Organisms are complex - even the most primitive ones require the activity of many genes and the interaction of many physiological processes. Consequently the evolution of organisms is equally complex, involving the evolution of thousands of genes and many phenotypic traits. Dealing with this level of complexity requires strategies to reduce the complexity of the problem to a manageable size. The most effective complexity reduction strategy proved to be `methodological reductionism', the idea that studying simple part processes will ultimately lead to an understanding of complex reality (Provine, 1971). In evolutionary biology this strategy takes a variety of forms, as for instance genic selectionism (Williams, 1966; Dawkins, 1976) with its powerful impact on understanding the evolution of altruism (see for instance Wilson, 1975). In the study of adaptation, we mostly rely on the analysis of a single character or a tightly integrated complex of characters (Mayr, 1983), and in theoretical quantitative genetics one first concentrates on single character models.
Methodological reductionism is a powerful tool to get a handle on complex phenomena. Its validity rests on a prudent choice of characters to study (Rosenberg, 1985) and an understanding of the possible interaction effects ignored by a single trait or single gene approach. For instance, measuring natural selection on a phenotypic character may overestimate the strength of stabilizing selection acting on the character directly. This is because selection on a correlated character leads to apparent selection on the character under study (Lande, 1980; Lande and Arnold, 1983). Even in the absence of genetic and phenotypic correlations, the presence of hidden pleiotropic effects influences the mutation-stabilizing-selection balance (Turelli, 1985; Wagner, 1989). In addition, completely neutral phenotypic characters may experience `apparent' stabilizing selection due to pleiotropic effects on fitness (Robertson, 1956; Barton, 1990; Keightley and Hill, 1990; Zhivotovsky and Gavrilets, 1992; Kondrashov and Turelli, 1992; Gavrilets and de Jong, 1993; Caballero and Keightley, 1994). A change in the mean of a character in response to natural selection may not be caused by direct selection on this character either, since genetic correlations can cause correlated selection responses (Falconer, 1981; Lande, 1979). In this paper we study the response of uncorrelated characters to directional selection in the presence of hidden pleiotropic effects. Pleiotropic effects are called "hidden" if they do not contribute to genetic correlations (Turelli, 1985).
The focus of this study is a simple model for the evolution of complex organisms. It is based on three assumptions which capture some of the features characteristic of organismic evolution: 1) the first assumption is that pleiotropic effects are extensive and universal. It is thus based on the Wright's universal pleiotropy hypothesis. The background for this assumption will be reviewed below. 2) Only one character (or a linear combination of characters) is under directional selection at any time. This assumption is in line with the pattern of mosaic evolution, which means that complex organisms do not change all their characteristics at the same time (Simpson, 1953). For the most parts, episodes of adaptive transformation lead to a selection response in a small number of characters, like either teeth or the limbs. 3) While some of the characters are under directional selection, most of the others are either neutral or under stabilizing selection. This is a corollary of the mosaic evolution assumption. It is also a direct consequence of the assumption that adaptation can be understood as an approach to a local optimum in a multivariate phenotype space. If a population approaches an adaptive optimum, the direction of steepest ascent is the only direction of directional selection, while all the other dimensions of the phenotype are under stabilizing selection (Wagner, 1996). Hence we think that a combination of directional and stabilizing selection is a common pattern. A simple model with pure directional selection in one direction and stabilizing selection in all other directions has been called a `corridor model' (Wagner, 1984).
There is some similarity of the corridor model to the model analyzed by Zeng (1988). In this paper Zeng also consideres two characters under a mixed regime of directional and stabilizing selection and pointed out that long term and short term selection responses can be different. The corridor model, in contrast, does not make long term predictions. It is intended as a simple model to predict the micro-evolutionary response to directional selection.
The extent and importance of pleiotropic effects is still a matter of controversy. The possible views range from the extreme of the one-gene-one-character view of early Mendelism (see e.g. Darden 1992), ignoring pleiotropy completely, to Wright's universal pleiotropy hypothesis (Wright, 1968). The one-gene-one-character view was abandoned early in the history of genetics owing to the discovery of numerous pleiotropic effects of mutations with major effects on morphology. The universal pleiotropy hypothesis of Wright was the reaction to this discovery. Recently Bonner proposed a intermediate view arguing that universal pleiotropy is incompatible with adaptive versatility (Bonner, 1988). He assumes that the genome is organized in more or less discrete `gene nets' (`modules' sensu Raff, 1996 and Wagner, 1996) each responsible for the development of a functionally independent character. The idea is that independently coded characters can be adapted with minimal interference with the performance of other characters.
Empirical evidence on the extent and pattern of pleiotropic effects is sketchy and often indirect. As mentioned above, the first argument in favor of extensive pleiotropic effects came from the analysis of mutations with morphological effects (Wright, 1968). However, as noted by Barton (1990) it is not clear whether this observation can be generalized to mutations with less dramatic effects. There is for instance no evidence of extensive pleiotropy of genes influencing abdominal and sternopleural bristle number in Drosophila melanogaster (Davies, 1971; Mackay et al., 1992a). Mapping techniques for quantitative trait loci (QTL) will soon resolve this issue. Preliminary evidence seem to be in favor of Bonner's modularity model of pleiotropy (Cheverud, 1996). In mice, strong pleiotropy among tightly integrated sets of characters and only limited pleiotropy among such sets has been found so far.
Indirect evidence for extensive pleiotropy, though not about the pattern of pleiotropy, comes from various quantitative genetic arguments summarized by Barton (1990). One argument follows from the comparison of the average mutation rate of a quantitative character with the total mutation rate for deleterious effects. On the basis of published data, Turelli (1984) estimated an average mutation rate for a quantitative trait of 0.01, and the rate of viability mutations in Drosophila has been estimated to be at least one order of magnitude higher (Mukai, et al. 1972, Simmons and Crow, 1977; Houle et al. 1992). Again this leads to the conclusion that there has to be extensive pleiotropy of a majority of genes in the genome (Barton, 1990).
Strong pleiotropic effects on fitness have been demonstrated for genes affecting a (nearly) neutral quantitative trait, abdominal and sternopleural bristle number in Drosophila. Several lines of experimental evidence show that these characters are effectively neutral (Clayton et al., 1957; Latter and Robertson, 1962; Kearsey and Barnes, 1970; Nuzhdin et al., 1995). Furthermore alleles with large effects on bristle number are found at intermediate frequencies in natural populations (Lai, et al. 1994; Long et al., 1995). This is incompatible with strong stabilizing selection on the character directly (Turelli, 1984). Nevertheless the effect of P-element insertions on bristle number is associated with low fitness (Mackay et al. 1992b), and decreased response of inbred lines to selection shows strong apparent selection on bristle number (Mackay et al., 1994, 1995). However, crossing experiments effectively demonstrate that this stabilizing selection is due to deleterious pleiotropic effects (Nuzhdin, et al., 1995).
There are two ways of modeling pleiotropic effects and their influence on fitness. Pleiotropic effects can be modeled as contributions to fitness independent of the quantitative character under directional selection (Gavrilets and deJong, 1993; Keightley and Hill, 1990; Kondrashov and Turelli, 1992; Zhivotovsky and Gavrilets, 1992). In the model of Keightley and Hill (1990) and Kondrashov and Turelli (1992) the pleiotropic effects are assumed to be unconditionally deleterious. Another strategy is to take into account a second quantitative character which is under stabilizing selection (Turelli, 1985; Bürger, 1986a,b; Wagner, 1984, 1988, 1989). If one of the characters is under directional selection, these models have been called corridor models, since they restrict phenotypic evolution to a narrow corridor within the phenotype space (Rechenberg, 1973). In these models pleiotropic effects are only conditionally deleterious, since they can be compensated by additive effects on other loci.
Corridor models have been studied extensively with phenotypic evolution equations which assume constant genetic and phenotypic variance and covariance (Bürger, 1986a/b; Wagner, 1984, 1988) and to some extent with polygenic two-allele models (Gavrilets and Hastings, 1994; Zhivotovsky and Gavrilets, 1992). A main result from phenotypic evolution models is that selection on the second character should not influence the evolution of the character under directional selection, as long as the Malthusian fitness surface is at most polynomial of degree two (`well behaved'). Below we will show that this result is a direct consequence of assuming constant genetic variances implicit in phenotypic evolution equations. It is concluded that explicit genetic models are necessary to obtain an accurate prediction of selection response.
Tue Apr 9 13:43:34 EDT 1996