Are imprinting and inbreeding two related phenomena?

Summary - This article presents a molecular theory of inbreeding mechanisms involving interactions between regions of the male and female genomic complement. This theory is based on the recent developments in imprinting effects on male and female gametes, which are now explained in terms of protein-DNA interactions which are manifested in some organisms in the form of cytosine methylation. Such interactions are illustrated in examples from transposable elements, which also play a key role in genetic load. This theory accounts for the effects observed in particular mating systems of inbreeding and may be of interest for heterosis as well.


INTRODUCTION
The classical theories of inbreeding effects are based on an increase in the degree of homozygosity of the inbred individuals (Wright, 1921(Wright, , 1922aMal6cot, 1948).
Inbreeding depression is thus the result of segregation at overdominant loci or of the expression of recessive deleterious or lethal alleles usually concealed in the genome (Dobzhansky et al, 1963). The high homozygosity is also believed to decrease the number of enzymatic paths that control metabolism (Haldane, 1954), and to perturb the system of homeostatic regulations of individuals (developmental homeostasis) as well as of populations (genetic homeostasis) which then become incapable of adapting to modifications in the environment (Lerner, 1954).
Experiments carried out on the fruit fly Drosophila and the Bruchidae Acanthoscelides obtectus, in the first generation of various inbred mating systems, have shown however that depending on the mating system used, fitness components such as egg hatchability, larvo-pupal viability, fecundity (egg production), and some other traits measured in adult flies, are not altered in the same way (Bi6mont, 1972a(Bi6mont, ,b, 1974a(Bi6mont, , 1976Bi6mont and Bi6mont, 1973). It was found, for example, that father-daughter matings lead to decreased larval and pupal viability and fecundity of F 1 females, whereas mother-son matings decreased embryonic mortality. Such results are not explainable globally by classical genetic theory based on simple increased homozygosity of deleterious recessive genes, even with the addition of complex cytoplasmic controls or maternal effects. The present paper is thus an attempt to present evidence regarding recent discoveries on imprinting effects and mechanisms to explain how maternal and paternal chromosome sets might be differentiated and might lead to the above inbreeding effects. THE

FACTS
It has been theoretically demonstrated that crosses between brothers and sisters, fathers and daughters, and mothers and sons, lead to the same value of the inbreeding coefficient for autosomal loci (of 1/4). An inbreeding depression of identical extent should then result in the inbred offspring of these crosses, although as postulated by Franklin (1977), the parent-child crosses should lead to less inbreeding depression than brother-sister crosses. By working on early and late development in Drosophila melanogaster, we have shown that the above 3 kinds of crosses actually give different patterns of inbreeding depression for characteristics such as egg hatchability (No of hatched eggs/No of fertilized eggs), larval and pupal viability (No of F 2 adults/No of hatched eggs), and adult egg production (total egg production during the lifetime of the F 2 adult flies, maximum egg production, longevity of the inbred adult). Tables I and II summarize the effects of the 3 mating systems on these traits. Note that total viability, which is what is usually measured, is the product of the egg hatchability by the larvo-pupal viability values. Tables I and II clearly show that fatherdaughter crosses do not decrease egg hatchability (and thus lead to a normal embryonic development), but greatly increase mortality during larval and pupal stages (table I) and decrease egg production characteristics of the adult inbred females (2 way analysis of variance: F = 4.5, P < 0.05 for total egg production; F = 8.4, P = 0.008 for maximum daily egg production). Mother-son crosses increase the embryonic mortality but have only a slight effect on larvo-pupal development (table I) and egg production measurements (F = 5.3, P < 0.05 for total egg production while there was no statistically significant difference for maximum daily egg production, F < 1). Sib crosses provoke a general negative effect on all these characteristics of the inbred generations: low egg-to-adult survival (table I), low total egg production of the adult inbred females (F = 14.4, P < 0.001), low maximum daily egg production (F = 8.4, P = 0.007).
An interesting result that is worth pointing out is the observation that total viability is reduced in the same way in the 3 crosses, thus leading to the apparently similar inbreeding depression in the 3 mating systems. Because only total viability is usually determined in experiments on inbreeding, we have no other data on viability components, even in birds where parent-child crosses were experimentally analysed (Bulmer, 1973), and in which 2 developmental stages sensitive to inbreeding were reported (Lucotte, 1975). New experiments on inbreeding could then be performed in sea urchins, for example, in which embryonic development processes are now well known, and in vertebrates where many components of viability can be analysed and in which development cannot succeed satisfactorily without the paternal genome.

THE INBREEDING MODEL
The above differential effects of parent-child crosses led us to distinguish 2 phases in the way inbreeding depression takes place; a phase in which the first stages of embryonic development are perturbed and which depends on presence of a F l spermatozoon; and a second phase in which larvo-pupal viability and some characteristics of the F 2 offspring are perturbed, and which depends on presence of an F 1 ovum.
To explain the above results of inbreeding, we postulated that these 2 phases imply the existence of interactions between the male and female chromosomal complements in the zygote and embryo (Bi6mont et al, 1974;Bi6mont, 1974b).
We then formulated the hypothesis that there exist on the male and female chromosomes particular regions capable of interacting. These regions possess some sites in an active or inactive state; the inactive state needs information from the active state to become activated. What is important in this hypothesis is not only the number of active and inactive sites, but the number of interactions, ie, the number of couples of active-inactive homologous sites. These interactions are postulated to be necessary for complete embryonic development. Moreover, the model implies that the maternal and paternal complements are asynchronously activated so as to explain the divergence in inbreeding depression following fatherdaughter and mother-son crosses. Paternal factors are thus postulated to act first to activate the maternal complement; such interactions control embryonic development. The maternal complement acts second to activate the homologous zones on the paternal complement, and these interactions are necessary for later stages of development. Any perturbations on either the first or the second phase lead to deleterious effects on either embryonic development or late development and some adult characteristics (Bi6mont and Boul6treau-Merle, 1978;Bi6mont and Lemaitre, 1978).
It is important to note that normal development involves the confrontation of gametes. We can thus understand how inbred matings can lead to deleterious effects throughout development as a result of gamete incompatibility. The similarity of the homologous complements between brothers and sisters makes many interactions impossible (see the fig 1); deleterious effects for both early and late development result. In the father-daughter mating system, the pattern of active/inactive sites of the father is common to that of his daughter; nevertheless, the daughter complement contains some specific active sites not seen in her father; the interactions, thus possible, account for the normal egg hatchability observed in such a mating system, yet provoke a perturbation in late development. In the mother-son crosses, the interactions involved are opposite to that of the father-daughter crosses; hence, the opposite effects are observed in this mother-son mating system: embryonic development is perturbed while the later developmental stages are almost normal.
As a result of the site interactions, the 2 genomic complements have similar patterns of activated/inactivated sites along the chromosome; spontaneous changes in such patterns must then exist to allow some interactions to proceed, avoiding thus a complete blocking of development. Variation in intensity of such a process accounts for the differential responses to inbreeding of organisms.
Note that in the years 1973-1974 no molecular knowledge was available to render the above hypotheses testable and acceptable by the scientific community. Indeed, little was known on how the genes were activated and regulated throughout development, and repression of gene expression by non-histone chromosomal proteins was only mentioned (Spiegel et al, 1970;Asao, 1972;Kostraba and Wang, 1973;Stein et al, 1974). The recognition of the existence of a phenomenon termed &dquo;imprint-ing&dquo; by Crouse (1960) was required in order to distinguish between maternal and paternal chromosome complements in many processes such as specific chromosomal elimination and inactivation by heterochromatization in various organisms. In 1975, Holliday and Pugh (1975) presented their theory of imprinting based on protein-DNA interaction and cytosine methylation. In the following sections, I summarize our current knowledge on this very exciting phenomenon of imprinting and discuss its importance and pertinence for the above model of inbreeding mechanisms.

IMPRINTING
Heterochromatization and chromosome elimination in many organisms have in common the selective silencing by inactivation or elimination of specific chromosomes or parts of chromosomes in the presence of unaffected homologs. The sex chromosomes of paternal origin are eliminated in ratlike bandicoots, inactivated in kangaroos while random inactivation occurs in placental mammals (Lyon, 1961;Sharman, 1971). In the coccids, Hemiptera, the chromosomes of paternal origin are inactivated or eliminated. For example, in lecanoids the paternally derived chromosomal set becomes heterochromatic and functionally inactive and remains so in most tissues throughout development (Brown and Nelson-Rees, 1961;Brown and Nur, 1964;Nur, 1967;Brown and Wiegmann, 1969;Kitchin, 1970;Sabour, 1972;Berlowitz, 1974); in diaspidids the effective haploidization of the male is accomplished by elimination of the paternal chromosomal set. In the olive scale insect Parlatoria olea (Kitchin, 1970) the heterochromatic chromosomes disappear by intranuclear destruction in the primary spermatocyte shortly before meiosis. Oogenesis is normal in ,Sciara where the egg receives a haploid set of autosomes and one X chromosome (Crouse et al, 1971), but in spermatogenesis the paternally derived X chromosome and autosomes are discarded (Crouse et al, 1971;Sager and Lane, 1972); the male transmits through the sperm only the chromosomes that he received from his mother. In Chlamydomonas, the chloroplast genome from the male parent is not transmitted because it disappears soon after zygote formation (Sager, 1972;Sager and Ramanis, 1974).
Hence, a phenomenon is required to distinguish between the maternal and paternal chromosome complements. Crouse (1960) has used the term imprinting to describe the alteration which allows a given chromosome to be distinguished from its homolog. Preferential expression of maternal or paternal genes throughout development in some species (Courtright, 1967;Dickinson, 1968;Wright et al, 1972;Sayles et al, 1973;Shannon, 1973) or in interspecific hybrids (Whitt et al, 1972) is also a good example of imprinting.
According to   , genomic imprinting could confer on some elements of the genome of reproductive cells a memory of their parental origin, so that the chromosomes or certain genes are marked by their path through the father and the mother. The maternal and paternal genornes may &dquo;remember&dquo; this parental origin throughout the development and life of the individuals. The simultaneous presence of the 2 chromosomal complements marked by the father and the mother are necessary for the embryonic development to be complete Modlinski, 1980). From all these studies it appears that the paternal genome is more important for development of extra-embryonic tissues while the maternal complement is necessary for embryonic development. Brown and Chandra (1973) proposed for mammals the existence of sensitive sites subject to imprinting, which activate receptor sites, which in turn, regulate heterochromatization of the X chromosome.
It has been shown in animals that for particular chromosomal regions with maternal duplication/paternal deficiency and its reciprocal, anomalous phenotypes depart from normal in opposite directions (Cattanach and Kirck, 1985). Such departure suggests a differential functioning of some gene loci within this region and also suggests the existence of a form of chromosome imprinting that affects gene activity. According to these authors, the male chromosomal region may thus have a single or earlier activity while inactivity or later activity may be a characteristic of the corresponding female region.

PROTEIN-DNA INTERACTIONS AND DNA METHYLATION
The mode of action of genes during development of the organism from the egg to adult is very poorly understood, and the changes in gene activity throughout development are generally referred to as epigenetic (Waddington, 1965). It is usually believed that specific protein-DNA interactions are responsible for such epigenetic changes in gene activity. It has been shown that such imprinting is associated with DNA methylation, which is a key element in the control mechanisms that govern gene function and differentiation (Razin and Riggs, 1980;Kolata, 1985;Reik et al, 1987;Sapienza et al, 1987). In eukaryotic methylation, certain cytosines are converted to 5methylcytosine which acts just like a new DNA base. Holliday and Pugh (1975), Riggs (1975) and Holliday (1987) have proposed that methylation is heritable, passed on from generation to generation as cells divide (Kolata, 1985;Reik et al, 1987;Sapienza et al, 1987); their proposition was further verified and suggests the existence of specific factors (maintenance methylase) (Harrison and Karrer, 1989) capable of recognizing the hemimethylated DNA formed after replication and that can methylate the nascent DNA strands (Holliday and Pugh, 1975;Riggs, 1975). Holliday (1987) then postulated that loss of methylation, which can result from DNA damage, leads to heritable abnormalities in gene expression. Such epigenetic defects in germline cells as a result of this loss of methylation can be repaired by recombination at meiosis, but some are transmitted to offspring. Defects that are not repaired at meiosis will have properties formally equivalent to mutations, since they are heritable and can have specific phenotypic effects. When heterozygous, an epigenetic defect can then be converted to wild type by recombination at meiosis (Holliday, 1987); the defects are thus &dquo;eliminated&dquo; by meiosis. With inbreeding, however, some epigenetic defects will become homozygous and will stay in this state throughout generations, depending on their probability of being removed as heterozygotes at meiosis. Holliday thus proposed that such processes could explain inbreeding effects.
According to Sager and Kitchin (1975) differential heterochromatization and chromosome elimination are regulated by modification of DNA by enzymes, as is the case in bacterial systems (Luria and Human, 1952), with specificity for particular recognition sites. It is postulated that the modification enzymes protect the recognition sites by DNA methylation from attack by the endonucleases. Razin and Riggs (1980) proposed that methylation could also lock nucleosomes into position on the DNA, the control regions of active genes not wound up in these nucleosomes being fixed by this methylation process until a new state of differentiation is established. This agrees with the observation that nucleosome positions on the DNA vary according to the state of differentiation of the cell. In such a model, methylation is only a secondary controller of gene expression, the primary stage being assumed by some kind of &dquo;determinator&dquo; proteins (Razin and Riggs, 1980). It is striking that researchers have not yet found the enzymes that originally add methyl groups to DNA in genes which are then permanently turned off during development; only &dquo;maintenance&dquo; enzymes (Harrison and Karrer, 1989) keeping methyl groups on during cell division are known. Note that the functional differences between maternal and paternal nuclei were found to be retained after the activation of the embryonic genome at the 2-cell stage (Surani et al, 1986), although the somatic methylation pattern has been found in 3-d embryos of chickens, in clusters of repeated DNA sequences (Sobieski and Eden, 1981).
Although it now appears that DNA methylation plays an important role in gene expression during development, some organisms manage quite well without any extensive methylation. The mechanisms for marking expressed genes in such organisms are still unknown. Lower vertebrates in general have far less methylation than mammals. Twenty percent of the lower vertebrate DNA is methylated as compared to 80% in mammalian DNA, and the DNA of the fruit fly does not seem to be methylated at all (Bird, 1980(Bird, , 1984. It is possible that some specific protein-DNA interactions, which are associated in higher organisms with the methylation pattern, survive to transmit the memory, and that these interactions alone are sufficient to account for imprinting in Drosophila (Razin and Riggs, 1980). Such DNA-protein interactions have been suggested to be themselves heritable (Weintraub, 1985). The lack of methylation in Drosophila may at first sight eliminate this species as a candidate for imprinting, but remember that preferential expression of some paternal and maternal genes occurs during development in Drosophila melanogaster (Courtright, 1967;Dickinson, 1968;Wright et al, 1972;Sayles et al, 1973;Shannon, 1973). Moreover, as noted above, the genome imprinting process was first discovered in various invertebrates, but the methylation of cytosine has not yet been searched for in most of the organisms. THE TRANSPOSONS Transposable elements have recently been shown to be submitted to a regulation system involving methylation. Because of their effects on genes and their ability to induce chromosomal rearrangements, these elements are an important source of genetic variability (Syvanen, 1974) and thus participate in the genetic load (Mukai and Yukuhiro, 1983;Bi6mont et al, 1985;Yukuhiro et al, 1985;Fitzpatrick and Sved, 1986;Mackay, 1986). Transposition rates are usually found to be ,--10-3 per generation (Pierce and Lucchesi, 1981;Young and Schwartz, 1981) but higher rates of transposition can be obtained either in crosses between certain strains of Drosophila melanogaster (Br6gliano and Kidwell, 1983) or under particular conditions (Gerasimova et al, 1983;Junakovic et al, 1986). Although in the long run an elevated mutation rate could be advantageous for population adaptation (Bi6mont et al, 1984;Georgiev, 1984), the potentially harmful effects of high rates of transposition may lead to selection for some mechanisms that regulate the activity of the transposable elements.
The controlling element Ac (activator) in Zea mags is capable of transposition, and a derivative that has lost transposase activity has been shown to have methylated cytosine that is inherited through sexual crosses; this inactive element can revert to active Ac by loss of methylation (Kunze et al, 1988). The activities of this maize transposable element Ac, as well as ,Spm (En), are thus correlated with hypomethylation (Burr and Burr, 1981;Dellaporta and Chomet, 1985;Chomet et al, 1987;Fedoroff et al, 1988;Raboy et al, 1988). DNA methylation of the maize transposable element Ac interferes with its transcription. In the inactive phase, the Ac DNA is highly methylated and no Ac transcript is detectable (Kunze et al, 1988).
In the same way, the majority of Mu elements in the maize genome are unmethylated in active stocks and methylated in inactive stocks (Schwartz and Dennis, 1986;Bennetzen, 1987;Bennetzen et al, 1988). An interesting observation is that intercrossing diverse mutator lines of maize leads to a discrete hypermodification of the Mu elements with a loss of mutagenic and transpositional potential (Bennetzen et al, 1987). Modification of Mu elements may block their ability to interact with a putative transposase as is the case with the IS 10 element in prokaryotes which is regulated by adenosine methylation (Roberts et al, 1985).
In mice, methylation concerns some but not all copies of the IAP repetitive sequences (Nlays-Hoopes et al, 1983). In the L1 element family, concerted hypomethylation of sequences has been observed in mouse extraembryonic cells and in transformed cell lines (Tolberg et al, 1987). It is thus speculated that in L1, methylation may modulate transcription of some selected sites.
Thus DNA methylation may be a mechanism for heritably controlling genetic element transposition. Such modification may be one mechanism regulating the possible deleterious activity in the cell (Chandler and Walbot, 1986). Transposition rate may also be under genetic control as in the switch in mating type of yeasts, which is normally confined to the mother cell lineage (Hicks et al, 1977). Whether mobile elements are really involved in an imprinting phenomenon is not yet clear, but this merits further investigation, especially since the sequence methylation pattern of the spm element in maize can be both reset and heritably reprogrammed during development, and such elements have a differential probability of being inactivated upon transmission through male or female gametes (Fedoroff, 1989).

A UNIFIED THEORY
It is still a matter of speculation as to whether the effects of inbreeding are due mainly to loss of homeostatic capacity of the more homozygous individuals or to the effects of recessive deleterious factors present in all wild chromosomes and exposed by the increasing homozygosity of the genome. The inbreeding depression thus results in a low viability due to numerous causes of mortality throughout the development of the organism (Lewontin, 1974); viability has thus been postulated to be controlled by polygenes with an extremely high spontaneous mutation rate (Simmons and Crow, 1977). From the above considerations, we now propose that inbreeding interferes with, or is strongly connected with mechanisms controlling embryonic development. Such an inbreeding model does not of course eliminate the classical hypotheses (Wright, 1921(Wright, , 1922aMal6cot, 1948;Haldane, 1954;Lerner, 1954;Dobzhansky et al, 1963); the inbreeding depression reported throughout development in many organisms surely involves more than 1 mechanism. Inbreeding and imprinting have common bases: -the molecular memory of parental origins of the maternal and paternal genomic complements, -the necessity of the simultaneous presence of the chromosomal complements marked by the father and the mother for the embryonic development to be complete; hence the existence of interactions between the 2 chromosomal sets, -the occurrence of sensitive sites which activate receptor sites in imprinting, or of interactions between activated and inactivated sites in inbreeding, -a differential activity during development of the male and female complements, -the existence of some spontanous site deactivation, or errors in the activation process, which avoid a complete blocking of development from the first generation of inbreeding on. Note that this latter consideration agrees well with the ideas that changes in protein/DNA interaction pattern can lead to heritable abnormalities in gene expression (Holliday, 1987), and that some specific interactions which survive to transmit the memory can themselves be heritable (Weintraub, 1985); it is also supported by the recent observation of the failure of the germline in mice to erase the epigenetic modifications at the TKZ751 locus, thus leading to cumulative modifications of this locus through successive generations (Allen et al, 1990).
Hence, inbreeding depression viewed in terms of interactions between the 2 parental chromosomal sets as occurs in imprinting is more a quantitative than a qualitative modification of a process existing normally in non-inbred individuals. The number of interactions involved in development is merely lowered by inbreeding, thus resulting in a higher probability for abnormal development. Such a quantitative effect agrees with the observation of an increased amount of histone proteins in inbred lines of rye (Kirk and Jones, 1974) and a disappearance of some biochemical components in Drosophila (Hoenigsberg and Castiglioni, 1958;King, 1969), as could result if inbreeding is associated with an increased repression of According to our model, the absence of interaction between 2 related gametic chromosomal complements blocks the first stages of embryonic development. But a population submitted to strong inbreeding such as brother-sister matings does not disappear in the first generations as could result due to null fitness. Even in the species most sensitive to inbreeding such as Gallinacea, 3 inbred generations are necessary for the population to collapse (Cole and Halpin, 1916;Dunn, 1928). Thus some spontaneous changes in the pattern of activated/inactivated sites along the chromosomal sets are needed to permit some interactions without blocking development entirely. Such changes in pattern could happen as a result of error in either the methylation process or the protein-DNA interactions involved in the imprinting mechanism. These spontaneous modifications and also the variation in the number of sites interacting could be responsible for the divergence existing between inbred individuals and among sublines.
Indeed, a problem in mouse genetics is the unexpected variation in homozygous inbred animals. For example, the frequency of variation of some skeletal structures is far higher than expected from classical mutation rates. Subline differentiation is a continuing process, the frequency of changes per variant being as high as 0.01 per generation (Hoi-Sen, 1972), 1000 times as common as the average mutation rate for a number of genes in the mouse (Schlager and Dickic, 1967). Murphy (1966), moreover, described a high frequency of tumors in 16 major inbred mouse stocks, as if inbreeding caused an increased rate of tumorigenesis. Fitch and Atchley (1985) supposed that if a mutation process, such as conversion or switching, were to occur to explain subline divergence in mice, it would be as high as 10-3 , a rate similar to that observed in switching on and off loci responsible for phase variation in Salmonella. Such a rate of 10-3 is exactly the average value of transposition rate found in Drosophila for transposable elements (Pierce and Lucchesi, 1981;Young and Schwartz, 1981), even in highly inbred lines maintained by systematic brother-sister mating during * 108 generations (data on mdg-1 and P elements; unpublished results). Holliday (1987) has thus postulated that such morphological variation is due to heritable modification of germline DNA. There is, however, no evidence of a high visible mutation rate in mouse inbred lines (Johnson et al, 1981). It may thus be that the factors promoting line divergence do not always lead to emergence of visible and detectable mutations, as if only some particular regions of the chromosomes were concerned.
Our inbreeding model fits the data on heterosis as well, with fitness values being correlated with the number of interacting sites (Bi6mont, 1974b(Bi6mont, , 1980Biémont et al, 1974). The more the lines diverge the higher the number of interactions resulting from their crossing: a high value of fitness of the hybrid should result. Because many interacting sites are concerned, crossing sibs of such hybrids should lead to a strong inbreeding depression, as experimentally observed (Falconer, 1981).
Such processes recall a heterosis model of self-incompatibility based on prezygotic expression of genetic load mediated through pollen-style interactions determined by the genotype of the 2 parents (Mulcahy and Mulcahy, 1983).
A mathematical analysis of the interaction system has been developed with sib matings (Bi6mont, 1974b(Bi6mont, , 1980Bi6mont et al, 1974). This probabilistic approach gives the tendencies for inbreeding depression, measured by the viability value, with generations of inbreeding; the tendencies are compatible with the experimental observations: a deleterious effect of inbreeding is usually observed which can even lead to line extinction, depending on the values of the model parameters. It has been observed that inbreeding depression generally decreases with generations and leads to stable lines (King, 1918;Wright, 1922a,b;Wright and Heaton, 1922;Hyde, 1924;Petit, 1963;Ootmersen, 1970;Legay, 1971;Kosuda, 1972). This asymptotic value could correspond to the &dquo;inbred minimum&dquo; reported by King (1918) in certain species of rodents. Beneficial or neutral effects can also be obtained with the model, as sometimes experimentally reported (Castle and Carpentier, 1906;Rasmusson, 1951;Lints, 1961). One problem with our model is that it requires spontaneous changes in state (active/inactive) with a higher rate than that usual for mutations.
This problem now seems to be overcome since processes such as transposition of mobile elements have a rate in the order of 10-3 or even more, and it appears quite reasonable that change in methylation pattern may be modified with an elevated rate, at least under some conditions. For example, Mu elements in maize may become modified after self-pollination (Chandler and Walbot, 1986) or inbreeding of mutator stocks (stocks with high rate of mutations and presence of active Mu transposons) (Bennetzen, 1987;Bennetzen et al, 1988), and such modifications are correlated with lack of activity (Chandler et al, 1988). CONCLUSION It is clear that the kind of interactions between the 2 chromosomal complements is one of the numerous facts in genome structuring and functioning that population genetics should take into account in the near future. Even so, as stated by Lewontin (1985), the existence of such phenomena does not in itself guarantee their importance to population genetic considerations, although a recent mathematical approach tends to demonstrate the potential population genetic consequences of molecular imprinting: apparent heterozygote deficiency and a concurrent hybrid vigor (Chakraborty, 1989). The knowledge of the fine structure of these phenomena may lead to the wish that, by changing the environmental and physiological conditions, they could be acted upon and their effects modified in some way; they would then become of considerable importance for population genetics, applied quantitative genetics and evolutionary biology.