Loci under balancing selection facilitate the emergence of pseudo-overdominance and recombination suppression

Loci under balancing selection facilitate the emergence of pseudo-overdominance and recombination suppression | bioRxiv /* */ /* */ <!-- <!-- /*! * yepnope1.5.4 * (c) WTFPL, GPLv2 */ (function(a,b,c){function d(a){return"[object Function]"==o.call(a)}function e(a){return"string"==typeof a}function f(){}function g(a){return!a||"loaded"==a||"complete"==a||"uninitialized"==a}function h(){var a=p.shift();q=1,a?a.t?m(function(){("c"==a.t?B.injectCss:B.injectJs)(a.s,0,a.a,a.x,a.e,1)},0):(a(),h()):q=0}function i(a,c,d,e,f,i,j){function k(b){if(!o&&g(l.readyState)&&(u.r=o=1,!q&&h(),l.onload=l.onreadystatechange=null,b)){"img"!=a&&m(function(){t.removeChild(l)},50);for(var d in y[c])y[c].hasOwnProperty(d)&&y[c][d].onload()}}var j=j||B.errorTimeout,l=b.createElement(a),o=0,r=0,u={t:d,s:c,e:f,a:i,x:j};1===y[c]&&(r=1,y[c]=[]),"object"==a?l.data=c:(l.src=c,l.type=a),l.width=l.height="0",l.onerror=l.onload=l.onreadystatechange=function(){k.call(this,r)},p.splice(e,0,u),"img"!=a&&(r||2===y[c]?(t.insertBefore(l,s?null:n),m(k,j)):y[c].push(l))}function j(a,b,c,d,f){return q=0,b=b||"j",e(a)?i("c"==b?v:u,a,b,this.i++,c,d,f):(p.splice(this.i++,0,a),1==p.length&&h()),this}function k(){var a=B;return a.loader={load:j,i:0},a}var l=b.documentElement,m=a.setTimeout,n=b.getElementsByTagName("script")[0],o={}.toString,p=[],q=0,r="MozAppearance"in l.style,s=r&&!!b.createRange().compareNode,t=s?l:n.parentNode,l=a.opera&&"[object Opera]"==o.call(a.opera),l=!!b.attachEvent&&!l,u=r?"object":l?"script":"img",v=l?"script":u,w=Array.isArray||function(a){return"[object Array]"==o.call(a)},x=[],y={},z={timeout:function(a,b){return b.length&&(a.timeout=b[0]),a}},A,B;B=function(a){function b(a){var a=a.split("!"),b=x.length,c=a.pop(),d=a.length,c={url:c,origUrl:c,prefixes:a},e,f,g;for(f=0;f<d;f++)g=a[f].split("="),(e=z[g.shift()])&&(c=e(c,g));for(f=0;f<b;f++)c=x[f](c);return c}function g(a,e,f,g,h){var i=b(a),j=i.autoCallback;i.url.split(".").pop().split("?").shift(),i.bypass||(e&&(e=d(e)?e:e[a]||e[g]||e[a.split("/").pop().split("?")[0]]),i.instead?i.instead(a,e,f,g,h):(y[i.url]?i.noexec=!0:y[i.url]=1,f.load(i.url,i.forceCSS||!i.forceJS&&"css"==i.url.split(".").pop().split("?").shift()?"c":c,i.noexec,i.attrs,i.timeout),(d(e)||d(j))&&f.load(function(){k(),e&&e(i.origUrl,h,g),j&&j(i.origUrl,h,g),y[i.url]=2})))}function h(a,b){function c(a,c){if(a){if(e(a))c||(j=function(){var a=[].slice.call(arguments);k.apply(this,a),l()}),g(a,j,b,0,h);else if(Object(a)===a)for(n in m=function(){var b=0,c;for(c in a)a.hasOwnProperty(c)&&b++;return b}(),a)a.hasOwnProperty(n)&&(!c&&!--m&&(d(j)?j=function(){var a=[].slice.call(arguments);k.apply(this,a),l()}:j[n]=function(a){return function(){var b=[].slice.call(arguments);a&&a.apply(this,b),l()}}(k[n])),g(a[n],j,b,n,h))}else!c&&l()}var h=!!a.test,i=a.load||a.both,j=a.callback||f,k=j,l=a.complete||f,m,n;c(h?a.yep:a.nope,!!i),i&&c(i)}var i,j,l=this.yepnope.loader;if(e(a))g(a,0,l,0);else if(w(a))for(i=0;i (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0];var j=d.createElement(s);var dl=l!='dataLayer'?'&l='+l:'';j.src='//www.googletagmanager.com/gtm.js?id='+i+dl;j.type='text/javascript';j.async=true;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-M677548'); Skip to main content Home About Submit ALERTS / RSS Search for this keyword Advanced Search New Results Loci under balancing selection facilitate the emergence of pseudo-overdominance and recombination suppression Lou Guyot , Tatiana Giraud , View ORCID Profile Paul Jay doi: https://doi.org/10.1101/2025.06.19.660549 Lou Guyot 1 Master de Biologie, Ecole Normale Supérieure de Lyon, Université Claude Bernard Lyon 1, Université de Lyon , 69342 Lyon Cedex 07, France 2 Ecologie, Société et Evolution, CNRS, Universite Paris-Saclay, AgroParisTech , Gif-sur-Yvette, France 3 Laboratoire d’Ecologie Alpine, CNRS, Univ. Grenoble Alpes, Univ. Savoie Mont Blanc , 38000 Grenoble, France Find this author on Google Scholar Find this author on PubMed Search for this author on this site For correspondence: lou.guyot{at}ens-lyon.fr Tatiana Giraud 2 Ecologie, Société et Evolution, CNRS, Universite Paris-Saclay, AgroParisTech , Gif-sur-Yvette, France Find this author on Google Scholar Find this author on PubMed Search for this author on this site Paul Jay 3 Laboratoire d’Ecologie Alpine, CNRS, Univ. Grenoble Alpes, Univ. Savoie Mont Blanc , 38000 Grenoble, France Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Paul Jay Abstract Full Text Info/History Metrics Preview PDF Abstract Loci under strong balancing selection, such as sex-determining, mating-type, and self-incompatibility loci, are frequently flanked by regions of suppressed recombination. The reasons why recombination suppression evolves around these loci remain poorly understood. Here, we propose that one reason may be that loci under balancing selection facilitate the emergence of pseudo-overdominance—a phenomenon under which linked recessive deleterious mutations in repulsion mimic overdominance. Pseudo-overdominance arises when linkage disequilibrium gradually builds up between recessive deleterious mutations, often due to strong genetic linkage and genetic drift. Once complementary haplotypes form, homozygous and recombinant offspring are selected against because they carry homozygous recessive deleterious mutations. Using individual-based simulations, we demonstrate here that the presence of loci under balancing selection eases the establishment of pseudo-overdominance, by facilitating the maintenance of recessive deleterious mutations and linkage disequilibrium in their flanking regions. We further show that, under some conditions, such resulting pseudo-overdominant zones can ultimately lead to selection for crossing-over suppression around permanently heterozygous loci, preventing the creation of unfit homozygous recombinant offspring. These results suggest new avenues for understanding the evolution of loci under balancing selection, sex chromosomes and supergenes, and shed new light on mechanisms driving genome evolution. Introduction Recombination is fundamental in evolution as it generates new allelic combinations upon which selection can act. Yet, in many genomic regions, recombination is suppressed, either entirely or between some haplotypes ( Dapper and Payseur 2017 ; Stapley et al. 2017 ; Peñalba and Wolf 2020 ; Schwander, Libbrecht, and Keller 2014 ). Textbook examples include sex chromosomes, mating-type chromosomes, self-incompatibility loci, as well as many supergenes in which recombination is inhibited between alternative haplotypes ( Vittorelli et al. 2023 ; Hartmann et al. 2021 ; B. Charlesworth 1991 ; D. Charlesworth 2017 ; 2016 ; Schwander, Libbrecht, and Keller 2014 ). Beyond these well-known cases, many other genomic regions—for example, the major histocompatibility complex in mammals ( Yoo et al. 2025 )—also exhibit unusual recombination patterns, such as the presence of specific hotspots of recombination separated by non-recombining regions ( Jeffreys, Kauppi, and Neumann 2001 ). Besides the absence of recombination, another common feature of these regions is the maintenance of high genetic diversity through some form of balancing selection ( Jay et al. 2021 ; Küpper et al. 2016 ; Kamau and Charlesworth 2005 ; Hartmann et al. 2021 ; Carey et al. 2021 ; Le Veve et al. 2023 ). Why recombination suppression evolves in these regions, whether the same forces are involved, and whether it is linked to their specific selective pressures remain long-standing questions in evolutionary biology ( Wright et al. 2016 ; Jay et al. 2024 ; Ponnikas et al. 2018 ). For sex chromosomes, it has long been considered that recombination suppression evolves because it allows linkage between sex-determining loci and sexually antagonistic loci, i.e. loci with alleles that are beneficial in one sex but deleterious in the other (D. Charlesworth 2017 ; Rice 1987 ; Bergero and Charlesworth 2009 ; D. Charlesworth 2016 ; Flintham et al. 2025 ). A similar, more general scenario can be formulated for many supergenes and many other loci under balancing selection, where recombination suppression would evolve to preserve beneficial combinations of co-adapted alleles at epistatic loci ( Schwander, Libbrecht, and Keller 2014 ; Hartmann et al. 2021 ; Jay, Aubier, and Joron 2024 ; see also Kirkpatrick and Barton 2006 for non-epistatic loci). Because of its simplicity and inherent logic, this model is appealing. Yet, decades of research on sex chromosomes have provided limited empirical support for the sexual antagonism hypothesis ( Ponnikas et al. 2018 ; Wright et al. 2017 ; Beukeboom et al. 2014 ; Wright et al. 2016 ; Jay et al. 2024 ). More importantly, this model cannot account for the progressive recombination suppression observed around fungal mating-type loci, as no form of antagonistic selection exists between mating types ( Bazzicalupo et al. 2019 ; Fraser et al. 2004 ; Branco et al. 2017 ; Hartmann et al. 2021 ; Jay et al. 2024 ). This highlights the need to consider alternative mechanisms that could drive the evolution of recombination suppression on sex chromosomes and other genomic regions ( Lenormand and Roze 2022 ; Jeffries et al. 2021 ; Jay et al. 2024 ). Here, we propose that recombination suppression can evolve around some loci under balancing selection because this peculiar selective pressure could promote the emergence of a phenomenon known as pseudo-overdominance in nearby regions. Pseudo-overdominance refers to the apparent overdominance of a locus or group of loci caused by their linkage disequilibrium with clusters of sites with deleterious recessive mutations arranged in repulsion, e.g., one haplotype with +−+− and the other with −+−+, with + being wild-type alleles and – recessive deleterious mutations ( Ohta and Kimura 1969 ; Waller 2021 ; Gilbert et al. 2020 ; Abu-Awad and Waller 2023 ). This configuration creates complementary haplotypes, carrying different recessive deleterious alleles, such that homozygotes for these haplotypes suffer a strong fitness disadvantage while heterozygotes have their load sheltered to some extent. As a result, heterozygotes are favoured and each site with a deleterious mutation behaves as if it was overdominant, so that genetic diversity is maintained at high levels within these “pseudo-overdominant zones”. Although crossing-overs are not necessarily physically suppressed in regions of pseudo-overdominance, recombinant haplotypes incur a fitness cost. This is because individuals with recombinant haplotypes tend to be homozygous for numerous deleterious mutations, due to the disruption of haplotype complementation. As a result, the recombination rate is de facto reduced in these regions, not by crossing-over suppression but by strong selection against recombinants. This might eventually select for mechanisms suppressing crossing-overs, such as chromosomal inversions, that would prevent the formation of unfit progeny. The occurrence of pseudo-overdominance depends on the buildup of linkage disequilibrium between recessive deleterious mutations, typically driven by genetic linkage and drift ( Ohta and Kimura 1969 ; Waller 2021 ; Gilbert et al. 2020 ; Abu-Awad and Waller 2023 ). Theoretical works have shown that pseudo-overdominance is, as a result, more likely to arise in regions of low recombination rates, in species with small effective population sizes, under high mutation rates and when deleterious mutations are strongly recessive ( Ohta and Kimura 1969 ; Waller 2021 ; Gilbert et al. 2020 ; Abu-Awad and Waller 2023 ). More recent works have shown that higher ploidy, lower selfing rate and stronger population structure can also promote the evolution of pseudo-overdominance zones ( Booker and Schrider 2025 ; Abu-Awad and Waller 2023 ; Bierne, Tsitrone, and David 2000 ). While the existence of pseudo-overdominant zones essentially remains a theoretical prediction, empirical studies in natural populations have recently identified genomic regions characterized by both low recombination rates and high genetic diversity that may be shaped by pseudo-overdominance. Notable examples include centromeric regions, the MHC locus in humans, the region surrounding the mating-type locus in Sordariales fungi and the supergene controlling wing colour patterns in the butterfly Heliconius numata (van Oosterhout 2009 ; Gilbert et al. 2020 ; Jay et al. 2021 ; Guyot et al. 2025 ). Although this has been untested, it has been suggested that loci under balancing selection may promote the emergence of pseudo-overdominance zones ( Abu-Awad and Waller 2023 ). Indeed, loci under balancing selection are known to affect deleterious mutations dynamics around them, especially promoting the maintenance of deleterious mutations at an intermediate frequency ( Tezenas et al. 2023 ; Lenz et al. 2016 ; Glémin et al. 2001 ; Antonovics and Abrams 2004 ; Uyenoyama 2005 ; Leach, Mayo, and Morris 1986 ; Llaurens, Gonthier, and Billiard 2009 ) and likely promoting the formation of linkage blocks, although this has not been investigated to our knowledge. These processes may thus facilitate the evolution of pseudo-overdominance zones, i.e. the formation of complementary haplotypes carrying different sets of deleterious mutations in repulsion, which, in turn, could lead to selection against recombination. However, the conditions under which balancing selection favours the establishment of pseudo-overdominance zones remain unexplored. It also remains unknown whether pseudo-overdominance can select for crossing-over suppression around loci under balancing selection. Here, aiming at filling these gaps, we used multi-locus, individual-based simulations to investigate how, why and under what conditions pseudo-overdominance zones can emerge around loci under balancing selection. We modelled scenarios reflecting mating-type loci, sex-determining loci and overdominant loci. We first show that the segregating time and heterozygosity of recessive deleterious mutations is higher in their vicinity. Then, we show that such maintenance of recessive deleterious mutations around loci under balancing selection substantially broadens the range of parameter values under which pseudo-overdominant zones form. Finally, we show that, because pseudo-overdominance leads to reduced fitness of recombinant offspring, this can favour the evolution of crossing-over suppression on mating-type chromosomes and related architectures. Results Aiming at determining whether and how loci under balancing selection promote the establishment of pseudo-overdominance, we begin by focusing on a bi-allelic, permanently heterozygous locus—an extreme form of balancing selection, representative of systems such as mating-type loci in fungi. We then extend our analysis to other types of loci under balancing selection, i.e. to a sex-determining locus mimicking XY systems or ZW systems, and overdominant loci with various strengths of selection. Permanently heterozygous loci facilitate the maintenance of heterozygous recessive deleterious mutations in their flanking regions Because pseudo-overdominance relies on the presence of linked recessive deleterious mutations, we first explored in detail how the presence of bi-allelic permanently heterozygous loci affected the dynamics of such a mutation in their flanking regions. Using individual-based simulations, we introduced a single mutation at varying genetic distances from a permanently heterozygous locus in a population of 1000 individuals. As expected following previous studies ( Lenz et al. 2016 ; Glémin et al. 2001 ; Llaurens, Gonthier, and Billiard 2009 ; Tezenas et al. 2023 ), we found that mutations persisted longer when they were closer to the permanently heterozygous locus. For example, a recessive deleterious mutation with selective and dominance coefficients of s =-0.001 and h =0.1 is maintained about 40 times longer when at 1 × 10⁻⁶ cM to the permanently heterozygous locus than when totally unlinked to it, i.e., at 50 cM. We also found that mutations were maintained more frequently at the heterozygous state when they were closer to the permanently heterozygous locus ( Fig 1A , 1B ). For example, a recessive deleterious mutation with selective and dominance coefficients of s =-0.001 and h =0.1 has about a 100 times higher excess of heterozygosity when at 1 × 10⁻⁶ cM to the permanently heterozygous locus than when totally unlink to it, i.e., at 50 cM. Additionally, as expected, the less deleterious and the more recessive a mutation was, the longer it persisted and remained in the heterozygous state. Such peculiar dynamics of deleterious mutations around permanently heterozygous loci should facilitate the build-up of a cluster of multiple deleterious alleles in repulsion and thus promote the establishment of pseudo-overdominance. Download figure Open in new tab Figure 1: Mutation dynamics as a function of their distance from a permanently heterozygous locus. A) Mean mutation segregating time as a function of their distance from a permanently heterozygous locus. Mean segregating time for 40,000 mutations introduced individually at a distance ranging from 1 × 10⁻⁶ to 50 cM of a permanently heterozygous locus, for various selection and dominance coefficients. B) Excess of heterozygosity as a function of mutation distance from a permanently heterozygous locus. Mean deviations of observed heterozygosity from Hardy-Weinberg equilibrium expectations (measured heterozygosity minus 2 f (1–f), with f being the mutation frequency) over the course of the mutation lifetime, averaged for 40,000 mutations introduced individually at a distance ranging from 1 × 10⁻⁶ to 50 cM of a permanently heterozygous locus, under various selection and dominance coefficients. Simulations were halted at generation 100,000 in cases where the mutation had not yet been fixed or been lost. Permanently heterozygous loci favour pseudo-overdominance To test whether pseudo-overdominance is in fact favoured around permanently heterozygous loci, we conducted individual-based simulations under a Wright-Fisher model, tracking the evolution of a panmictic population of diploid individuals during 100,000 generations. Each individual had a single chromosome, subjected to recombination and mutation, carrying in its centre a bi-allelic permanently heterozygous locus. For the purpose of illustration, we first focused on a single set of parameter values, with a population of size N =1000 individuals, a recombination rate r =1 × 10⁻⁹ events per base pair per generation, a mutation rate µ =1 × 10⁻⁸ mutations per base pair per generation, a selective coefficient of mutations s =-0.04 and a dominance coefficient h =0.3. We then also conducted sets of simulations i) with only neutral mutations ( s =0), as a control to assess the influence of selection, and ii) without any permanently heterozygous locus, as a control to assess the influence of this type of locus on pseudo-overdominance establishment. In simulations with a permanently heterozygous locus and deleterious mutations, the mean number of sites with derived mutations per individual steadily increased along generations, going from 0 to around 4000 in 100,000 generations ( Fig 2A ). The mean number of sites with derived mutations per individual peaked at the permanently heterozygous locus; the peak height and width increased along generations ( Fig 2B ), showing that deleterious, partially recessive mutations accumulated around the permanently heterozygous locus. The fraction of sites with heterozygous mutations in individuals also tended towards 1 along generations ( Fig 2C ), indicating that the deleterious mutations were mostly heterozygous. At generation 50,000, the chromosome showed an 8 Mb block of sites in strong linkage disequilibrium with each other around the permanently heterozygous locus ( Fig 2D ). Linkage disequilibrium was progressively established between the sites with deleterious mutations over generations, reaching 4000 sites in strong linkage disequilibrium in 100,000 generations ( Fig 2E ). Hierarchical clustering indicates the presence of two complementary haplotypes composed of recessive deleterious mutations arranged in repulsion ( Fig 2F ), i.e. the existence of a pseudo-overdominant zone. Download figure Open in new tab Figure 2: Dynamics of mutation accumulation with time and along the genome depending on their selective coefficient and the presence of a permanently heterozygous locus. Results from the evolution of a panmictic population during 100,000 generations under a Wright-Fisher model. Each individual is diploid with a 10 Mb chromosome containing a central permanently heterozygous locus in some cases. Simulations used a population size ( N ) of 1000, a recombination rate ( r ) of 1 × 10⁻⁹, a mutation rate ( µ ) of 1 × 10⁻⁸, and a dominance coefficient ( h ) of 0.3. A) Mutation accumulation over time. Mean number of sites with derived mutations per individual over generations, computed every 100 generations in 100 individuals across 1000 simulations, depending on the presence of a permanently heterozygous locus and the selective coefficients of mutations. Standard deviation is represented in grey. Y-axis in logarithmic scale. B) Recessive deleterious mutation accumulation around a permanently heterozygous locus. Mean number of sites with derived mutations along a chromosome measured in 100 individuals per segment of 10,000 bp in 1000 simulations with mutations with a selective coefficient of s =-0.04. The three lines represent the mean number of segregating mutations at three generations: 5000, 50000, and 100000. Standard deviation is represented. C) Percentage of heterozygosity in individuals over time. Mean percentage of heterozygous sites per individual (among sites with derived mutations in each individual) over generations, measured in 100 individuals every 100 generations in 1000 simulations, depending on the presence of a permanently heterozygous locus and the selective coefficients of mutations. Standard deviation is represented in grey. Y-axis in logarithmic scale. D) Linkage disequilibrium around a permanently heterozygous locus. Linkage disequilibrium map established from 100 genomes at generation 50000 with a mutation having a selective coefficient of s =-0.04 in the presence of a permanently heterozygous locus. E) Number of sites in linkage disequilibrium over generations. Number of sites in the largest cluster of sites in strong linkage disequilibrium (LD) with each other (r²>0.95) measured from 200 genomes every 1000 generations from 1000 simulations, depending on the presence of a permanently heterozygous locus and the selective coefficients of mutations. Standard deviation is represented in grey. Y-axis in logarithmic scale. F) Haplotype structure across polymorphic sites when deleterious mutations and a permanently heterozygous locus. Each row represents an individual haplotype and each column a polymorphic site. Colours indicate allele states (grey: ancestral allele, orange: derived allele). Haplotypes are clustered based on similarity using hierarchical clustering. In these simulations, recombination tended to generate individuals with lower fitness than average and this effect was stronger when the recombination event occurred closer to the permanently heterozygous locus ( Fig 3A ), as this led to offspring with a higher number of homozygous recessive deleterious mutations ( Fig 3B ). Because the number of deleterious mutations and sites in linkage disequilibrium increased along generations ( Fig 2A,E ), the mean fitness of offspring resulting from recombination decreased along generations ( Fig 3C ). The mean relative fitness of recombinant offspring went from 1 to around 0.1 in 100,000 generations and recombination events became lethal at generation 100,000 when occurring at less than 2.5 Mb to the permanently heterozygous locus; these recombination events indeed led to homozygosity for ca. 1000 mutations. A pseudo-overdominant zone (i.e. arrays of recessive deleterious mutations behaving as overdominant) can thus progressively form, be maintained and extend around a permanently heterozygous locus, despite recombination, which is effectively suppressed due to the death of recombinant offspring. Download figure Open in new tab Figure 3: Fitness cost of recombination across genome and over generations when pseudo-overdominance evolves. Results from 1000 simulations of the evolution of a panmictic population during 100,000 generations under a Wright-Fisher model. Each individual is diploid with 10 Mega bp chromosomes containing a central permanently heterozygous locus. Simulations used a population size ( N ) of 1000, a recombination rate ( r ) of 1 × 10⁻⁹, a mutation rate ( µ ) of 1 × 10⁻⁸, a dominance coefficient ( h ) of 0.3 and a selective coefficient ( s ) of −0.04. A) Mean relative fitness of individuals resulting from a single recombination event over generations, computed every 100 generations. B) Relative fitness of individuals resulting from a single recombination event according to the position of the recombination breakpoint, measured at generation 5001 and 100,001. Each dot represents a recombinant individual, and the curve represents the locally estimated scatterplot smoothing. C) Number of homozygous sites among sites with derived mutations in individuals resulting from a single recombination event according to the position of the recombination breakpoint computed at generation 5001 and 100,001. Each dot represents a recombinant individual, and the curve represents the locally estimated scatterplot smoothing. In contrast, our simulations with the same set of parameter values but without any permanently heterozygous locus and/or with only neutral mutations ( s =0) did not show such an accumulation of heterozygous mutations nor the formation of large blocks of sites in linkage disequilibrium ( Fig 2A,C,D ). The absence of accumulation of neutral mutation confirms that drift alone cannot explain the maintenance of such arrays of deleterious mutations, and therefore that selection plays a role in the formation of blocks of deleterious mutations in repulsion (i.e. pseudo-overdominant zone). The absence of mutation accumulation without any permanently heterozygous locus in these conditions further confirms that a permanently heterozygous locus promotes pseudo-overdominance establishment. Conditions for pseudo-overdominance establishment To explore further the impact of population genetics parameters and of the presence of a permanently heterozygous locus on the establishment of pseudo-overdominance, we simulated populations with sizes N of 1,000 or 10,000, with recombination rates r of 1 × 10⁻⁷, 1 × 10⁻⁸, or 1 × 10⁻⁹ events per base pair per generation, mutation rates µ of 1 × 10⁻⁸ or 1 × 10⁻⁹ events per base pair per generation, selection coefficients s of −0.01, −0.04, −0.07, −0.001, −0.005 or 0 and dominance coefficients h of 0.1, 0.3 or 0.5; we performed simulations with and without a permanently heterozygous locus. We considered that pseudo-overdominance was established at generation 100,000, when, for a given set of parameter values, the mean number of sites in the largest cluster of sites in strong linkage disequilibrium with each other (r²>0.95), averaged over 30 replicates, was significantly higher than the corresponding mean obtained in simulations with only neutral mutations. This indeed indicates that selection promoted the formation of complementary blocks of deleterious mutations, leading to an apparent overdominance of loci with deleterious alleles (see Fig 2D ). Hereafter, we refer to as pseudo-overdominant zone the region spanned by this cluster of sites in strong linkage disequilibrium. Overall, the range of parameter values leading to pseudo-overdominance was larger in the presence of a permanently heterozygous locus than without it. Indeed, among the 180 conditions tested, 27 lead to pseudo-overdominance with a permanently heterozygous locus, while only 15 lead to pseudo-overdominance without such a locus, that is around 1.8 times more cases with a permanently heterozygous locus. In agreement with previous studies ( Ohta and Kimura 1969 ; Waller 2021 ; Gilbert et al. 2020 ; Abu-Awad and Waller 2023 ), we also found that pseudo-overdominance was more often established with smaller population sizes (2 times more cases with N =1000 than with N =10000), higher mutation rates (7.4 times more cases with µ =1 × 10⁻⁸ than with µ =1 × 10⁻⁹), lower recombination rates (5 times more cases with r =1 × 10⁻⁹ than with r =1 × 10⁻⁸ and 0 with r =1 × 10⁻⁷), lower coefficients of dominance (2.8 times more cases with h =0.1 than h =0.3 and 0 with h =0.5) and higher selection coefficients (3.25 times more cases with s =-0.001 than with s =-0.07) ( Fig 4 ). In addition, the variance in the number of sites in the pseudo-overdominant zone between replicates tended to be smaller in systems with permanently heterozygous loci ( Fig 4 ; 12 conditions out of the 15 had a significantly higher variance), suggesting a higher influence of stochasticity in the absence of permanently heterozygous loci. Finally, the mean number of sites in linkage disequilibrium in the pseudo-overdominant zone tended to be higher in the presence of a permanently heterozygous locus than without it, which suggests that, beyond expanding the range of conditions under which pseudo-overdominance can occur, permanently heterozygous loci also increases the speed and extent of its establishment ( Fig 4 ; 12 conditions out of the 15 had a significantly higher mean). Download figure Open in new tab Figure 4: Effect of population size, mutation rate, recombination rate, selective and dominance coefficient of mutations and the presence of a permanently heterozygous locus on the establishment of pseudo-overdominance. Number of sites in the largest cluster of sites in strong linkage disequilibrium (LD) with each other (r²>0.95) at generation 100,000 in 30 replicates of simulations (expect for s =0, 90 replicates were performed) run with various combinations of parameters: population size N (1000 or 1000), mutation rate µ (1 × 10⁻⁸, 1 × 10⁻⁹), recombination rate r (1 × 10⁻⁷, 1 × 10⁻⁸, 1 × 10⁻⁹), selective coefficient s (−0.01, −0.04, −0.07, −0.001, −0.005, 0) and dominance coefficient h (0.1, 0.3, 0.5) including or not a permanently heterozygous locus in the centre of the chromosome. The corresponding population size and mutation rate are indicated on top of each graph and for each set of parameter values, the boxplot on the left and on the right correspond respectively to simulation with and without a permanently heterozygous locus. Stars correspond to parameter values for which the mean value of replicates was significantly higher than the mean for the corresponding set of parameters (i.e. N , µ , r, genetic system) with s =0 (T-tests with p-value corrected with Bonferroni method for multiple tests). Boxplot elements: central line: median, box limits: 25th and 75th percentiles, whiskers: 1.5× interquartile range. To investigate whether pseudo-overdominance can be favoured around other types of loci under balancing selection — less extreme than permanently heterozygous loci — we ran simulations with either a sex-determining locus or overdominant loci with varying degrees of heterozygote advantage, using a reduced set of parameter values to save computation time ( Table 1 ). In the latter case, the fitness advantage of heterozygotes at the overdominant locus was set to either 0.1 or 0.4, while the fitness advantage of each homozygote was set to 0.0002 and 0, respectively, in both scenarios. These two overdominant loci will be referred to as the locus under weak or strong overdominant selection, depending on the fitness advantage of the heterozygote. View this table: View inline View popup Download powerpoint Table 1: Explored parameter values in simulations. As with permanently heterozygous loci, we found that pseudo-overdominance occurred across a slightly broader range of parameter values around sex-determining loci or loci under strong balancing selection than in cases without such loci ( Fig 5 ). Indeed, among the 32 conditions tested, 11 led to pseudo-overdominance with a sex-determining locus, 10 with a strongly overdominant locus, while only 8 led to pseudo-overdominance without such loci. This represented around 1.4 times more cases with a sex-determining locus and 1.3 more cases with a strongly overdominant locus, respectively, than without such loci. The locus under weak overdominant selection did not show any detectable effect on the establishment of pseudo-overdominance under the conditions tested. Download figure Open in new tab Figure 5: Effect of population size, mutation rate, recombination rate, selective and dominance coefficient of mutations and genetic system (sex-determining locus, overdominant loci or none) on the establishment of pseudo-overdominance. Number of sites in the largest cluster of sites in strong linkage disequilibrium (LD) with each other (r²>0.95) at generation 100,000 in 30 replicates of simulations (expect for s =0, 90 replicates were performed) run with various combinations of parameters: population size N (1000 or 1000), mutation rate µ (1 × 10⁻⁸, 1 × 10⁻⁹), recombination rate r (1 × 10⁻⁸, 1 × 10⁻⁹), selective coefficient s (−0.01, −0.001, 0) and dominance coefficient h (0.1, 0.3) in a XY system or including a locus under overdominant selection or not. The corresponding population size and mutation rate are indicated on top of each graph, and for each set of parameter values, the boxplot from left to right corresponds respectively to simulation in a system, including a sex-determining locus, a locus under strong overdominant selection (with a fitness gain for heterozygous at this locus being set to be 0.4 while the fitness gain for each of the homozygous were respectively set to 0.0002 and 0); a locus under weak overdominant selection (with a fitness gain for heterozygous at this locus being set to be 0.1 while the fitness gain for each of the homozygous were respectively set to 0.0002 and 0), or none of them. Stars correspond to parameter values for which the mean value of replicates was significantly higher than the mean for the corresponding set of parameters (i.e. N , µ , r, genetic system) with s =0 (T-tests with p-value corrected with Bonferroni method for multiple tests). Boxplot elements: central line: median, box limits: 25th and 75th percentiles, whiskers: 1.5× interquartile range. Overall, these results confirm our hypothesis that loci under balancing selection favour pseudo-overdominance, and further show that this effect intensifies with stronger balancing selection. Pseudo-overdominance zones can select for crossing-over suppression around permanently heterozygous loci The strong selection against recombinant offspring shown above ( Fig 3 ) suggests that genuine recombination suppression could be favoured in pseudo-overdominant zones, as it would avoid the production of unfit offspring via crossing-over. To test this hypothesis, we introduced a recombination suppressor near the permanently heterozygous locus at generation 100,000 and tracked its fixation rate in a population of size N =1000 individuals with a recombination rate r =1 × 10⁻⁹ events per base pair per generation, a mutation rate µ =1 × 10⁻⁸ mutations per base pair per generation, a selective coefficient of mutations s =-0.04 and a dominance coefficient h =0.3. We compared this scenario where multiple recessive deleterious mutations were present in repulsion (i.e., forming a pseudo-overdominant zone) to control cases containing only neutral mutations (see Fig 2 ). The size for the recombination suppressor was set here at 1 Mb, which is a reasonable inversion size given those found in genomes across various organisms ( Berdan et al. 2023 ; Karageorgiou et al. 2019 ; Mérot et al. 2020 ). Inversion sizes range for example from a few bp to 5 Mb in the human genome ( Feuk 2010 ; Porubsky et al. 2022 ). We found that the presence of a pseudo-overdominant zone led to a significantly higher fixation rate of the recombination suppressor compared to the neutral case (1.08-fold increase; Fig 6A ). Using the classical fixation probability equation from Kimura ( Kimura 1962 ) and the rate of fixation of the recombination suppressor p fixation =0.00106 observed in simulations, we estimated the selective coefficient of the non-recombining fragment to be s ≈0.00044. The non-recombining fragments that eventually fixed did not, on average, carry a lower mutational load than those that were lost ( Fig 6B ). This indicates that recombination suppressors were selected for because they prevented the formation of unfit recombinant haplotypes and not because non-recombining fragments were simply less loaded than average ( Jay et al. 2024 ; Nei, Kojima, and Schaffer 1967 ). These results indicate that pseudo-overdominance can favour the evolution of recombination suppression around permanently heterozygous loci. Download figure Open in new tab Figure 6: Fixation rate of a non-recombining fragment in the presence or the absence of recessive deleterious mutations. Results from 1500,000 simulations of the evolution of a panmictic population under a Wright-Fisher model. Each individual is diploid with a 10 Mb chromosome containing a central permanently heterozygous locus. Simulations used a population size ( N ) of 1000, a recombination rate ( r ) of 1 × 10⁻⁹, a mutation rate ( µ ) of 1 × 10⁻⁸, a dominance coefficient ( h ) of 0.3 and a selective coefficient ( s ) of either −0.04 or 0. A) Fixation rate of a 1 Mb recombination suppressor fragment (within the subpopulation of chromosomes bearing the permanently heterozygous allele contained in the non recombining fragment initially introduced) introduced at generation 100,001 in the presence or the absence of recessive deleterious mutations. Results inferred from simulations following the loss or fixation of the non-recombining fragment centred. P-value correspond to a Fisher’s exact test. Error bars represent standard errors. B) Initial number of mutations in the non-recombining fragments, in fixed vs. non-fixed non-recombining fragments. P-value corresponds to a Wilcoxon rank-sum test. (ns: non-significant; *: p<0.05). Boxplot elements: central line: median, box limits: 25th and 75th percentiles, whiskers: 1.5× interquartile range. Discussion In this study, we demonstrated that recessive deleterious mutations can accumulate around loci under balancing selection and give rise to pseudo-overdominance. We showed that permanently heterozygous loci, sex-determining loci and loci under strong overdominant selection facilitate the evolution of pseudo-overdominance, characterized by the formation of complementary haplotypes carrying deleterious mutations in repulsion. Furthermore, we showed that, once pseudo-overdominance is established around permanently heterozygous loci, selection can favour the evolution of genuine recombination suppression through crossing-over suppression. Loci under balancing selection favour pseudo-overdominance establishment Together with associative overdominance, pseudo-overdominance has already been relatively well described and studied theoretically ( Ohta 1971 ; Abu-Awad and Waller 2023 ; Gilbert et al. 2020 ; Waller 2021 ; Zhao and Charlesworth 2016 ; Sianta et al. 2023 ; B. Charlesworth and Jensen 2021 ; Bierne, Tsitrone, and David 2000 ; Pamilo and Pálsson 1998 ; Berdan et al. 2021 ). The key difference between associative overdominance and pseudo-overdominance lies in the types of loci involved: associative overdominance affects neutral loci linked to deleterious alleles, whereas pseudo-overdominance involves deleterious mutations themselves. Various models theoretically investigated the conditions under which pseudo-overdominance and associative overdominance can emerge ( Ohta 1971 ; Abu-Awad and Waller 2023 ; Gilbert et al. 2020 ; Berdan et al. 2021 ; Waller 2021 ; Zhao and Charlesworth 2016 ; Sianta et al. 2023 ; B. Charlesworth and Jensen 2021 ; Bierne, Tsitrone, and David 2000 ; Pamilo and Pálsson 1998 ; Booker and Schrider 2025 ), highlighting the effect of recombination rate, mutation rate, selection and dominance coefficients, as also supported in the present study, but also of ploidy, selfing rate and population structure. Other studies have highlighted how associative overdominance can establish as a consequence of recombination suppression ( Brookfield 2020 ; Berdan et al. 2021 ), its consequences on genetic load and polymorphism at neutral sites ( Ohta 1971 ; Abu-Awad and Waller 2023 ; Zhao and Charlesworth 2016 ; Pamilo and Pálsson 1998 ; Lenz et al. 2016 ), or studied the transition from background selection to associative overdominance ( Gilbert et al. 2020 ). Here, we illustrated in more detail how pseudo-overdominance establishes, extends, strengthens and is maintained—especially around permanently heterozygous loci, and how it shapes haplotype structure and affects the fitness of recombinant offspring. We further demonstrated that, beyond the extreme case of permanent heterozygosity, loci under balancing selection more generally favour pseudo-overdominance establishment. This had been verbally suggested ( Abu-Awad and Waller 2023 ) but, to our knowledge, pseudo-overdominance around loci under balancing selection has only been previously theoretically studied to explain the evolution of the MHC region, although not referred to as such (van Oosterhout 2009 ). Our results showed that the presence of a permanently heterozygous locus, a sex-determining locus or a locus under strong overdominant selection substantially expands the range of conditions under which pseudo-overdominance arises, by increasing the number of tested parameter sets under which pseudo-overdominance emerge by factors of 1.8, 1.4 and 1.3, respectively. Pseudo-overdominance can indeed be established around a locus under balancing selection in systems with a higher recombination rate, a lower mutation rate, a lower selective coefficient, a higher dominance coefficient and a larger population size compared to conditions enabling pseudo-overdominance without any specific loci. We further demonstrated that the impact of a locus under balancing selection on the establishment of pseudo-overdominance increased with the strength of its balancing selection. We show here that it is because permanently heterozygous loci favour the maintenance of linked mutations at intermediate frequencies that they promote the emergence of pseudo-overdominance in their vicinity. The effect of balancing selection on neutral loci has been well described ( Kirkpatrick, Guerrero, and Scarpino 2010 ; Gao, Przeworski, and Sella 2015 ; and reviewed in D. Charlesworth 2006 ), showing that a locus under balancing selection affects coalescence times and thus increases neutral polymorphism and linkage disequilibrium at closely linked sites. Similar effects have been shown for deleterious mutation dynamics around loci under balancing selection, but they either focused on particular loci with multiple alleles and diversifying selection ( Lenz et al. 2016 ; Llaurens, Gonthier, and Billiard 2009 ; Glémin et al. 2001 ), relied on analytical approximations that may not hold in realistic genomic contexts ( Tezenas et al. 2023 ), or focused on a specific mating system ( Antonovics and Abrams 2004 ), and without detailed studies on the influence of the selective and dominance coefficients of the mutations ( Tezenas et al. 2023 ; Leach, Mayo, and Morris 1986 ; Uyenoyama 2005 ; Lenz et al. 2016 ). The results presented here further support the conclusions of previous studies and extend them to additional systems, incorporating more detailed analyses of the effects of dominance and selective coefficients. Empirical and experimental analyses supported these theoretical findings, by providing evidence for the presence of deleterious mutations at the margin of permanently heterozygous loci ( Le Veve et al. 2023 ; Llaurens, Gonthier, and Billiard 2009 ; Mena-Alí, Keser, and Stephenson 2009 ; Goubet et al. 2012 ; Guyot et al. 2025 ; Stone 2004 ). The mechanisms promoting the maintenance of deleterious mutations around loci under balancing selection remain, however, to be fully understood (see discussions in Lenz et al. 2016 ; D. Charlesworth 2006 ; Abu-Awad and Waller 2023 ; van Oosterhout 2009 ). Three processes are likely involved. First, a local subdivision of the effective population size due to linkage to a locus under balancing selection may increase genetic drift and reduce the efficacy of purifying selection on deleterious mutations ( Lenz et al. 2016 ). This should lead to increased polymorphism at the population level, through the fixation of different mutations on distinct haplotypes. Second, the prolonged maintenance of mutations may be due to the rarity of recombination events breaking the association between the site under balancing selection and nearby loci. This prevents mutations from moving between the different backgrounds maintained around the locus under balancing selection, which hinders the purging or fixation of mutations, thereby extending their segregation time (B. Charlesworth, Charlesworth, and Barton 2003 ; D. Charlesworth 2006 ). Third, the linkage of deleterious recessive mutations to a locus under balancing selection may favour their maintenance in the heterozygous state. This could reduce their apparent selection coefficient and delay their purging from the population, a phenomenon referred to as the “sheltering effect” ( Lenz et al. 2016 ; Jay et al. 2024 ; van Oosterhout 2009 ; Nei 1970 ). While these mechanisms have been discussed, their relative importance remains unclear. Pseudo-overdominance can lead to the selection for crossing-over suppression Previous studies have shown that pseudo-overdominance could emerge in regions with low recombination rates ( Gilbert et al. 2020 ; Abu-Awad and Waller 2023 ; Berdan et al. 2021 ) and that strong pseudo-overdominance prevented the evolution of increased recombination rates ( Palsson 2002 ). Here, we show that, in the presence of a permanently heterozygous locus, pseudo-overdominance can promote the selection for crossing-over suppression. Indeed, recombination between complementary haplotypes in pseudo-overdominant zones generates unfit haplotypes. Therefore, recombination suppressors, such as chromosomal inversions, could be favoured in those regions because they prevent the formation of unfit, recombinant haplotypes. The idea has been verbally suggested for sex and mating-type chromosomes, but without any mention of pseudo-overdominance ( Branco et al. 2017 ). The difference in the fixation rate of a recombination suppressor between a system under pseudo-overdominance and the neutral case was significant and yielded an estimate of s =0.00044 for a 1 Mb recombination suppressor under the conditions analysed. For reference, the majority of beneficial mutations in genomes have been estimated to have small selection coefficients ( Eyre-Walker and Keightley 2007 ), with for example 98% of the beneficial mutations in humans having a s < 0.0005 ( Huber et al. 2017 ). The selective advantage of a recombination suppressor in a pseudo-overdominant zone depends on how many offspring it prevents from becoming homozygous for recessive deleterious mutations, which depends on the recombination rate. The selective advantage conferred by a recombination suppressor also depends on the cost of being homozygous for the mutations contained within the non-recombining fragment, i.e., the size of the fragment, the number of mutations, and their selection and dominance coefficients. Even in the absence of any locus under balancing selection, or in a less extreme case than a permanently heterozygous locus, similar selection for crossing-over suppression may be expected in pseudo-overdominant zones, because recombination also produces unfit haplotypes in these cases. In these systems, random mating would also produce homozygous individuals, which may favour the evolution of mechanisms that limit mating between gametes carrying the same haplotype, e.g., disassortative mating ( Jay et al. 2021 ). Model relevance to natural populations We use here the number of sites in the largest cluster of sites in strong linkage disequilibrium with each other at a given time point—averaged across multiple simulations and compared to the neutral case—as a criterion to estimate whether a given parameter combination would allow pseudo-overdominance emergence. A significantly higher number of sites in linkage disequilibrium when deleterious mutations are present, compared to the neutral case, implies selection against the breaking of linkage disequilibrium, i.e., against individuals with homozygous sites, a hallmark of pseudo-overdominant zones. As an additional (albeit arbitrary) criterion, we assessed whether pseudo-overdominance could be detected at generation 100,000, based on the average outcome of 30 replicate simulations. Because the emergence of pseudo-overdominance is probabilistic, the timing and extent of its onset are expected to vary following conditions and replicas; therefore, a lower or higher number of replicas or generations followed would have likely led to pseudo-overdominance detection under wider or narrower ranges of parameter values. The exact parameter values at which pseudo-overdominance was detected in this study should therefore be taken with caution for inferring whether conditions would be favourable for pseudo-overdominance to emerge. Other criteria for pseudo-overdominance detection have been used in previous simulation studies, for example, the presence of intermediate median allele frequencies ( Booker and Schrider 2025 ;) or the nucleotide diversity at neutral sites compared to the neutral case ( Gilbert et al. 2020 ). The various parameter values used here were chosen in agreement with the ones used in previous similar models ( Booker and Schrider 2025 ; Gilbert et al. 2020 ) and of the order of magnitude of estimates in natural populations ( Park 2011 ; Stapley et al. 2017 ; Wang and Obbard 2023 ; Eyre-Walker and Keightley 2007 ). In nature, genome-wide average recombination rates have been estimated to vary between 10⁻⁵ to 3 × 10⁻⁹ per bp per generation across plants, animals and fungi ( Stapley et al. 2017 ). The recombination rate also varies by several orders of magnitude along genomes and numerous genomic regions display recombination rates much below 10⁻⁹ ( Halldorsson et al. 2019 ; Rifkin et al. 2021 ). Regarding mutation rates, recent estimates across various species are almost all above 10⁻⁹ mutations per base pair per generation, such as 7.97 × 10⁻⁹ on average in mammals and 1.01 × 10⁻⁸ in birds ( Bergeron et al. 2023 ). However, mutation rate variation along the genomes is poorly known and the proportion of deleterious mutations, which matter for pseudo-overdominance establishment, is subject to debate ( Agrawal and Whitlock 2012 ; Conrad et al. 2011 ; Lesecque, Keightley, and Eyre-Walker 2012 ; Henn et al. 2015 ). Yet, most mutations have been estimated to be slightly deleterious, with more than 50% having a selective coefficient s between −0.001 and −0.1 ( Eyre-Walker, Woolfit, and Phelps 2006 ; Eyre-Walker and Keightley 2007 ). For population size, estimates are around 10⁴ for humans ( Park 2011 ; Eyre-Walker, Woolfit, and Phelps 2006 ), 6 × 10⁵ for mice ( Halligan et al. 2010 ) and 5 × 10⁶ for drosophila ( Duchen et al. 2013 ). Dominance coefficients have been estimated to be on average around 0.2 ( Kyriazis and Lohmueller 2024 ; Manna, Martin, and Lenormand 2011 ; Di and Lohmueller 2024 ; see Mrnjavac, Vicoso, and Connallon 2025 for a more detailed discussion). These estimates seem, according to our analyses, consistent with conditions allowing the evolution of pseudo-overdominance, at least in some species and genomic regions where the right conditions are met. Other conditions not tested here could likely facilitate pseudo-overdominance in natural populations. A higher number of alleles at the locus under balancing selection and a higher ploidy are, for instance, expected to facilitate deleterious mutation maintenance and thus favour even more broadly pseudo-overdominance (van Oosterhout 2009 ; Booker and Schrider 2025 ; D. Charlesworth 2006 ). Similarly, population structure and population bottleneck are expected to facilitate the establishment of pseudo-overdominance, potentially broadening the conditions under which it arises in nature ( Bierne, Tsitrone, and David 2000 ; Gilbert et al. 2020 ). Other mating systems are also likely to favour pseudo-overdominance establishment, especially selfing, and in particular with intra-tetrad mating, under which deleterious mutation maintenance has been shown to be particularly facilitated ( Bierne, Tsitrone, and David 2000 ; Tezenas et al. 2023 ; Antonovics and Abrams 2004 ). The heterozygous advantage values tested for the overdominant loci were chosen to be high compared to known estimates ( Satta et al. 1994 ; Yasukochi and Satta 2013 ), to avoid the loss of one or the other allele in the presence of deleterious mutations in the condition tested. We did not detect any effect of the loci with a weak overdominant selection on pseudo-overdominance emergence, suggesting that strong balancing selection is required to substantially promote the emergence of pseudo-overdominance in our conditions. A limitation of our study is that the Wright-Fisher model used here inherently prevents population extinction. In natural populations, where population sizes fluctuate and extinction is possible, such an accumulation—if occurring in a large genomic region—could lead to population extinction unless compensatory mechanisms evolve. However, as discussed above, recombination rates are not uniform across genomes and notably include recombination hotspots ( Halldorsson et al. 2019 ; Stapley et al. 2017 ), making it unlikely that the pseudo-overdominant zone extends over large regions. Model-based predictions and signature of pseudo-overdominance The model described here allows us to predict how to detect and where to search for pseudo-overdominant zones (see also Waller 2021 ). At the genomic level, pseudo-overdominant zones are predicted to display an elevated level of heterozygosity and polymorphism, with numerous deleterious mutations maintained at intermediate frequencies, and strong linkage disequilibrium across the region, with the coexistence of multiple haplotypes within the population. In addition to these genomic features, pseudo-overdominant zones are expected to occur more frequently in regions of low recombination rates and high mutation rates, as well as near loci under balancing selection. Pseudo-overdominant zones are also predicted to expand and intensify over time, provided that population genetic parameters are favourable (in particular effective population size, mutation rate and recombination rate). In addition, pseudo-overdominant zones are expected to co-occur with regions of suppressed recombination, such as chromosomal rearrangements, as both can trigger the emergence of each other. Pseudo-overdominant zones are also predicted to result in a reduced fitness of individuals homozygous for an haplotype or recombinant individuals, while heterozygous non-recombinant individuals maintain higher fitness due to the presence of a sheltered load. Altogether, these predictions may help pinpoint pseudo-overdominant zones in genomes and clarify their role in genome evolution. Empirical evidence of pseudo-overdominance around loci under balancing selection In line with these predictions, several studies found genomic regions in fish, Drosophila , plants and humans, characterized by a high genetic diversity and a low recombination rate, that may actually be pseudo-overdominant zones ( Gilbert et al. 2020 ; van Oosterhout 2009 ; Becher, Jackson, and Charlesworth 2020 ; Leitwein, Cayuela, and Bernatchez 2021 ; Hedrick, Hellsten, and Grattapaglia 2016 ; Schou et al. 2017 ; Frydenberg 1963 ). In some cases, it has been suggested that a locus under balancing selection might be present in regions where pseudo-overdominance has been detected, even though no causal effect has been established ( Becher, Jackson, and Charlesworth 2020 ; Frydenberg 1963 ). To our knowledge, the MHC is the only locus under balancing selection for which the establishment of pseudo-overdominance, though not explicitly referred to as such, has been proposed to explain the surrounding patterns of high polymorphism organized into haplotype blocks (van Oosterhout 2009 ). However, many well-characterized loci under balancing selection are also surrounded by polymorphic regions structured into haplotype blocks, often associated with a load of recessive deleterious mutations, and may thus be affected by pseudo-overdominance. Classic examples include plant and vertebrate disease resistance genes, hemoglobin genes in mammals, sex-determining regions and permanently heterozygous loci (e.g., self-incompatibility and mating-type loci)—( Guyot et al. 2025 ; Le Veve et al. 2023 ; Mena-Alí, Keser, and Stephenson 2009 ; Le Veve et al. 2024 ; Llaurens, Gonthier, and Billiard 2009 ; Stone 2004 ; Moya et al. 2025 ; Lenz et al. 2016 ; Llaurens, Whibley, and Joron 2017 ; B. Wang et al. 2019 ; Berdan et al. 2022 ; Judelson, Spielman, and Shattock 1995 ; Hartmann et al. 2021 ). For instance, in the fungi Schizothecium tetrasporum and Podospora anserina , the mating-type locus is surrounded by a non-recombining region spanning approximately 1 Mb but the proximal or evolutionary causes of this recombination suppression remain unresolved ( Guyot et al. 2025 ; Idnurm et al. 2015 ; Vittorelli et al. 2023 ; Filippo et al. 2025 ; Grognet, Debuchy, and Giraud 2025 ; Grognet and Silar 2015 ; Hartmann et al. 2021 ). This region is characterized by high heterozygosity, the presence of deleterious mutations, a sheltered load, rare detected recombination events, an absence of chromosomal rearrangement and a clear haplotype structure. This is consistent with a role in pseudo-overdominance around mating-type loci. In addition, recombination suppression around mating-type loci has been so far only found in fungal organisms with a main diploid phase, in which pseudo-overdominance can evolve ( Filippo et al. 2025 ; Jay et al. 2024 ; Booker and Schrider 2025 ). This indicates that pseudo-overdominance may be more prevalent than previously appreciated. Perspectives Better estimates of recombination rates, mutation rates, dominance coefficients and selection coefficients across the tree of life and along the genome are needed to determine whether pseudo-overdominance could play an important role in genome evolution. Progress in sequencing should allow us to detect genomic regions displaying signatures of pseudo-overdominance (Gilbert et al), which will help understand the biological relevance of this phenomenon. In genomic regions previously suggested to be shaped by pseudo-overdominance ( Schou et al. 2017 ; Becher, Jackson, and Charlesworth 2020 ; Leitwein, Cayuela, and Bernatchez 2021 ; Gilbert et al. 2020 ), it may be worthwhile to investigate whether some of these regions were influenced by loci under balancing selection (see discussion in Frydenberg 1963 ). However, identifying such loci is challenging once pseudo-overdominance has become established, especially since these pseudo-overdominant zones may have originally arisen due to the presence of an overdominant locus that is no longer under selective pressure. In addition, pseudo-overdominance leads to selection against recombinant haplotypes, generating signatures of recombination suppression while crossing-over events still occur. It would therefore be interesting to determine whether crossing-overs are really suppressed in the multiple genomic regions where recombination suppression has been previously detected without chromosomal rearrangements ( Filippo et al. 2025 ; Guyot et al. 2025 ). Our results prompt new avenues for understanding pseudo-overdominance, recombination suppression and sheltered load around loci under balancing selection. This has implications not only for understanding the evolution of mating-type chromosomes but also for multi-allelic incompatibility systems, regions under balancing selection genome-wide and perhaps even sex chromosomes. Future research focusing on empirical validations of our model could provide further insights into its evolutionary implications. Methods Model We simulated a panmictic population of N diploid individuals, each carrying a pair of 10 Mb chromosomes, under a Wright-Fisher model with a genomic recombination rate r , a mutation rate µ , and mutation selection and dominance coefficients s and h , respectively. Fitness was calculated multiplicatively, with each mutation conferring a fitness effect of 1 + s when homozygous and 1 + hs when heterozygous. Relative fitness determined the probability of an individual being selected for reproduction. SLiM version 4.2.2 was used for all simulations ( Haller and Messer 2023 ). The parameter values explored are given in Table 1 . In some simulations ( Table 1 ), we added at the centre of the chromosome a permanently heterozygous bi-allelic locus controlling mating compatibility at the haploid stage (i.e. mimicking a mating-type locus), a sex-determining locus controlling mating compatibility at the diploid stage (similar to a XY or ZW system), or a locus under overdominant balancing selection (with a fitness gain for heterozygous at this locus being set to be 0.1 or 0.4 while the fitness gain for each of the homozygous were respectively set to 0.0002 and 0 in both cases). Deleterious mutation dynamics around a permanently heterozygous locus To evaluate how permanent heterozygosity at a locus influences the fate of nearby mutations, we analyzed the trajectories of mutations introduced individually at varying genetic distances from a permanently heterozygous locus in a population of 1000 individuals. Distances ranged from 1 × 10⁻⁶ to 50 cM (specifically: 1 × 10⁻⁶, 1 × 10⁻⁵, 1 × 10⁻⁴, 1 × 10⁻³, 1 × 10⁻², 0.1, 1, 10, and 50 cM). Dominance coefficients ( h ) were set to 0.1, 0.3, or 0.5, and selection coefficients ( s ) varied from 0 to −0.07 (specifically: 0, −0.005, −0.01, −0.07). For each combination of parameters, 40,000 mutations were simulated. For each mutation, we recorded: its segregating time and the average deviation of observed heterozygosity from Hardy-Weinberg expectations (i.e., observed heterozygosity minus 2 f (1– f ), where f is the mutation frequency) over the course of its lifetime. Simulations were terminated at generation 100,000 if the mutation had neither fixed nor been lost by that point. Illustration of pseudo-overdominance For a subset of parameters values ( N =1000, h =0.3, s =-0.04 or s =0, r =1×10⁻⁹, and μ =1×10⁻⁸), and under conditions with or without a permanently heterozygous locus, we recorded the mean percentage of heterozygous sites per individual (among sites with derived mutations in each individual) and the mean number of sites with derived mutations per individual, and averaged them across 100 individuals. These metrics were computed every 100 generations over 100,000 generations, across 1000 simulation replicates. The mean number of sites with derived mutations per individual was also calculated from a sample of 100 individuals in 10 Kb sliding windows along the chromosome at generations 5000, 50000 and 100000 in 1000 simulation replicates. VCFtools ( Danecek et al. 2011 ) was used to calculate the linkage disequilibrium coefficient (r²) between all loci along the genome in 100 individuals, sampled every 1000 generations over the course of 100,000 generations, across 1000 replicate simulations. The number of sites in the largest cluster of sites in strong linkage disequilibrium with each other of sites (r²>0.95) was counted for each of the 1000 simulations every 1000 generations. A linkage disequilibrium map was generated from a single simulation at generation 100,000 by averaging r² values across pairs of 150,000 bp genomic regions along the chromosome. A full classical output from SLiM was also produced at generation 100,000 and clustering was performed using hierarchical clustering with the method used in ( Berdan et al. 2021 ). As a control, the same simulations and analyses were run for s=0. In addition, the fitness of individuals carrying a chromosome that had undergone a single recombination event in the previous generation was recorded every 100 generations over 100,000 generations, in 1000 simulation replicates. The number of homozygous mutations, the recombination breakpoint position and the fitness of the individuals resulting from a single recombination event were also recorded at generations 5001 and 100,001 in 1000 simulation replicates. Sensitivity analysis For all combinations of parameter values ( Table 1 ), 30 replicate simulations were run during 100,000 generations. For each simulation, the mean number of sites in the largest cluster of sites in strong linkage disequilibrium with each other (r²>0.95) was counted at generation 100,000 using VCFtools ( Danecek et al. 2011 ) on a sample of 200 genomes from 100 individuals. T-tests with the Bonferroni correction for multiple testing were used to compare, for each set of parameter values, the mean number of sites in the largest cluster of sites in strong linkage disequilibrium with each other at generation 100,000 to the corresponding one in simulations with only neutral mutations (for s =0 all 3 dominance coefficients were grouped so that 90 replicates were used). For each set of parameter values in which pseudo-overdominance has been detected both with and without permanently heterozygous loci, T-tests with the Bonferroni correction for multiple testing were also used to compare the mean number of sites in the largest cluster of sites in strong linkage disequilibrium with each other at generation 100,000 with a permanently heterozygous loci to the corresponding one without a permanently heterozygous loci. F-test to compare the variance of the number of sites in the largest cluster of sites in strong linkage disequilibrium with each other were also performed between the latter with the Bonferroni correction for multiple testing. Recombinaison suppressor introduction In each of the 30 simulations previously run with a permanently heterozygous locus and N =1000, h =0.3, r =1 × 10⁻⁹, µ =1 × 10⁻⁸ and s =-0.04, and the corresponding ones with s =0, a recombination suppressor of 1 Mb was then introduced 50,000 times at generation 100,001 centred around the permanently heterozygous allele of one randomly chosen genome. The fixation rate of the recombination suppressor fragment (within the subpopulation of chromosome bearing the permanently heterozygous allele contained in the non-recombining fragment initially introduced) when deleterious mutations and when neutral mutations were then calculated from each of the 1,500,000 simulations. A Fisher’s exact test was used to compare the proportion of fragments fixed (within the subpopulation of chromosomes bearing the permanently heterozygous allele contained in the non-recombining fragment initially introduced) between cases with neutral and deleterious mutations. In all simulations, we also counted the initial number of mutations in each randomly chosen non-recombining fragment. A Wilcoxon rank-sum test was used to assess whether the number of mutations differed between fixed and non-fixed non-recombining fragments. To estimate the selective coefficient of the recombination suppressor in these conditions, we considered that a permanently heterozygous locus does not affect the fixation rate of mutation nearby and used the classical fixation probability equation from Kimura ( Kimura 1962 ). To do so, we numerically solved: p fixation =(1−exp(−2s)/1−exp(−4Ns)) with N =1000 and the estimated probability of fixation p fixation of the recombination suppressor when pseudo-overdominance obtained with simulations. However, note that because we considered that here the rate of fixation in the population of chromosomes bearing the permanently heterozygous allele contained in the non-recombining fragment initially introduced and not in the whole population, such an estimate might be slightly overestimated. Plot and statistical analyses Plot and statistical analyses were performed using R software v 4.3.2 ( R Core Team 2020 ). Codes and data availability Codes and data used to generate figures are available at: https://gitlab.com/Louguyot/article_guyot_2025/-/tree/97bba3f0ef3c9fc388d99c8d2e54444852d6ebcb/ . Acknowledgements We thank Amandine Veber and Diala Abu-Awad for discussion. 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Share Loci under balancing selection facilitate the emergence of pseudo-overdominance and recombination suppression Lou Guyot , Tatiana Giraud , Paul Jay bioRxiv 2025.06.19.660549; doi: https://doi.org/10.1101/2025.06.19.660549 Share This Article: Copy Citation Tools Loci under balancing selection facilitate the emergence of pseudo-overdominance and recombination suppression Lou Guyot , Tatiana Giraud , Paul Jay bioRxiv 2025.06.19.660549; doi: https://doi.org/10.1101/2025.06.19.660549 Citation Manager Formats BibTeX Bookends EasyBib EndNote (tagged) EndNote 8 (xml) Medlars Mendeley Papers RefWorks Tagged Ref Manager RIS Zotero Tweet Widget Facebook Like Google Plus One Subject Area Evolutionary Biology Subject Areas All Articles Animal Behavior and Cognition (7640) Biochemistry (17706) Bioengineering (13902) Bioinformatics (41978) Biophysics (21465) Cancer Biology (18611) Cell Biology (25528) Clinical Trials (138) Developmental Biology (13387) Ecology (19920) Epidemiology (2067) Evolutionary Biology (24332) Genetics (15615) Genomics (22519) Immunology (17747) Microbiology (40424) Molecular Biology (17194) Neuroscience (88662) Paleontology (667) Pathology (2838) Pharmacology and Toxicology (4827) Physiology (7650) Plant Biology (15160) Scientific Communication and Education (2046) Synthetic Biology (4302) Systems Biology (9826) Zoology (2271)