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Operational sex ratio

The operational sex ratio (OSR) is defined as the ratio of sexually active or receptive males to sexually receptive or available females in a population's mating pool at a given time, typically expressed as males:females (M:F).^[1]^[2] Introduced by Emlen and Oring in 1977, the concept originally framed OSR as the ratio of fertilizable females to sexually active males, emphasizing its role in linking ecological constraints to the evolution of mating behaviors and sexual selection.^[3] Unlike the broader adult sex ratio (ASR), which measures the proportion of adult males to adult females in a population and is shaped by factors like birth sex ratios and differential mortality, OSR focuses exclusively on individuals immediately available for mating, excluding those engaged in parental care or otherwise unavailable.^[4] A biased OSR—whether toward males (M:F > 1) or females (M:F < 1)—predicts the direction and intensity of intrasexual competition, with the more abundant sex typically investing more in mate attraction, defense, or rivalry.^[1]^[5] For instance, male-biased OSRs often result in heightened male-male agonism and elaborate sexual traits, as seen in many birds and fish, while female-biased OSRs can promote female competition and choosiness reversal, as observed in pipefish and some insects.^[2]^[6] Dynamic factors influencing OSR include sex differences in potential reproductive rates (PRR), breeding phenology, adult lifespan, and operational sex differences in maturation or remating intervals, which can fluctuate seasonally or across populations and thus drive variation in mating systems from monogamy to polygyny or polyandry.^[4]^[1] Empirical support for OSR theory comes from experimental manipulations, such as in guppies (Poecilia reticulata), where altering OSR shifts female mate preferences and male competition intensity, and in gobies (Pomatoschistus minutus), where latitudinal gradients reveal temporal OSR changes affecting sex-specific behaviors.^[7]^[5] Overall, OSR provides a mechanistic bridge between ecology and evolutionary outcomes, informing predictions about sexual conflict, parental roles, and trait evolution across diverse taxa, though its measurement requires careful consideration of context-specific availability.^[3]^[2]

Definition and Concepts

Definition of OSR

The operational sex ratio (OSR) is defined as the ratio of potentially receptive males to receptive females available for mating within a population at a given time or during a specific breeding period.^[3] This metric emphasizes the availability of individuals actively participating in mating opportunities, rather than the overall population composition.^[8] The basic formulation of OSR is expressed as:

\text{OSR} = \frac{\text{number of potentially receptive males}}{\text{number of receptive females}}

Here, "potentially receptive males" typically refers to mature males capable of insemination and competing for mates, while "receptive females" are those in breeding condition, such as estrus, when they are fertile and willing to mate.^[3]^[9] Sexual receptivity thus serves as a key prerequisite, highlighting the temporal and physiological constraints on mating availability that distinguish OSR from broader demographic measures like the adult sex ratio (ASR), which simply counts adult individuals regardless of reproductive readiness.^[8] The concept of OSR was coined by Emlen and Oring in their seminal 1977 paper, where they linked it to the ecological determinants of mating systems, particularly how biases in OSR influence the potential for polygamy versus monogamy in relation to resource distribution and parental investment.^[3] This framework underscored OSR's role in shaping intrasexual competition and intersexual selection pressures.^[9] The primary sex ratio refers to the proportion of males to females at fertilization or conception, which is typically close to 1:1 in most sexually reproducing species due to Fisher's principle of frequency-dependent selection favoring the rarer sex to maximize parental fitness.^[10] This ratio is largely irrelevant to mating dynamics, as it precedes developmental stages where mortality and maturation can alter availability for reproduction.^[11] In contrast, the secondary sex ratio is the proportion of males to females at birth or hatching, often slightly male-biased (around 1.05:1 in humans) due to differential prenatal mortality rates that affect males more severely.^[12] Like the primary ratio, it focuses on early life stages and does not account for the sexually active phase, making it a poor predictor of competition for mates.^[13] The adult sex ratio (ASR), also known as the tertiary sex ratio, measures the proportion of adult males to total adults in a population and is frequently male-biased owing to higher male mortality rates across life stages.^[14] The operational sex ratio (OSR), however, is a subset of the ASR, specifically the ratio of sexually active (receptive) males to sexually active females in the mating pool at a given time, rendering it more temporally dynamic and behaviorally focused.^[15] OSR can deviate substantially from ASR due to factors such as asynchronous maturation timing between sexes, where one sex becomes reproductively available earlier than the other, thereby biasing immediate mating opportunities independent of overall adult demographics. This distinction underscores OSR's greater relevance for understanding intrasexual competition and sexual selection pressures during breeding periods.^[15]

Determinants of OSR

Demographic and Life History Factors

The adult sex ratio (ASR), defined as the proportion of adult males in the population, serves as a foundational determinant of the operational sex ratio (OSR), which measures the availability of sexually receptive individuals for mating. ASR imbalances often arise from sex-specific differences in survival probabilities across life stages, with juvenile mortality showing the strongest influence in many species. For instance, in shorebirds like plovers, female-biased juvenile mortality—driven by slower growth rates in females—results in male-biased ASRs, thereby skewing the OSR toward greater male availability during breeding periods.^[16] Similarly, adult survival differences can perpetuate these biases, though their impact is typically less pronounced than juvenile effects. Parental care duration further modulates OSR by temporarily reducing the availability of the caring sex in the mating pool. In species where one sex invests more time in offspring care, such as females in mammals or males in certain pipefishes, this extended commitment limits their reproductive opportunities, biasing the OSR toward the non-caring sex. For example, prolonged female lactation or brooding in birds decreases female receptivity, increasing the relative number of available males and amplifying mating competition among them.^[1] The potential reproductive rate (PRR), which quantifies the maximum number of offspring an individual can produce per unit time unconstrained by mate availability, complements this effect; females often exhibit lower PRRs due to physiological limits like gestation or egg production, while males can achieve higher rates through multiple matings, thus shifting the OSR male-ward in many taxa.^[1] Sex-specific age at sexual maturity introduces temporal fluctuations in OSR, particularly during breeding seasons. When males mature earlier than females, the initial influx of sexually active males creates a transient male-biased OSR before females become receptive, heightening early-season male competition. Conversely, delayed male maturity in some insects can produce female-biased OSRs initially. Sex-biased migration and dispersal patterns exacerbate these dynamics by altering local sex ratios at breeding or mating sites. For example, in birds and mammals, males often disperse or migrate to breeding grounds ahead of females, temporarily skewing local OSRs toward males and influencing the timing of mating opportunities. Natal dispersal differences, such as greater female juvenile dispersal in some parrotlets, can also contribute to long-term ASR biases that propagate into OSR variations.

Environmental and Behavioral Influences

Resource availability plays a critical role in shaping the operational sex ratio (OSR) by constraining the number of individuals available for mating, particularly when essential resources like food or nesting sites are scarce. In scenarios of resource limitation, such as limited nesting sites, fewer females may be able to breed successfully, leading to a male-biased OSR that favors resource-defense polygyny, where males monopolize scarce sites to attract multiple females. For instance, in the common brushtail possum, the availability of den sites directly predicts offspring sex ratios, with scarcity prompting adjustments that produce more daughters to fill available space, potentially skewing the OSR female-ward.^[17] Similarly, nest shortages in species like the sand goby have been shown to increase intrasexual selection potential, amplifying competition among the abundant sex and altering local OSR dynamics.^[18] The spatial distribution and density of resources further influence OSR by creating local biases in sex availability and intensifying competition. When resources are clumped, such as in patchy food distributions, individuals of the sex seeking those resources aggregate, often resulting in uneven local OSR that heightens mate competition for the scarcer sex. Higher population densities exacerbate this effect, as seen in pipefish populations where biased OSR and increased density lead to more clumped spatial distributions of the competing sex, promoting aggressive interactions and shifts in mating opportunities.^[19] Experimental manipulations of breeding resource distribution in bitterling fish demonstrate that clumped resources increase intrasexual competition, altering selection gradients on phenotypic traits related to mate acquisition.^[20] Temperature and climate exert profound effects on OSR through mechanisms like temperature-dependent sex determination (TSD) in reptiles, where incubation temperatures determine hatchling sex ratios and, consequently, future adult OSR. In species such as alligators and sea turtles, warmer temperatures produce more females, potentially leading to female-biased OSR that influences mating competition over generations.^[21] Seasonal climate variations also shift the timing of female receptivity, dynamically altering OSR during breeding periods; for example, in marine fish like the common goby, changing temperatures affect spawning phenology, resulting in temporal mismatches that bias OSR toward one sex at peak mating times.^[5] Behavioral tactics, including mate searching and desertion strategies, can rapidly modify OSR by changing the pool of available individuals during the breeding season. Male desertion to pursue additional mates, common in species with high potential reproductive rates, temporarily increases the relative availability of females, shifting OSR toward female bias and intensifying male-male competition in subsequent pairings. In birds like the Kentish plover, sequential polygyny arises from such desertions, favoring remating opportunities for deserters while leaving the remaining sex to handle parental duties.^[22]^[23] Mate searching behaviors further contribute, as active searching by one sex can deplete the operational pool, creating biases that evolve in response to ecological pressures.^[22] Human-induced factors, including habitat fragmentation and selective harvesting, skew OSR in conservation contexts by disproportionately affecting one sex. Habitat fragmentation disrupts dispersal and increases mortality risks, often altering sex ratios through differential survival. Selective harvesting targeting one sex creates biases by removing individuals from the mating pool, disrupting social structures and reducing population viability. Recent post-2020 studies link climate change to OSR shifts across latitudes, with warming temperatures exacerbating TSD in reptiles and altering phenology in waterfowl; for example, a 2024 study observed changes in adult sex ratios in duck species including mallards, potentially leading to male-biased OSR due to sex-specific vulnerabilities.^[24]^[25]^[5]

Consequences of OSR

Impact on Mating Systems

A male-biased operational sex ratio (OSR), where receptive males outnumber receptive females, typically promotes polygynous or promiscuous mating systems in which males engage in intense competition for access to limited females. This bias intensifies male-male rivalry, leading to increased mate guarding behaviors to prevent female desertion and the evolution of alternative reproductive tactics, such as sneaking copulations, to circumvent dominant males.^[8] In such systems, the scarcity of females relative to males heightens the potential for polygyny, as successful males may monopolize multiple partners while many males remain unmated.^[26] Conversely, a female-biased OSR, with more receptive females than males, fosters polyandrous mating systems or sex-role reversal, where females compete more aggressively for male partners. In species like pipefish, where males provide parental care through brood pouches, this bias results in females courting males, displaying ornaments, and engaging in intrasexual competition, while males become choosier about mates.^[27] Such role reversals reduce pair bonding duration and shift investment toward female competition for male availability.^[26] Skewed OSRs in general amplify the intensity of intrasexual competition within the more abundant sex, influencing key aspects of mating interactions such as the duration of pair bonds and the defense of territories or resources.^[8] When one sex predominates, members of that sex experience heightened rivalry for mating opportunities, which can shorten or destabilize pair bonds and escalate territorial conflicts to secure access to potential mates.^[1] The OSR interacts with resource distribution in shaping mating systems, as outlined in the Emlen-Oring model, where a biased OSR favors resource-defense polygyny over lekking when resources are patchily distributed and defensible by the competing sex. In male-biased scenarios, males are more likely to defend clustered resources to attract females, promoting polygynous structures, whereas balanced or female-biased OSRs may support monogamy or female defense if resources align with parental care asymmetries.^[9] Post-2020 studies have further demonstrated that OSR predicts sex-role flexibility, particularly in response to population density changes, with shifts in density altering the relative availability of sexes and prompting rapid adjustments in competitive behaviors across taxa.^[28] For instance, experimental manipulations of density alongside OSR have shown that increased density in female-biased populations enhances female intrasexual competition and role reversal, highlighting the dynamic interplay in mating system evolution.^[29]

Effects on Sexual Selection

A biased operational sex ratio (OSR) significantly influences the opportunity for sexual selection by altering the variance in reproductive success between the sexes. When the OSR favors the rare sex, individuals of that sex experience heightened variance in mating opportunities, as competition among the abundant sex intensifies for access to limited partners, thereby amplifying the potential for selection on traits that enhance competitive ability or attractiveness. Conversely, a bias toward the abundant sex reduces variance for the rare sex, potentially weakening selection pressures on it. This dynamic underscores how OSR acts as a key predictor of the overall intensity of sexual selection across diverse taxa.^[30] The direction of sexual selection—whether intrasexual or intersexual—shifts with OSR biases. In male-biased OSR scenarios, intrasexual competition among males escalates, favoring the evolution of traits such as weapons (e.g., antlers) or elaborate displays that facilitate male-male rivalry for mates.^[8] Female-biased OSR reverses this pattern, promoting intersexual selection where males compete through courtship displays or resources to attract choosy females, while female-female competition may emerge for male access.^[31] These shifts highlight OSR's role in determining the primary mode of mate competition, with empirical evidence showing stronger male-male agonism in populations with male-biased OSR.^[8] Prolonged male-biased OSR contributes to the evolution of sexual dimorphism by intensifying selection on male traits, leading to greater male body size, weaponry, or ornaments relative to females. In polygynous primates, empirical studies link higher degrees of sexual size dimorphism to male-biased OSR, as chronic competition drives divergence in morphology that enhances male fighting ability or mate-guarding efficiency.^[32] In birds and insects, OSR biases correlate with the direction and opportunity for sexual selection, supporting patterns of exaggerated male ornaments and dimorphism levels over evolutionary timescales.^[33] OSR integrates with Bateman's principle to explain amplified sex differences in reproductive variance, where the sex investing more in offspring (typically females) faces stronger selection due to limited mating opportunities, while OSR biases exacerbate variance in the less-investing sex. The Bateman gradient, measuring fitness gains per mating, complements OSR by quantifying how biases translate into differential selection strength; for instance, male-biased OSR steepens the male Bateman gradient, intensifying selection on male traits.^[30] This integration reveals that OSR modulates the baseline asymmetries from Bateman's principle, with the investing sex under persistent selection regardless of bias direction.^[34] Despite these effects, OSR's influence on sexual selection has limitations, as alternative reproductive tactics (ARTs) such as satellite or sneaking behaviors can mitigate intense competition in biased scenarios by allowing subordinate males to bypass direct rivalry. Recent models incorporating population density and latitude further refine OSR predictions, showing that higher densities amplify OSR effects on selection intensity, while latitudinal gradients modulate responses in display behaviors across taxa like fish. These advancements highlight the need to contextualize OSR within broader ecological factors to avoid overgeneralizing its role.^[29]

Measurement and Empirical Studies

Methods for Estimating OSR

Direct observation remains a foundational method for estimating the operational sex ratio (OSR), involving the direct counting of sexually receptive individuals during breeding periods. Researchers typically monitor behaviors indicative of readiness to mate, such as calling in males or gravidity in females, often at peak breeding times to capture the pool of available mates. For instance, in field studies of amphibians and insects, observers tally vocalizing males relative to egg-laying females along breeding sites. However, this approach faces challenges, including incomplete detection of cryptic or hidden behaviors, which can bias estimates toward more conspicuous sexes.^[35] Proxy measures offer an indirect way to approximate OSR when direct counts are infeasible, often adjusting the adult sex ratio (ASR) for differences in maturation timing, parental care duration, or potential reproductive rates (PRR). A common formula is the adjusted OSR = ASR × (male PRR / female PRR), where PRR represents the maximum number of offspring each sex can produce per unit time, accounting for factors like gestation or lactation that limit female availability. This method, rooted in the understanding that OSR deviates from ASR due to sex-specific reproductive constraints, is particularly useful in species with asynchronous breeding.^[36] Temporal sampling addresses the dynamic nature of OSR by tracking ratios across breeding cycles or seasons to account for fluctuations driven by arrival, departure, or mortality of receptive individuals. Repeated censuses at fixed intervals allow researchers to model availability over time, revealing patterns such as male-biased OSR early in the season shifting toward parity as females arrive. Statistical techniques like capture-recapture models can estimate the size of the receptive pool by accounting for detection probabilities and movement, enhancing accuracy in mobile species.^[15]^[14] Experimental manipulation of OSR tests causal relationships by altering sex ratios in controlled enclosures or semi-natural settings, such as adding or removing individuals to create biased conditions. This approach, applied in studies of fish and insects, isolates OSR's effects on mating behaviors while controlling for other variables. Ethical considerations are paramount in wild populations, including minimizing stress and ensuring non-lethal interventions to avoid disrupting natural dynamics.^[19] Modern tools have advanced OSR estimation through genetic markers and technology for non-invasive assessments. Genetic parentage analysis using microsatellite loci or SNPs infers effective OSR by reconstructing mating events and identifying the number of participating individuals, providing a retrospective view of the breeding pool. Post-2020 innovations include drone-based surveys equipped with high-resolution cameras to count receptive animals from afar, as demonstrated in sea turtle nesting sites where aerial imagery reveals male-female ratios during mating aggregations. Emerging AI algorithms further process drone footage for automated sex identification, reducing human bias and enabling large-scale monitoring in challenging habitats.^[37]

Case Studies Across Taxa

In birds, the red-winged blackbird (Agelaius phoeniceus) exemplifies how a male-biased operational sex ratio (OSR) arises from behavioral timing, with males arriving at breeding sites earlier than females to establish territories, creating an imbalance that favors polygynous mating systems where some males secure multiple mates.^[38] This early male arrival skews the OSR toward males during the initial breeding period, intensifying male-male competition and allowing dominant males to achieve higher reproductive success through polygyny.^[39] Across avian species, latitudinal studies reveal gradients in sexual selection pressures, showing stronger intensity at higher latitudes for most species (driven by factors like seasonality), though reversed patterns occur in certain lineages such as frugivores, highlighting ecological influences on mating dynamics.^[40] In amphibians, the strawberry poison frog (Dendrobates pumilio) demonstrates how environmental factors like clutch loss can skew the OSR. In this species, where males provide tadpole transport, clutch predation or failure increases male parental investment time, reducing the number of available receptive males relative to females and resulting in a less male-biased OSR, as confirmed by field observations across three seasons.^[41]^[42] Among fish, laboratory studies on the Japanese medaka (Oryzias latipes) illustrate how OSR manipulations alter variance in mating success, with male-biased OSR increasing male intrasexual competition and reducing average male reproductive output while elevating success for dominant individuals.^[43] Synchrony in female receptivity further mediates this effect, as clustered female availability heightens the OSR bias and variance in male mating outcomes under controlled conditions.^[44] In contrast, the broad-nosed pipefish (Syngnathus typhle) shows role reversal under female-biased OSR, where limited male brooding capacity creates an excess of receptive females, prompting female-female competition and male choosiness in mate selection.^[45] This bias persists across breeding cycles, reinforcing polyandrous tendencies and female ornaments.^[46] Mammalian examples include northern elephant seals (Mirounga angustirostris), where extreme male-biased OSR stems from high male mortality during aggressive contests and female breeding synchrony, culminating in harem polygyny dominated by a few alpha males.^[47] Males fast for up to three months while defending harems, leading to biased OSR as females aggregate briefly on beaches, with only 2-4% of males achieving most matings due to this imbalance.^[48] Cross-taxa syntheses underscore OSR's role in sex role evolution, with a 2024 analysis of shorebirds linking male-skewed adult sex ratios (a proxy for OSR) to reversed roles like polyandry and male parental care, explaining 31-43% of variance across 41 species.^[28] In conservation contexts, harvesting in populations like impala (Aepyceros melampus) skews OSR toward females by selectively removing males, reducing population density and altering mating systems, with implications for demographic recovery post-management changes.^[49]

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