. A biometrical study on the semi-species of the Drosophila paulistorum complex. Evolution 24:156-168.

Prout, T. 1958. A possible difference in genetic variance between wild and laboratory populations. Drosophila Information Service 32:148-149.

Rachootin, S. P., and K. S. Thomson. 1981. Epigenetics, palaeontology, and evolution. Pp. 181-193 in Proceedings of the second international congress of systematics and evolutionary biology. Carnegie-Mellon University Press, Pittsburgh.

Raup, D., and R. Crick. 1981. Evolution of single characters in the Jurassic ammonite Kosmoceras. Paleobiology 7:200-215.

Reed, S. C., and E. W. Reed. 1948. Morphological differences and problems of speciation in Drosophila. Evolution 2:40-48.

Reyment, R. A. 1982. Phenotypic evolution in a Cretaceous foraminifer. Evolution 36:1182-1199.

-----. 1983. Phenotypic evolution in microfossils. Evolutionary Biology 16:209-254.

Ridley, M. 1983. The explanation of organic diversity: the comparative method and adaptations for mating. Clarendon Press, Oxford.

Riska, B., T. Prout, and M. Turelli. 1989. Laboratory estimates of heritabilities and genetic correlations in nature. Genetics 123:865-871.

Rizki, M.T.M. 1951. Morphological differences between two sibling species, Drosophila pseudoobscura and Drosophila persimilis. Proceedings of the National Academy of Sciences 37:156-159.

Roff, D. A., and T. A. Mousseau. 1987. Quantitative genetics and fitness: Lessons from Drosophila. Heredity 58:103-118.

Santiago, E., J. Albornoz, A. Dominguez, M. A. Toro, and C. Lopez-Fanjul. 1992. The distribution of spontaneous mutations on quantitative traits and fitness in Drosophila melanogaster. Genetics 132:771-781.

Savalli, U. M. 1993. An application of the neutral model to the evolution of tail length in the genus Euplectes (Aves, Ploceidae). Evolution 47:696-699.

Simpson, G. G. 1944. Tempo and mode in evolution. Columbia University Press, New York.

-----. 1953. The major features of evolution. Columbia University Press, New York.

Spassky, B. 1957. Morphological differences between sibling species of Drosophila. University of Texas Publication 5721:48-61.

Spicer, G. S. 1988. Molecular evolution among some Drosophila species as indicated by two-dimensional electrophoresis. Journal of Molecular Evolution 27:250-260.

-----. 1991a. The genetic basis of a species-specific character in the Drosophila virilis species group. Genetics 128:331-337.

-----. 1991b. Molecular evolution and phylogeny of the Drosophila virilis species group as inferred by two-dimensional electrophoresis. Journal of Molecular Evolution 33:379-394.

-----. 1992. Reevaluation of the phylogeny of the Drosophila virilis species group (Diptera: Drosophilidae). Annals of the Entomological Society of America 85:11-25.

Sokal, R, R., and F. J. Rohlf. 1981. Biometry. W. H. Freeman and Co., New York.

Stalker, H. D., and H. L. Carson. 1947. Morphological variation in natural populations of Drosophila robusta Sturtevant. Evolution 1:237-248.

-----. 1949. Seasonal variation in the morphology of Drosophila robusta Sturtevant. Evolution 3:330-343.

Stanley, S. 1979. Macroevolution, pattern and process. W. H. Freeman and Co., San Francisco.

Swofford, D. L. 1993. PAUP. Phylogenetic analysis using parsimony (ver. 3.1.1). Illinois Natural History Survey, Champaign, Ill.

Swofford, D. L., and W. P. Maddison. 1987. Reconstruction ancestral character states under Wagner parsimony. Mathematical Biosciences 87:199-229.

Swofford, D. L., and G. J. Olsen. 1990. Phylogeny reconstruction. Pp. 411-501 in D. M. Hillis and C. Moritz, eds. Molecular systematics. Sinauer, Sunderland, Mass.

Townsend, J. I. 1954. Cryptic subspeciation in Drosophila belonging to the subgenus Sophophora. American Naturalist 88:339-351.

Turelli, M., J. H. Gillespie, and R. Lande. 1988. Rate tests for selection on quantitative characters during macroevolution and microevolution. Evolution 42:1085-1089.

Weber, K. E., and L. T. Diggins. 1990. Increased selection response in larger populations. II. Selection for ethanol vapor resistance in Drosophila melanogaster at two population sizes. Genetics 125:585-597.

Wiley, E. O. 1981. Phylogenetics: the theory and practice of phylogenetic systematics. John Wiley and Sons, New York.

Wilkens, H. 1988. Evolution and genetics of epigean and cave Astyanx fasciatus (Characidae, Pisces). Support for the neutral mutation theory. Evolutionary Biology 23:271-367.

Williamson, P. G. 1981. Morphological stasis and development constraint: real problems for neo-Darwinism. Nature 294:214-215.

-----. 1987. Selection or constraint?: a proposal on the mechanisms for stasis. Pp. 129-142 in K.S.W. Campbell and M. F. Day, eds. Rates of evolution. Allen and Unwin, London.

Wright, S. 1938. Size of population and breeding structure in relation to evolution. Science 87:430-431.

-----. 1968. Evolution and the genetics of populations. I. Genetic and biometric foundations. University of Chicago Press, Chicago.

-----. 1977. Evolution and the genetics of populations. III. Experimental results and evolutionary deductions. University of Chicago Press, Chicago.

@ @
COPYRIGHT 1993 Society for the Study of Evolution
No portion of this article can be reproduced without the express written permission from the copyright holder.
Copyright 1993 Gale, Cengage Learning. All rights reserved.

Article Details
Printer friendly Cite/link Email Feedback
Author:Spicer, Greg S.
Publication:Evolution
Date:Aug 1, 1993
Words:9029
Previous Article:The genetics and cost of chemical defense in the two-spot ladybird (Adalia bipunctata L.).
Next Article:Genetic variation for stress resistance and species borders.
Topics:

Terms of use | Privacy policy | Copyright © 2019 Farlex, Inc. | Feedback | For webmasters