Epigenetics and the environment: emerging patterns and implications

Dynamics of finite populations : II. A time-homogeneous stochastic process describing the ultimate probability of and the expected time to fixation or loss of an allele or type in a population of variable size

A time-homogeneous stochastic process was used to derive exact expressions for the ultimate probability of fixation or loss and the expected time to fixation or loss of an allele in a haploid population whose size is a Poisson random variable. The treatment included selection and multiple alleles.

Disruptive selection

A population is exposed to disruptive selection if more than one phenotype has optimal fitness and intermediate phenotypes have lower fitnesses. Maintenance of the two or more optima may depend upon their relative fitnesses being frequency dependent. Such selection may be expected in two contrasting types of situation. First the two or more optimal phenotypes may depend on one another as do the two sexes in a bisexual species. Secondly the optima may be set by heterogeneity of the environment. Then we may think in terms of a mosaic of ecological niches or a clinal situation, and may expect that gene flow will tend to promote convergence of the sub-populations while disruptive selection tends to promote their divergence. Disruptive selection may therefore be relevant both to the evolution and maintenance of polymorphisms and to the divergence of parts of populations one from another, under the influence of variation of ecological conditions within the range of gametic and/or zygotic dispersal. Disruptive selection has been shown to be capable of increasing phenotypic and genetic variance, of producing and maintaining polymorphisms, of causing divergence of sub-populations between which substantial gene exchange occurs, and of splitting a population into two which are genetically isolated from one another. These results are reviewed and their relevance to natural populations discussed.

Enzyme variability in the Drosophila Willistoni group. V. Genic variation in natural populations of Drosophila equinoxialis

We have studied genetic variation at 27 loci in 42 samples from natural populations of a neotropical species,Drosophila equinoxialis, using standard techniques of starch-gel electrophoresis to detect allelic variation in genes coding for enzymes. There is considerarle genetic variability inD. equinoxialis. We have found allelic variation in each of the 27 loci, although not in every population. On the average, 71% of the loci are polymorphic – that is, the most common allele has a frequency no greater than 0·95 – in a given population. An individual is heterozygous on the average at 21·8% of its loci.

The amount of genetic variation fluctuates widely from locus to locus. At theMdh-2locus arout 1% of the individuals are heterozygotes; at the other extreme more than 56% of the individuals are heterozygous at theEst-3. At any given locus the configuration of allelic frequencies is strikingly similar from locality to locality. At each and every locus the same allele is generally the most common throughout the distribution of the species. Yet differences in gene frequencies occur between localities. The pattern of genetic variation is incompatible with the hypothesis that the variation is adaptively neutral. Genetic variation inD. equinoxialisis maintained by balancing natural selection.

The amount and pattern of genetic variation is similar inD. equinoxialisand its sibling species,D. willistoni. Yet the two species are genetically very different. Different sets of alleles occur at nearly 40% of the loci.

The genetic variability of polygenic characters under optimizing selection, mutation and drift

The effect of optimizing selection, mutation and drift on a metric character determined by a large number of loci with equal effects without dominance was investigated theoretically. Conditions for a stable equilibrium under selection and mutation, in the absence of drift, have been obtained, and hence the amount of genetic variability which can be maintained by mutation has been determined. An approximate expression for the average amount of genetic variability to be expected in the presence of drift in a population of finite size has also been obtained and evaluated.

The sociobiological aspects of the national survey on fecundity and fertility in Belgium

In 1966, a National Survey on Fecundity and Fertility was organized in Belgium. Approximately 3000 married women under 41 years of age and living with their husbands were interviewed and asked about their reproductive histories. The present paper records the sociobiological aims and methods and some preliminary results of this survey. The aims were to:

(1) study the influences of contraception on human needs and qualities, in this case mainly potential fecundity;

(2) study the influence of attempts to increase the potential fecundity level in modern society on fecundity gene frequencies;

(3) study the influences of the overall socio-cultural environment on fecundity and fertility variables with particular reference to differences in social status in Western society;

(4) analyse the role of social assortment of fecundity and fertility variables on the biological structure, and possibly the composition, of modern populations.

A relatively large, but far from complete body of data has been collected on a number of individual fecundity and fertility variables, on the medical processes employed to increase fecundity, on contraception, and on a number of conventional sociological and demographic variables.

The principles underlying the present approach to the study of fecundity are explained, and a few preliminary results for one of the general fecundity classifications are shown.

The information collected on contraception has been qualitatively analysed and a correction and evaluation method is described. Data on the use of the different contraceptive methods show that substantial sections of the Belgian population are limiting their family size in a way which is inefficient, from both sexual and familial standpoints.

Age distribution and the stable equivalent

Some populations, like that of the United States in the 1950’s, have a smaller proportion of women of reproductive age than they would ultimately attain with continuance of their age-specific birth and deaths rates, a continuance which produces the condition known in demography as stability. Others, like that of the United States in the 1930’s, have relatively more women of reproductive age than they would ultimately attain with stability. A way of studying ages is to calculate how many women of stable age distribution would be equivalent from the viewpoint of reproduction to the women observed. This stable equivalent was 69,535,000 or 16 percent below the observed United States female population in 1955, and 12 percent above the observed in 1935. The stable equivalent is a measure of fertility potential, closely related to R. A. Fisher’s reproductive value. Calculations for four countries illustrate how a fall of the birth rate, for example in demographic transition, occasions an age distribution in which the stable equivalent is greater than the observed number of women. The notion of stable equivalent is useful for comparison because changes in it are nearly invariant with respect to the age-pattern of fertility used. The statement that the United States stable equivalent increased by 11 percent between 1960 and 1965 holds irrespective of whether the 1960 or the 1965 age-specific fertility and mortality rates are used as standard.

Natural selection and population diversity

It is an observed fact that human populations differ in genetic composition. Some of the inherited diversity is due to combined effects of many genes. Although it would be interesting to know the magnitude and nature of the genetic contribution to some characters under polygenic control, such as intelligence or physique, environmental effects may be so great that no genetic analysis is possible—as Thoday has pointed out earlier in this symposium. With other polygenic characters, such as skin colour, the genetic component is more obvious but still difficult to analyse precisely. The number of genes involved, their frequency and dominance have not been established. This is one of the reasons why selective effects on such characters are not readily measured, although they probably exist.

Natural selection and gene substitution

Using models which describe the change, by natural selection, of the actual numbers of genes rather than their relative frequencies, it is demonstrated that the equation familiar to geneticists, i.e.dp/dt=sp(1 −p), is appropriate under a wide range of circumstances. It was pointed out that, for realistic treatment of the evolutionary process through which gene substitutions are repeated, the models must have the property such that the total population number remains constant or nearly constant throughout the process, and is not appreciably influenced by the genes being substituted.

The load or cost for a gene substitution was studied assuming a haploid population and the effects on the load of such factors as epistatic gene interaction in fitness, finite population number and slow change of environment were investigated. The load may become very large under a strong ‘reinforcing’ type epistasis between advantageous genes. In a finite population, the load for one gene substitution may be inflated by about unity if the product of the effective population number (Ne) and the selection coefficient (s) is large butNesp0is much smaller than unity, wherep0is the initial gene frequency. On the other hand, slow change of environment may decrease the load somewhat. It was concluded that despite these and other complicating factors, Haldane's original formula, –logep0, for a haploid population (−2 logep0for the case of a diploid without dominance) is still useful for assessing the approximate amount of selective elimination that accompanies the process of gene substitution in evolution.

On the fixation of genes of large effects due to continued truncation selection in small populations of polygenic systems with linkage

The proportion of fixed loci for desirable genes and the time required for fixation is studied in simulated diploid populations, which have initially aHARDY-WEINBERG structure. A symmetric ten-locus system of additive or dominant genes is simulated with linkages between adjacent loci varying as .005, .05, or .5. A constant degree of upper truncation selection within a population is considered over the generations. In different populations the intensity of truncation is varied asN/N,N/N+2,N/N+4, ..., whereN is the parental population size, specified as 2,4,8 or 16. The selection differential in initial generation, ī, thereby varies from zero to more than two standard deviations in some cases. The initial mean gene frequency,p, simulated in an initial population is .1 or .5.It is pointed out that when selective advantage of a gene is large and is changing with gene frequency, diffusion approximations assuming constant selective advantage, gives higher values for proportion of fixed genes in the case ofp equal to .1 and lower values forp equal to .5. With parental population size of 16 or less, a relation withN ī alone does not give the proportion of fixed genes. Higher order terms ofN ī appear to be involved in the relation. For the sameN ī, the proportion is much higher for lowN.The depressing effect of low recombinations between loci is of different magnitude for differentN andp for a givenN ī. The increase in the proportion of fixed genes due to increasingN is not as large when π is low. High intensity of selection offsets considerably the effects of population size and linkage when gene effects are large. It appears that with increased inbreeding and selection intensity, almost all the genes of large effects and at intermediate frequencies can be rapidly fixed regardless of linkage.Linkage has been shown to cause faster fixation of genes in the absence of selection. With selection, linkage tends to delay fixation. But in the case of very low recombinations, there appears to be a level of population size and selection intensity, below which there is more rapid fixation because of linkage. Selection for dominant genes in the case of very close linkage, delays fixation for a number of generations and this delay results in reducing the depressing effect of linkage.

Correlated responses in reproductive fitness to selection in chickens

The correlated changes in reproductive fitness with selection for single traits for six generations in five Leghorn lines and five generations in three Fayoumi lines were analysed. The Leghorn lines, originating from crosses between four commercial strains, were: lineA, selected for high egg production; linesBandC, selected for high and low nine-month body weight; and linesDandE, selected for high and low nine month egg weight. The Fayoumi lines,J, KandL, corresponding to theA, BandDLeghorn lines, respectively, were selected from a random mating population maintained over several years without selection. The breeding populations for theAandJlines each consisted of 16 sires mated to 9–16 dams each, while all the other lines were produced from eight sires, each mated to 9–16 dams. TheAandJlines showed no consistent improvement in egg production or reproductive fitness and were used as control lines in this study. Body weight in theBandKlines increased by 55·8 and 45·2%, respectively, while egg weight in theDandLlines increased by 17·7 and 15·1%, respectively. TheCline declined in body weight by 21·5%, while theEline declined in egg weight by 16·3%.

A reproductive fitness index was measured as the product of rate of egg production, fertility, hatchability, and percent survival of offspring from housing to nine months of age. The mean values of the fitness index as percentages of the control lines were Leghorn linesB66,C81,D74,E85 and Fayoumi linesK54 andL74.

Reproductive fitness and all fitness components except offspring survival declined more in the high lines than in the low lines. The body weight lines were lower in fitness than the egg weight lines, mainly because of lower rate of egg production The patterns of correlated changes in the fitness index were more regular in the Fayoumi than in the Leghorn lines. The linear regressions of fitness index on direc selection response in theKandLFayoumi lines were statistically significant. Offspring survival contributed only 14% to the variation in the fitness index in the Leghorn lines and only 8% in the Fayoumi lines. The relative contributions to the variation in fitness index were 35% for rate of egg production, 24% for fertility and 23% for hatchability in the Leghorn lines. The corresponding figures were 35, 30 and 27% for the Fayoumi lines, respectively.

The average linear regression coefficients of fitness index on body weight, calculated on an individual hen basis (selected breeders only) within lines and generations, were - 4·77 for theBline, 11·53 for theCline, and – 1·01 for theKline. The corresponding coefficients of fitness index on egg weight in the egg weight lines were – 0·543 for theDline, 0·947 for theEline, and – 0·712 for theLline. With the exception of theKline, the regressions on body weight were larger in the body weight lines than in the egg weight lines, and, similarly, the regressions on egg weight were larger in the egg weight lines than in the body weight lines. The differences between the regression coefficients of the high and low lines were statistically significant.

Genetic variability maintained in a finite population due to mutational production of neutral and nearly neutral isoalleles

1. The average and the effective numbers of alleles maintained in a finite population due to mutational production of neutral isoalleles were studied by mathematical analysis and computer simulation.

2. The exact formula was derived for the effective number (ne) of alleles maintained in a population of effective sizeNe, assuming that there areKpossible allelic states and mutation occurs with equal frequency in all directions. If the number of allelic states is so large that every mutation is to a new, not pre-existing, allele, we havene= 4Neu+1 − 2Neu2, whereuis the mutation rate. Thus, the approximation formula,ne= 4Neu+1, given by Kimura & Crow (1964) is valid as long as 2Neu2≪ 1.

3. The formula for the average number of alleles (na) maintained in a population of actual sizeNand effective sizeNewas derived by using the method of diffusion approximation. If every mutation is to a new, not pre-existing, allele, we obtain

whereM= 4Neu. The average number of alleles as a function ofMandNis listed in Table 1.

4. In order to check the validity of the diffusion approximations, Monte Carlo experiments were carried out using the computer IBM 7090. The experiments showed that the approximations are satisfactory for practical purposes.

5. It is estimated that among the mutations produced by DNA base substitutions, synonymous mutations, that is, those which cause no alterations of amino acids, amount roughly to 0·2–0·3 in vertebrates.Incompletely synonymous mutations, that is, those which lead to substitution of chemically similar amino acids at a different position of the polypeptide chain from the active site and therefore produce almost no phenotypic effects, must be very common. Together with synonymous mutations, they might constitute at least some 40% of all mutations. These considerations suggest that neutral and nearly neutral mutations must be more common than previously considered.

An elementary approach to the population projection-matrix, to the population reproductive value, and to related topics in the mathematical theory of population growth

Este artículo presenia una aproximación elemental al estudio de la matriz de proyeccian de poblaci'on, el reverso (o inversa) matriz de proyección, el proceso de desarrollo de la poblacian generado por la matriz de proyección, el “a priori” proceso de desarrollo de población asociado con la matriz de proyección inversa, la distribución de edades eetoble que pertenece a la matriz de proyección, la ecuación característica de la matriz de proyección y las raices laienies de la ecuación característica.

Nosotros introducimos algunos nuevos indices que miden el “valor reproductivo eventual” de los individuos en los varios intervalos de edades de una población, y mostramos porque los índices presentados aquí son preferibles a los indices de la misma naturaleza presentados anteriormente por R. A. Fisher y P. H. Leslie.

Para poder seguir la mayor parte de la presenie exposición, el lector precisa iener solamenie nociones elemeniales de algunos de los terminosusados en algebra de matrics. Esta aproximación elemental va a llevarnos a la introducción de algunas nuevas fórmulas las cuoles simplijican a la vez la comprensión y el cálculo de varias cantidades que son relevantes a la demografiá y a la teoría matemática del desarrollo de la población.