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We introduce the gonosomal algebra. Gonosomal algebra extend the evolution
algebra of the bisexual population (EABP) defined by Ladra and Rozikov. We show
that gonosomal algebras can represent algebraically a wide variety of sex
determination systems observed in bisexual populations. We illustrate this by
about twenty genetic examples, most of these examples cannot be represented by
an EABP. We give seven algebraic constructions of gonosomal algebras, each is
illustrated by genetic examples. We show that unlike the EABP gonosomal
algebras are not dibaric. We approach the existence of dibaric function and
idempotent in gonosomal algebras.

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... In such systems the accompanying algebra will play the role of the sex differentiation algebra. Then an ACM will play the role of an evolution algebra of such biological systems (see [8,10,13,15,17,18] for different kinds of evolution algebras). ...

We consider algebras of
-cubic matrices (with
). Since there are several kinds of multiplications of cubic matrices, one has to specify a multiplication first and then define an algebra of cubic matrices (ACM) with respect to this multiplication. We mainly use the associative multiplications introduced by Maksimov. Such a multiplication depends on an associative binary operation on the set of size m. We introduce a notion of equivalent operations and show that such operations generate isomorphic ACMs. It is shown that an ACM is not baric. An ACM is commutative iff
. We introduce a notion of accompanying algebra (which is
-dimensional) and show that there is a homomorphism from any ACM to the accompanying algebra. We describe (left and right) symmetric operations and give left and right zero divisors of the corresponding ACMs. Moreover several subalgebras and ideals of an ACM are constructed.

In their work \cite{Rozikov.book.2016} U.A. Rozikov and R. Varro considered normalized gonosomal evolution operator $W:S^{2,2}\rightarrow{S^{2,2}}$ of sex linked inheritance. They proved the operator $W$ has a unique fixed point $s_0=(\frac{1}{2},0,\frac{1}{2},0)$ and there is an open neighborhood $\cup(s_0)\subset{S^{2,2}}$ of $s_0$ such that for any initial point $s\in{\cup(s_0)}$, the limit point of trajectories $\{W^{m}(s)\}$ tends to $s_0$. Moreover they made a conjecture for initial point $s\in{S^{2,2}}$. In this article we give a proof of that conjecture.

Consider a bisexual population such that the set of females can be
partitioned into finitely many different types indexed by $\{1,2,\dots,n\}$
and, similarly, that the male types are indexed by $\{1,2,\dots,\nu \}$.
Recently an evolution algebra of bisexual population was introduced by
identifying the coefficients of inheritance of a bisexual population as the
structure constants of the algebra. In this paper we study constrained
evolution algebra of bisexual population in which type ``1'' of females and
males have preference. For such algebras sets of idempotent and absolute
nilpotent elements are known. We consider two particular cases of this algebra,
giving more constrains on the structural constants of the algebra. By the first
our constrain we obtain an $n+\nu$- dimensional algebra with a matrix of
structural constants containing only 0 and 1. In the second case we consider
$n=\nu=2$ but with general constrains. In both cases we study dynamical systems
generated by the quadratic evolution operators of corresponding constrained
algebras. We find all fixed points, limit points and some 2-periodic points of
the dynamical systems. Moreover we study several properties of the constrained
algebras connecting them to the dynamical systems. We give some biological
interpretation of our results.

We consider an evolution algebra which corresponds to a bisexual population
with a set of females partitioned into finitely many different types and the
males having only one type. For such algebras in terms of its structure
constants we calculate right and plenary periods of generator elements. Some
results on subalgebras of EACP and ideals on low-dimensional EACP are obtained.

Here we give basic properties of dibaric algebras which are motivated by genetic models. Dibaric algebras are not associative and they have a non trivial homomorphism onto the sex differentiation algebra. We define first join of dibaric algebras next indecomposable dibaric algebras. Finally, we prove the uniqueness of the decomposition of a dibaric algebra, with semiprincipal idempotent, as the join of indecomposable dibaric algebras.

▪ Abstract Most metazoans engage in recombination every generation. In theory this is associated with considerable cost, such as the production of males, so that asexual organisms, which do not pay this cost, should be able to invade populations of sexuals. Some asexuals depend on sperm of sexual males to trigger embryogenesis, a reproductive mode called gynogenesis. The genetic information of males is typically not used. Theory predicts that such mating complexes are short-lived and highly unstable. Sperm dependency is not only the defining feature of the biology of gynogenetic metazoans, it is also a major puzzle in evolutionary biology. Organisms that apparently combine disadvantages of both sexuality and asexuality are a serious challenge to theory. A number of questions about these systems are still unresolved.

We find conditions on ideals of an algebra under which the algebra is
dibaric. Dibaric algebras have not non-zero homomorphisms to the set of the
real numbers. We introduce a concept of bq-homomorphism (which is given by two
linear maps $f, g$ of the algebra to the set of the real numbers) and show that
an algebra is dibaric if and only if it admits a non-zero bq-homomorphism.
Using the pair $(f,g)$ we define conservative algebras and establish criteria
for a dibaric algebra to be conservative. Moreover, the notions of a Bernstein
algebra and an algebra induced by a linear operator are introduced and
relations between these algebras are studied. For dibaric algebras we describe
a dibaric algebra homomorphism and study their properties by bq-homomorphisms
of the dibaric algebras. We apply the results to the (dibaric) evolution
algebra of a bisexual population. For this dibaric algebra we describe all
possible bq-homomorphisms and find conditions under which the algebra of a
bisexual population is induced by a linear operator. Moreover, some properties
of dibaric algebra homomorphisms of such algebras are studied.

Meiosis in triploids faces the seemingly insuperable difficulty of dividing an odd number of chromosome sets by two. Triploid vertebrates usually circumvent this problem through either asexuality or some forms of hybridogenesis, including meiotic hybridogenesis that involve a reproductive community of different ploidy levels and genome composition. Batura toads (Bufo baturae; 3n = 33 chromosomes), however, present an all-triploid sexual reproduction. This hybrid species has two genome copies carrying a nucleolus-organizing region (NOR+) on chromosome 6, and a third copy without it (NOR-). Males only produce haploid NOR+ sperm, while ova are diploid, containing one NOR+ and one NOR- set. Here, we conduct sibship analyses with co-dominant microsatellite markers so as (i) to confirm the purely clonal and maternal transmission of the NOR- set, and (ii) to demonstrate Mendelian segregation and recombination of the NOR+ sets in both sexes. This new reproductive mode in vertebrates ('pre-equalizing hybrid meiosis') offers an ideal opportunity to study the evolution of non-recombining genomes. Elucidating the mechanisms that allow simultaneous transmission of two genomes, one of Mendelian, the other of clonal inheritance, might shed light on the general processes that regulate meiosis in vertebrates.

The genus Corbicula is one of the most invasive groups of molluscs. It includes both sexual and androgenetic lineages. The present study re-assessed the different morphotypes and haplotypes of West European Corbicula in order to clarify their taxonomic identification and phylogenetic relationships with American and Asian Corbicula clams. We studied several populations from West European river basins (Meuse, Seine, Rhine and Rhône) through an "integrative taxonomy" approach. We combined morphology, partial mitochondrial COI and cyt b sequences and eleven microsatellite loci. Furthermore, we looked for discrepancies between mtDNA and nrDNA/morphology, indicative of androgenesis between lineages.
There are three Corbicula morphotypes in Western Europe associated to three mitochondrial lineages and three genotypes. Form R shares the same COI haplotype as the American form A and the Japanese C. leana. Form S and the American form C have the same haplotype, although their morphologies seem divergent. The European form Rlc belongs to the same mitochondrial lineage as both the American form B and the Asian C. fluminea.Interestingly, within each haplotype/genotype or lineage, no genetic diversity was found although their invasive success is high. Moreover, we detected rare mismatches between mtDNA and nrDNA/morphology, indicative of androgenesis and mitochondrial capture between form R and form S and therefore challenging the phylogenetic relatedness and the species status within this genus. The global phylogenetic analysis revealed that the sexual Corbicula lineages seem restricted to the native areas while their androgenetic relatives are widespread and highly invasive.
We clarified the discrepancies and incongruent results found in the literature about the European morphotypes of Corbicula and associated mitochondrial lineages. The three West European morphotypes belong to three distinct nuclear and mitochondrial lineages. However mitochondrial capture occurs in sympatric populations of forms R and S. The species status of the morphotypes therefore remains doubtful. Moreover the androgenetic lineages seem widely distributed compared to their sexual relatives, suggesting that androgenesis and invasive success may be linked in the genus Corbicula.

Therian mammals have an extremely conserved XX/XY sex determination system. A limited number of mammal species have, however, evolved to escape convention and present aberrant sex chromosome complements. In this study, we identified a new case of atypical sex determination in the African pygmy mouse Mus minutoides, a close evolutionary relative of the house mouse. The pygmy mouse is characterized by a very high proportion of XY females (74%, n = 27) from geographically widespread Southern and Eastern African populations. Sequencing of the high mobility group domain of the mammalian sex determining gene Sry, and karyological analyses using fluorescence in situ hybridization and G-banding data, suggest that the sex reversal is most probably not owing to a mutation of Sry, but rather to a chromosomal rearrangement on the X chromosome. In effect, two morphologically different X chromosomes were identified, one of which, designated X*, is invariably associated with sex-reversed females. The asterisk designates the still unknown mutation converting X*Y individuals into females. Although relatively still unexplored, such an atypical sex chromosome system offers a unique opportunity to unravel new genetic interactions involved in the initiation of sex determination in mammals.

Genomic imprinting affects several dozen mammalian genes and results in
the expression of those genes from only one of the two parental chromosomes.
This is brought about by epigenetic instructions — imprints —
that are laid down in the parental germ cells. Imprinting is a particularly
important genetic mechanism in mammals, and is thought to influence the transfer
of nutrients to the fetus and the newborn from the mother. Consistent with
this view is the fact that imprinted genes tend to affect growth in the womb
and behaviour after birth. Aberrant imprinting disturbs development and is
the cause of various disease syndromes. The study of imprinting also provides
new insights into epigenetic gene modification during development.

The Arvicolidae is a widely distributed rodent group with several interesting characteristics in their sex chromosomes. Here, we summarize the actual knowledge of some of these characteristics. This mammalian group has species with abnormal sex determination systems. In fact, some species present the same karyotype in both males and females, with total absence of a Y chromosome, and hence of SRY and ZFY genes. Other species present fertile, sex-reversed XY females, generally due to mutations affecting X chromosomes. Furthermore, in Microtus oregoni males and females are gonosomic mosaic (the females are XO in the soma and XX in the germ cells, while the males are XY in the soma and OY in the germ cells). Regarding sex chromosomes, some species present enlarged (giant) sex chromosomes because of the presence of large blocks of constitutive heterochromatin, which have been demonstrated to be highly heterogeneous. Furthermore, we also consider the alterations affecting composition and localization of sex-linked genes or repeated sequences. Finally, this rodent group includes species with synaptic and asynaptic sex chromosomes. In fact, several species with asynaptic sex chromosomes have been described. It is interesting to note that within the genus Microtus both types of sex chromosomes are present.

Wolbachia are intracellular maternally inherited alpha-Proteobacteria infecting a wide range of arthropods. In the common pill bug Armadillidium vulgare, the known Wolbachia strain is responsible for feminization of genetic males. We have investigated Wolbachia diversity in 20 populations of A. vulgare from west and east Europe, north Africa and north America. A new Wolbachia strain (wVulM) was identified through the variability of the wsp gene, distantly related to that previously known (wVulC) in this host species. No individual with multiple infections was detected. Inoculation experiments indicated that the new wVulM bacterial strain also induces feminization in A. vulgare. However, the wVulC strain showed a higher transmission rate than the wVulM strain and was the most geographically widespread Wolbachia in A. vulgare populations. Mitochondrial 16SrDNA gene sequencing was conducted in Wolbachia-infected individuals, revealing the occurrence of four host lineages. The comparison of bacterial strains and their respective host mitochondrial phylogenies failed to show concordance, indicating horizontal transmission of the Wolbachia strains within populations of A. vulgare.

The aim of the present study was to determine whether the effects of sex-ratio segregation distorters on the fertility of male Drosophila simulans can explain the contrasting success of these X-linked meiotic drivers in different populations of the species. We compared the fertility of sex-ratio and wild-type males under different mating conditions. Both types were found to be equally fertile when mating was allowed, with two females per male, during the whole period of egg laying. By contrast sex-ratio males suffered a strong fertility disadvantage when they were offered multiple mates for a limited time, or in sperm competition conditions. In the latter case only, the toll on male fertility exceeded the segregation advantage of the distorters. These results indicate that sex-ratio distorters can either spread or disappear from populations, depending on the mating rate. Population density is therefore expected to play a major role in the evolution of sex-ratio distorters in this Drosophila species.

To persist, unisexual and asexual eukaryotes must have reproductive modes that circumvent normal bisexual reproduction. Parthenogenesis, gynogenesis, and hybridogenesis are the modes that have generally been ascribed to various unisexuals. Unisexual Ambystoma are abundant around the Great Lakes region of North America, and have variously been described as having all 3 reproductive modes. Diploid and polyploid unisexuals have nuclear genomes that combine the haploid genomes of 2 to 4 distinct sexual species, but the mtDNA is unlike any of those 4 species and is similar to another species, Ambystoma barbouri. To obtain better resolution of the reproductive mode used by unisexual Ambystoma and to explore the relationship of A. barbouri to the unisexuals, we sequenced the mitochondrial control and highly variable intergenic spacer region of 48 ambystomatids, which included 28 unisexuals, representatives of the 4 sexual species and A. barbouri. The unisexuals have similar sequences over most of their range, and form a close sister group to A. barbouri, with an estimated time of divergence of 2.4-3.9 million years ago. Individuals from the Lake Erie Islands (Kelleys, Pelee, North Bass) have a haplotype that demonstrates an isolation event. We examined highly variable microsatellite loci, and found that the genetic makeup of the unisexuals is highly variable and that unisexual individuals share microsatellite alleles with sexual individuals within populations. Although many progeny from the same female had the same genotype for 5 microsatellite DNA loci, there was no indication that any particular genome is consistently inherited in a clonal fashion in a population. The reproductive mode used by unisexual Ambystoma appears to be unique; we suggest kleptogenesis as a new unisexual reproductive mode that is used by these salamanders.

Multiple sex-determining factors have been found in natural populations of the housefly, Musca domestica. Their distribution seems to follow a geographical cline. The 'standard' system, with a male-determining factor, M, located on the Y chromosome, prevails at higher latitudes and altitudes. At lower latitudes and altitudes M factors have also been found on any of the five autosomes. Such populations often also harbour a dominant autosomal factor, FD, which induces female development even in the presence of several M factors. Autosomal M factors were first observed some 50 years ago. It has been hypothesized that following their initial appearance, they are spreading northwards, replacing the standard XY system, but this has never been systematically investigated. To scrutinize this hypothesis, we here compare the current distribution of autosomal M factors in continental Europe, on a transect running from Germany to southern Italy, with the distribution reported 25 years ago. Additionally, we analysed the frequencies of the FD factor, which has not been done before for European populations. In contrast to earlier predictions, we do not find a clear change in the distribution of sex-determining factors: as 25 years ago, only the standard XY system is present in the north, while autosomal M factors and the FD factor are prevalent in Italy. We discuss possible causes for this apparently stable polymorphism.

The purpose of these notes is to give a rather complete presentation of the mathematical theory of algebras in genetics and to discuss in detail many applications to concrete genetic situations. Historically, the subject has its origin in several papers of Etherington in 1939- 1941. Fundamental contributions have been given by Schafer, Gonshor, Holgate, Reiers¢l, Heuch, and Abraham. At the moment there exist about forty papers in this field, one survey article by Monique Bertrand from 1966 based on four papers of Etherington, a paper by Schafer and Gonshor's first paper. Furthermore Ballonoff in the third section of his book "Genetics and Social Structure" has included four papers by Etherington and Reiers¢l's paper. Apparently a complete review, in par ticular one comprising more recent results was lacking, and it was difficult for students to enter this field of research. I started to write these notes in spring 1978. A first german version was finished at the end of that year. Further revision and translation required another year. I hope that the notes in their present state provide a reasonable review and that they will facilitate access to this field. I am especially grateful to Professor K. -P. Hadeler and Professor P. Holgate for reading the manuscript and giving essential comments to all versions of the text. I am also very grateful to Dr. I. Heuch for many discussions during and after his stay in TUbingen. I wish to thank Dr. V. M.

We consider an evolution algebra which corresponds to a bisexual population with a set of females partitioned into finitely many different types and the males having only one type. We study basic properties of the algebra. This algebra is commutative (and hence flexible), not associative and not necessarily power-associative, in general. We prove that being alternative is equivalent to being associative. We find conditions to be an associative, a fourth power-associative, or a nilpotent algebra. We also prove that if the algebra is not alternative then to be power-associative is equivalent to be Jordan. Moreover it is not unital. In a general case, we describe the full set of idempotent elements and the full set of absolute nilpotent elements. The set of all operators of left (right) multiplications is described. Under some conditions it is proved that the corresponding algebra is centroidal. Moreover the classification of 2-dimensional and some 3-dimensional algebras are obtained.

A model is shown accounting for differences between males and females regarding both recombination and mutation rates at two-linked autosomal loci; males and females are supposed to mate at random. A canonical basis and the train roots of the genetic algebra which constitutes the model have been determined; it is pointed out that such a zygotic algebra is not a special train algebra. Additionally, an operative procedure for finding out the idempotents of the algebra is developed.

The zygotic algebra 3 for a finite number of sex-linked characters with arbitrary segregation rates is defined in two equivalent ways. A sufficient condition for the existence and uniqueness of non-trivial idempotents in a baric ideal B of 3 is given. A convergence theorem for the sequence of plenary powers of elements of B of unit weight is proved. In the case of Mendelian segregation in the male sex the conditions for uniqueness of idempotents and for convergence are the same for symmetric inheritance and sex-linked inheritance. The special cases of Mendelian and additive segregation rates in the females are discussed in greater detail.

Etherington introduced certain algebraic methods into the study of population genetics ( 6 ). It was noted that algebras arising in genetic systems tend to have certain abstract properties and that these can be used to give elegant proofs of some classical stability theorems in population genetics ( 4 , 5 , 9 , 10 ).

Ever since Mendel promulgated his famous laws, probability theory and statistics have played an important role in the study of heredity (9). Etherington introduced some concepts of modern algebra when he showed how a nonassociative algebra can be made to correspond to a given genetic system (1, 4). The fact that many of these algebras have common properties has led to their study from a purely abstract point of view (2, 3, 5, 6, 11, 12). Furthermore, the techniques of algebra give new ways of attacking problems in genetics such as that of stability.

Most work in genetic algebras has been concerned with inheritance which is symmetric with respect to sex, in that the characters studied are determined by genes located at autosomal loci, and it is assumed that the segregation pattern is the same in males and females. When asymmetric situations are studied, the development of the theory is complicated by the higher dimensions of the algebras, and by a feature to which Etherington (3, p. 40) drew attention, namely the fact that the passage from the gametic to the zygotic algebra no longer quite corresponds to the process of duplication, as it does in the symmetric case. Etherington gave some results for the gametic and zygotic algebras of a single sex linked diallelic locus, and its properties were discussed further by Gonshor (4, p. 44). In a second paper (5, p. 334) Gonshor studied sex linkage in the case of multiple alleles, choosing a canonical basis which exhibited very clearly the multiplication table and ideal structure of the algebra. His treatment from the statement of the multiplication table in terms of the natural basis to its expression in terms of a canonical basis, is repeated in the displayed relations (4)–(8) below, for completeness and to establish the present notation.(Received August 02 1969)

We shall extend some of the results of (7) to the case of multiple alleles, our primary concern being that of polyploidy combined with multiple alleles. Generalisations often tend to make the computations more involved as is expected. Fortunately here, the attempt to generalise has led to a new method which not only handles the case of multiple alleles, but is an improvement over the method used in (7) for the special case of polyploidy with two alleles. This method which consists essentially of expressing certain elements of the algebra in a so-called “ factored ” form, gives greater insight into the structure of a polyploidy algebra, and avoids a great deal of the computation with binomial coefficients, e.g. see (7), p. 46.

Ciliates are a diverse group of microbial eukaryotes that exhibit tremendous variety in several aspects of their mating systems. To understand the evolutionary forces driving mating system diversification in ciliates, we use a comparative approach synthesizing data from many ciliate species in light of recent phylogenetic analyses. Specifically, we investigate the evolution of number of mating types, mode of mating type inheritance, and the molecular determinants of mating types across the taxonomic diversity of ciliates, with an emphasis on three well-studied genera: Tetrahymena, Paramecium, and Euplotes. We find that there have been many transitions in the number of mating types, and that the requirement of nuclear reorganization may be a more important factor than genetic exchange in determining the optimum number of mating types in a species. We also find that the molecular determinants of mating types and mode of inheritance are evolving under different constraints in different lineages of ciliates. Our results emphasize the need for further detailed examination of mating systems in understudied ciliate lineages. © 2009 The Linnean Society of London, Biological Journal of the Linnean Society, 2009, 98, 187–197.

The joint allele frequency distribution is studied for any number of partially and completely sex-linked loci in an infinite population. The model assumes random mating and no selection or mutation, but includes arbitrary linkage distributions. The mathematical treatment is simplified by means of differential operators applied to elements in a linear algebra. Procedures are given which lead to explicit expressions for the frequencies after n generations. It is shown that the alleles at different loci are randomly distributed when nx.

The zygotic algebra for sex linkage with multiple alleles contains an idealB which is a baric algebra. This ideal possesses at least one idempotent with non negative coefficients. For the mutation case
and the case of simple Mendelian inheritance in the female sex convergence theorems are proved for the sequence of plenary
powers of a normalized element. For these two cases it is shown that the idealB is a special train algebra.

In this section we provide a short introduction to “algebras in genetics”. We explain how algebras arise in population genetics and we construct some examples of gametic algebras. These examples will be reconsidered and discussed in a wider frame-work in section 7. We introduce zygotic and copular algebras and we discuss the construction of these algebras from gametic algebras. The exposition will reveal various elementary though fundamental properties of these algebras.

We introduce an (evolution) algebra identifying the coefficients of inheritance of a bisexual population as the structure constants of the algebra. The basic properties of the algebra are studied. We prove that this algebra is commutative (and hence flexible), not associative and not necessarily power associative. We show that the evolution algebra of the bisexual population is not a baric algebra, but a dibaric algebra and hence its square is baric. Moreover, we show that the algebra is a Banach algebra. The set of all derivations of the evolution algebra is described. We find necessary conditions for a state of the population to be a fixed point or a zero point of the evolution operator which corresponds to the evolution algebra. We also establish upper estimate of the limit points set for trajectories of the evolution operator. Using the necessary conditions we give a detailed analysis of a special case of the evolution algebra (bisexual population of which has a preference on type "1" of females and males). For such a special case we describe the full set of idempotent elements and the full set of absolute nilpotent elements. Comment: 21 pages

Parthenogenesis is a phenomenon of undoubted biological interest which leads to the production of living young in many types of animals, as well as in plants. White (1977) has estimated that the proportion of animal 'species' which reproduce exclusively by parthenogenesis, and are therefore all female, is of the order of one in a thousand. Parthenogenesis may initiate early embryonic development in mammals, and its lack of success in this class poses some fundamental and as yet unresolved problems regarding the significance of fertilisation in the physiology of reproduction and embryonic development. Spontaneous and induced parthenogenesis in various species are reviewed in this article.

A general problem in evolutionary biology is that quantitative tests of theory usually require a detailed knowledge of the underlying trade-offs, which can be very hard to measure. Consequently, tests of theory are often constrained to be qualitative and not quantitative. A solution to this problem can arise when life histories are viewed in a dimensionless way. Recently, dimensionless theory has been developed to predict the size and age at which individuals should change sex. This theory predicts that the size at sex change/maximum size (L50/L(max)), and the age at sex change/age at first breeding (tau/alpha) should both be invariant. We found support for these two predictions across 52 species of fish. Fish change sex when they are 80% of their maximum body size, and 2.5 times their age at maturity. This invariant result holds despite a 60 and 25 fold difference across species in maximum size and age at sex change. These results suggest that, despite ignoring many biological complexities, relatively simple evolutionary theory is able to explain quantitatively at what point sex change occurs across fish species. Furthermore, our results suggest some very broad generalities in how male fitness varies with size and age across fish species with different mating systems.

In fish, an amazing variety of sex determination mechanisms are known, ranging from hermaphroditism to gonochorism and from environmental to genetic sex determination. This makes fish especially suited for studying sex determination from the evolutionary point of view. In several fish groups, different sex determination mechanisms are found in closely related species, and evolution of this process is still ongoing in recent organisms. The medaka (Oryzias latipes) has an XY-XX genetic sex determination system. The Y-chromosome in this species is at an early stage of evolution. The molecular differences between X and Y are only very subtle and the Y-specific segment is very small. The sex-determining region has accumulated duplicated sequences from elsewhere in the genome, leading to recombinational isolation. The region contains a candidate for the male sex-determining gene named dmrt1bY. This gene arose through duplication of an autosomal chromosome fragment of linkage group 9. While all other genes degenerated, dmrt1bY is the only functional gene in the Y-specific region. The duplication leading to dmrt1bY occurred recently during evolution of the genus Oryzias. This suggests that different genes might be the master sex-determining gene in other fish.

- M Ladra
- B A Omirov
- U A Rozikov

M. Ladra, B. A. Omirov and U. A. Rozikov. On dibaric and evolution algebras. arXiv:1104.2578v1 (13
Apr 2011).