On the evolution of dominance modifiers I. A nonlinear analysis

A well known mathematical model of evolution of dominance is subjected to a nonlinear analysis. For the case where the primary locus and the modifying locus are completely linked (r = 0) a global Ljapunov function is given. This proves that selection of dominance modifiers entirely due to their modifying effect is possible. This result is also extended to small recombination fractions r by using the method of Ljapunov functions in a more sophisticated way. For r = 0 and μ = 0 a lower bound for the success of selection of the modifier is given. Furthermore, the influence of the dominance relations between the alleles (measured by the parameters h and k) is investigated. Finally it is shown that differential and difference equations lead to the same results (which need not be the case in general). As a by-product we obtain a new equilibrium point in the classical one locus selection-mutation model.     

Ordering genes: controlling the decision-error probabilities.

Determination of the relative gene order on chromosomes is of critical importance in the construction of human gene maps. In this paper we develop a sequential algorithm for gene ordering. We start by comparing three sequential procedures to order three genes on the basis of Bayesian posterior probabilities, maximum-likelihood ratio, and minimal recombinant class. In the second part of the paper we extend sequential procedure based on the posterior probabilities to the general case of g genes. We present a theorem that states that the predicted average probability of committing a decision error, associated with a Bayesian sequential procedure that accepts the hypothesis of a gene-order configuration with posterior probability equal to or greater than pi *, is smaller than 1 - pi *. This theorem holds irrespective of the number of genes, the genetic model, and the source of genetic information. The theorem is an extension of a classical result of Wald, concerning the sum of the actual and the nominal error probabilities in the sequential probability ratio test of two hypotheses. A stepwise strategy for ordering a large number of genes, with control over the decision-error probabilities, is discussed. An asymptotic approximation is provided, which facilitates the calculations with existing computer software for gene mapping, of the posterior probabilities of an order and the error probabilities. We illustrate with some simulations that the stepwise ordering is an efficient procedure.     

On the evolution of dominance modifiers II: a non-equilibrium approach to the evolution of genetic systems

The evolution of dominance is both the simplest and best investigated example of the evolution of genetic systems. Nevertheless, there exists striking empirical material, e.g. industrial melanism, for which no satisfactory explanation could so far be provided. In this paper we take an approach to this classical problem based on a global analysis together with computer simulations. It reveals that during the evolution of dominance one has to distinguish a "nonequilibrium phase" and a "Fisherian phase". The non-equilibrium phase appears to be characterized by the fact that in general the selection intensity at the primary locus does not affect the degree of modifier selection but only the time necessary for passing through this phase. A further essential conclusion is that modifier evolution only obtains a reasonable amount of efficiency if the population reaches the Fisherian phase already with a high modifier frequency. Using these results, predictions on the population genetic prerequisites for the evolution of dominance are derived. From these we conclude that even in populations in which dominance evolution has occurred it cannot be expected that back-crosses into relics of the ancestral population lead to a breakdown of dominance within a few generations. These predictions are in accordance with empirical data on Biston betularia and Odontopera bidentata.     

The theory of the evolution of dominance

Journal of Genetics - In a population which is mainly self-fertilized the majority of nonlethal mutant genes are present in homozygotes and very few in heterozygotes. The intensity of selection for...     

The evolution of male dominance

Conclusions We have proposed that an alternative explanation of sex-role evolution is available which is, unlike the prevailing conservative explanation, based on empirically supported observations. The model proposed here focuses upon the differential access of men and women to scarce resources and goods. Generally, but not always, this involves control of communications systems, intergroup relations, surplus products, and special ritual and recreative ends. We have argued that men have had greater access to these sources of power than have women because of demographic factors, and because of the power reproducing character of social evolution.Our model explicitly rejects explanations based on conservative premises. We have rejected the conservative assumptions that systems are based on survival needs, that male and female role division accords with inherent male and female capacity to meet survival demands, that status and power are a consequence of an individual's contribution to the subsistence system or to defense systems, that females are incapable of coping with the rigors of traditional male roles such as hunting, that males need to protect females, that males carry out most subsistence activity, and that the activities males engage in are those which are most necessary to system survival. In its place we have formulated a constraint model which focuses on the demographic limitations placed on females and the greater access these limitations give males to social resources through their greater ability to occupy cultural interfaces.We have also shown that the introduction of conservative premises into work aimed at providing an alternative model of sex-role evolution has prevented the formulation of research based on an alternative model. From Marx and Engels through the cultural evolutionists and up to Sanday's work, the introduction of conservative premises dealing with system needs of subsistence or of defense have prevented social scientists from dealing with the main problem: that of the strategic basis, and potential, of power wielded by men merely because they are new.T.A. Caine teaches in the Department of Sociology, University of Minnesota, Minneapolis.C.A.H. Caine teaches in the Department of Anthropology, Hamline University, St. Paul, Minnesota.     

The evolution of dominance: Haldane v Fisher revisited.

Fisher's model for the evolution of dominance indicates that the accumulation of dominance modifiers will be accelerated by (1) an increased frequency of the mutant heterozygote, (2) increased selection for the phenotype of the normal homozygote. The model has been criticised by Haldane on the grounds that point (1) is not fulfilled, that is dominance appears to be more common in populations with a low frequency of mutant heterozygotes (populations of inbreeders). In support of Fisher's model it is argued that intense selection for the wild type phenotype is more common in inbreeders than outbreeders. This situation should promote the accumulation of dominance modifiers (point (2) above).     

On the relative roles of faster-X evolution and dominance in the establishment of intrinsic postzygotic isolating barriers

The modern theory of speciation assigns a prominent role to the recessivity of genetic incompatibilities in the two rules of speciation, namely Haldane's rule and the large X effect, and considers that the contribution of faster evolution of the X versus the autosomes to those patterns is generally of relatively minor importance. By extending Turelli and Orr's previous analysis of the model of two-locus Dobzhansky–Muller incompatibilities, I first show that when the X and the autosomes evolve at the same rate, the two dominance parameters involved in that model are not equally important for the declaration of a large X effect, but that the degree of recessivity of homozygous–homozygous incompatibilities is the major determinant for such a declaration. When the X evolves faster than the autosomes, the model obviously predicts that the importance of both dominance parameters will progressively vanish. It is then of importance to obtain estimates of the relative evolutionary rate of X-linked incompatibility loci. Several different procedures to obtain such estimates from the perspective of the large X effect are suggested. The application of the appropriate test to the only suitable data from Drosophila hybridizations so far available leads to the conclusion that the X actually evolves at least 2.5 times faster than the autosomes, as far as hybrid male sterility determinants are concerned, thus making dominance considerations absolutely irrelevant. Notwithstanding the necessity of further tests, the relative roles currently assigned to faster-X evolution and dominance in the theory of speciation should be revised, giving due prominence to faster-X evolution, at least for hybrid male sterility in the genus Drosophila.     

Ecological dominance and the final sprint in hominid evolution

In contrast to many other models of human evolution the “balance of power” theory of Alexander has a clear answer to the question why a runaway selection process for unique social and moral capacities occurred in our ancestry only and not in other species: “ecological dominance” is hypothesized to have diminished the effects of “extrinsic” forces of natural selection such that withinspecies, intergroup competition increased (Alexander, 1989). Alexander seems to be wrong, however, in his claim that already the common HUCHIBO (Humans, Chimps, Bonobo's)-ancestor has crossed the ecological dominance barrier. In this paper an adapted version of Alexander's model is presented and several different ways are proposed to make this adapted version testable. A preliminary survey of the available paleontological and paleoecological data suggests that there is some evidence of a less vulnerable position towards predators in earlyHomo and that there are clear signs related to a crossing of the ecological dominance barrier inHomo sapiens sapiens.     

On the probabilities of identity states in permutable populations.

Génin and Clerget-Darpoux recently discussed the derivation of the probabilities of identity states for populations in which there was some degree of kinship, primarily to allow the extension of the classical affected-sib-pair method to such populations. It is argued here that their derivation makes certain assumptions that are valid only for some very restricted population models and that are not needed for an appropriate treatment. Here the probabilities of the identity states of two individuals with a given genealogical relationship are specified in terms of the kinship parameters of the underlying population, from which the founders of the individuals'' genealogy have been randomly selected. It is argued that an appropriate representation for a permutable population, one in which gene identity does not depend on the pattern of genes across individuals, requires three parameters. This representation is related to that of Génin and Clerget-Darpoux and to that of Weir.     

Symmetric tests and confidence intervals for survival probabilities and quantiles of censored survival data

We describe existing tests and introduce two new tests concerning the value of a survival function. These tests may be used to construct a confidence interval for the survival probability at a given time or for a quantile of the survival distribution. Simulation studies show that error rates can differ substantially from their nominal values, particularly at survival probabilities close to zero or one. We recommend our new constrained bootstrap test for its good overall performance.