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Polygyny threshold model

The polygyny threshold model is an evolutionary framework in behavioral ecology that predicts females will tolerate polygyny—mating with a male already paired with other females—only if the net fitness gains from his superior resources or territory exceed the fitness achievable through monogamy with an unpaired, lower-quality male, thereby defining a resource-based "threshold" for adaptive polygynous choice. Formulated by Gordon H. Orians in 1969, the model assumes greater female parental investment leads to choosiness, with polygyny arising when ecological variability in male quality creates disparities where sharing a top-tier male outperforms solo pairing with inferiors. The model's core graphical representation plots female fitness against male resource quality, showing a curve for primary females and a lower, parallel curve for secondaries, with the as the point of intersection where choices equilibrate. Empirical validation includes experimental manipulations in red-winged blackbirds (Agelaius phoeniceus), where females preferred high-quality territories despite existing mates, confirming compensatory benefits offset sharing costs like reduced . Extensions to mammals highlight similar dynamics, with favored in resource-heterogeneous environments. In human societies, the model illuminates historical polygyny prevalence—documented in over 80% of preindustrial cultures—where wealthy s monopolize mates, potentially elevating reproductive success via resource access, though generalized versions incorporating male choosiness forecast reduced polygyny under extreme wealth due to surplus low-status males competing unsuccessfully. Defining characteristics include its emphasis on in decisions driven by fitness maximization, rather than male , challenging assumptions of inherent female detriment in polygyny. Notable controversies encompass reassessments questioning static thresholds amid temporal variability or offspring quality trade-offs, and critiques positing overlooked sexual conflicts where male interests diverge from female optima. Despite modifications, the model remains foundational for understanding , privileging causal links between , sex roles, and reproductive strategies over normative cultural interpretations.

Origins and Historical Development

Initial Proposal by Gordon Orians

Gordon H. Orians introduced the threshold model in his 1969 paper "On the Evolution of Mating Systems in Birds and Mammals," framing it within a theory of female mate selection aimed at maximizing individual . The model addresses resource-defense , where males control varying in quality due to habitat heterogeneity, and females must decide between monogamous pairing with a lower-quality male on a suboptimal or sharing a higher-quality male and . Orians posited that females should enter unions only if the benefits from superior resources exceed the costs of divided male and resource allocation, defining a "" as the critical disparity in territory productivity that tips the balance toward . Central assumptions include greater , making females the sex-limited ; male defense of territories as proxies for female reproductive potential; and a inherent cost to for females on equivalent territories, stemming from reduced per-female access and male assistance. Orians emphasized ecological drivers, predicting 's in contexts of pronounced variation, such as mammals (where male is lower) over , precocial over altricial , and habitats like marshes or early-successional stages with patchy, defensible over uniform terrestrial ones. The model also forecasts polyandry's rarity, as role reversals in are uncommon, and links to traits like widespread grounds paired with restricted nesting sites. This economic approach treated female choice as adaptive optimization, integrating habitat quality with male attributes to explain polygyny's persistence despite apparent biases in many taxa. Orians' predictions aligned partially with observed patterns, such as higher rates in mammals (around 10-15% of species versus under 5% in ), though incomplete fits highlighted needs for refinement, including imperfect information and genetic factors. The proposal shifted focus from male-male competition alone to female-driven evolutionary dynamics, influencing by underscoring causal links between environmental variance and mating strategies.

Early Theoretical Refinements (1970s–1980s)

In 1977, Stephen T. Emlen and Lewis W. Oring integrated the into a broader ecological theory of , positing that mating strategies arise from constraints on access to critical resources and mates, with females evaluating the net benefits of based on male-controlled breeding conditions versus unpaired alternatives. Their framework emphasized the and differential as factors modulating the threshold, predicting where high-quality males monopolize superior habitats, forcing some females to share mates rather than settle for inferior monogamous options. This refinement shifted focus from static territory quality to dynamic ecological pressures, including temporal variability in resource availability that influences female choice timing. James F. Wittenberger further developed the model in the late and early by incorporating temporal dimensions, such as the sequence of male establishment and mate searching, which he argued could alter the effective polygyny threshold by affecting knowledge of options. In a 1981 analysis, Wittenberger critiqued assumptions of and uniform assessment, proposing that continuous variation in leads to probabilistic decisions, with secondary females achieving comparable to primaries only in optimal sites. He also examined interference costs among co-mates, suggesting these reduce the threshold in dense populations but maintain polygyny where male variance exceeds such deductions. Concurrently, Jack Verner proposed dual models for evolution in 1977, distinguishing resource-defense systems—where territory productivity sets the —from scenarios emphasizing male defense of multiple s, refining Orians' original emphasis on alone by weighing male behavioral traits in calculations. These extensions highlighted potential synergies between male phenotypic indicators (e.g., complexity or display vigor) and holdings, anticipating later integrations of genetic benefits like enhanced offspring attractiveness. By the early , reassessments, such as those questioning untested assumptions about competitiveness, underscored the need for empirical validation of predictions across with varying ecological constraints.

Theoretical Foundations

Core Assumptions

The polygyny threshold model posits that female evolves such that females accept polygynous with a high-quality male when the benefits from his superior resources exceed those from monogamous with a lower-quality male. Central to this is the assumption of asymmetric between sexes, with females committing greater resources to gametes, , and care, rendering them more selective in to maximize . This disparity, formalized by Orians in , implies males compete primarily for access to females rather than direct parental roles, while females prioritize partners enhancing survival through resource provision. A second key assumption is that males vary in their ability to defend or control resources critical to female , such as territories with food abundance in or other provisioning s, leading to uneven distribution of opportunities. Females are presumed capable of assessing this variation, comparing the from sharing a resource-rich (despite diluted male investment or female-female competition) against exclusive access to a poorer one. The itself emerges when the resource quality differential offsets costs, typically modeled as a where curves for primary and secondary females intersect. Further assumptions include that male , if provided, declines modestly with size—insufficient to negate benefits from elite territories—and that females distribute themselves ideally, akin to selection models, without density-dependent interference below the . These elements collectively predict prevalence in resource-heterogeneous environments, though empirical tests reveal sensitivities to unmodeled factors like predation or male deception.

Fitness Benefits and Costs

In the polygyny threshold model, females accrue benefits from polygynously when the of a male's or resources exceeds that of available monogamous alternatives, enabling higher production or survival despite shared access to the male. Specifically, superior males defend territories with abundant food or nesting sites, which can elevate female above the threshold where the net gain from surpasses the attainable from sole pairing with a lower- male. This benefit arises because female is often resource-limited, and the marginal value of additional resources from a high- site compensates for dilution effects. Conversely, costs to female fitness in polygyny include reduced per capita paternal investment, as the male divides time, protection, and provisioning among multiple mates, potentially lowering offspring viability or quantity for secondary females. Resource sharing among co-mates can intensify intraspecific competition, further eroding individual fitness gains, particularly if territory quality does not scale sufficiently with harem size. The model posits that these costs are weighed against benefits, with polygyny favored only when the polygyny threshold—defined as the minimum resource differential required to offset sharing penalties—is met; below this threshold, monogamy yields higher fitness due to exclusive male support. Theoretical refinements emphasize that male quality influences both benefits and costs: high-quality males may mitigate dilution through greater absolute investment capacity, but fixed costs like guarding or remain, potentially rendering suboptimal if female alternatives improve. Empirical analogs in species like support this , though model assumptions of costs across contexts have faced reassessment, highlighting variability in how impacts nestling or fledging rates.

Mathematical and Graphical Representation

Key Equations and Variables

The polygyny threshold model formalizes through comparisons between monogamous and polygynous options, where s accept polygyny only if compensated by superior resources. Central variables include (or situation) quality, denoted E or q, representing resources like availability that influence ; functions F_m(E) for monogamous pairing, typically an increasing, often sigmoidal or reflecting sole access to resources and male aid; and F_s(E) or F_p(E) for secondary (polygynous) pairing, expressed as F_s(E) = F_m(E) \times (1 - c) or $0.9 \times q, where c (0 < c < 1) captures sharing costs such as reduced male parental investment, intraspecific competition, or resource depletion. The polygyny threshold E^* emerges as the quality level satisfying F_m(E^*) = F_s(E_h), with E_h > E^* denoting a high-quality ; below E^*, yields higher , while above it, females prefer sharing E_h over monopolizing inferior sites. This condition assumes female choice drives mating systems, with males holding fixed varying in E. Extensions incorporate population-level dynamics, where evolves if average polygynous exceeds that of unmated females on low-E sites, modulated by genetic alleles for receptivity and costs to primary females. Empirical parameterizations often set c \approx 0.1 for minor sharing penalties in resource-rich contexts, though values vary by and study.

Standard Graphical Depiction

The standard graphical depiction of the threshold model plots female on the y-axis against or on the x-axis. An upper represents the for a female as the primary (sole) mate on a of given , increasing with due to greater resource availability. A parallel lower depicts the success for a secondary female on the same , shifted downward to account for the of sharing and resources, typically assumed constant as a proportion or fixed decrement. The threshold is illustrated as the minimum increment in required for the secondary female's on a higher- site to match or exceed the primary female's on a lower- site, corresponding to the horizontal distance between the at equal levels. This threshold, first formalized by Orians in 1969, predicts that females accept only when available monogamous options fall below this compensatory difference, favoring resource defense in heterogeneous environments. In depictions with linear or , the threshold remains constant if are parallel, implying consistent across qualities.

Empirical Testing in Non-Human Animals

Experimental Confirmations in Birds

One key experimental test of the involved red-winged blackbirds (Agelaius phoeniceus), a species exhibiting facultative polygyny where territory quality varies significantly. In a 2001 field experiment conducted in , , researchers presented female red-winged blackbirds with a choice between adjacent territories: one held by an unmated male lacking over-water nesting sites (inferior quality, as over-water sites reduce nest predation) and another by an already-mated male possessing such sites (superior quality). Females strongly preferred the polygynous option with superior sites, reversing their typical preference for unmated males observed in prior studies. This preference aligns with PTM predictions, as prior data indicated that polygynous mating reduces female relative to (e.g., via shared male ), but high-quality territories compensate by enhancing nestling survival and fledging rates. The results demonstrate that females weigh the costs of mate-sharing against resource benefits, accepting polygyny only when the latter exceeds a threshold. Support for the PTM extends to normally monogamous species through manipulation experiments inducing polygyny. In prothonotary warblers (Protonotaria citrea), a cavity-nesting species rarely polygynous in natural conditions, researchers in 1991 experimentally created opportunities for bigamy by providing nest boxes in varied habitats. Nine bigamous pairings were induced exclusively in flooded habitats (with higher insect food abundance) despite available monogamous options in dry areas. Secondary females in these pairings achieved comparable fledging success to primary females and monogamously paired counterparts, suggesting that resource-rich environments lowered the polygyny cost below the , prompting female settlement. Male quality covaried with habitat in this setup, reinforcing that females assess net gains from superior provisioning potential over exclusivity. These avian experiments collectively validate core elements: female choice driven by resource compensation for polygyny's intrinsic costs, such as diluted paternal investment. However, outcomes depend on precise manipulations of independent of male traits, as confounding correlations (e.g., attractive males securing better sites) could inflate apparent thresholds in observational data. No evidence from these studies supports alternative explanations like or deception overriding resource assessment.

Field Studies and Comparative Evidence

Field studies in red-winged blackbirds (Agelaius phoeniceus) have experimentally confirmed aspects of the polygyny threshold model. In a 2001 field experiment conducted in Ontario, Canada, researchers presented free-ranging females with adjacent territories: one defended by an unmated male lacking over-water nesting sites (higher predation risk) and another by an already-mated male with over-water sites (superior quality due to reduced nest predation). Females overwhelmingly settled on the mated male's territory, reversing their typical preference for unmated males, indicating that enhanced territory quality offsets the fitness costs of sharing male parental care. Comparative analyses across species, particularly passerines, reveal correlations between frequency and environmental resource variation. In species exhibiting high heterogeneity in quality, such as wetland-dependent , polygynous systems predominate, as females gain net benefits from superior territories despite sharing males; conversely, uniform habitats favor under a reversed threshold framework. For instance, long-term observations in northern lapwings (Vanellus vanellus) demonstrate that climatic fluctuations dynamically shift the threshold, with wetter conditions enhancing prey abundance and increasing rates via improved secondary female success. further modulates this threshold, as secondary females related to primaries experience reduced costs through indirect gains. Despite these supports, field evidence often challenges full compensation in the model. Across multiple studies, secondary females typically fledge 20-30% fewer offspring than primary or monogamous females, with harem position failing to predict reproductive output as predicts; monogamous pairs also initiate breeding earlier than expected if avoiding solely for quality gains. A synthesis of data from over 20 underscores this pattern, attributing discrepancies to unaccounted costs like female-female , male care bias toward primaries, or sampling errors in mate under unpredictable conditions. Applications to non-avian taxa, such as resource-defending mammals and fishes, yield analogous but sparser comparative patterns, where aligns with male-controlled resource variance yet rarely shows complete female fitness equalization.

Applications to Human Mating Systems

Anthropological Correlations with Resource Distribution

In traditional human societies, the prevalence of polygyny correlates positively with the degree of variance in male-controlled resources, particularly in economies where wealth such as livestock or land can be accumulated and defended. Cross-cultural analyses of subsistence-level groups reveal that polygyny is rare among mobile hunter-gatherers, where resource sharing and low individual variance predominate, but becomes common in pastoralist and early agricultural societies permitting wealth disparities. For instance, in the Ariaal pastoralists of northern Kenya, men with larger camel herds (indicating higher resource holdings) acquire more wives, as females benefit from access to superior provisioning despite sharing, consistent with the polygyny threshold model's prediction of female mate choice based on resource quality exceeding monogamous alternatives. Pastoralist societies in exemplify this pattern, with rates often exceeding 30-50% among adult males, directly tied to ownership as a proxy for economic capacity. Among the Maasai, Turkana, and Kipsigis, ethnographic data show that elite males monopolize 40-60% of wives through bridewealth payments in , while poorer men remain unmarried; this resource-driven skew aligns with the model's emphasis on ecological conditions favoring polygynous when high-status males can subsidize multiple females above the for gains. In contrast, egalitarian forager groups like the !Kung San exhibit near-monogamy, with minimal wealth accumulation limiting such disparities. However, population-level analyses introduce nuance: while within-society resource variance predicts among wealthy males, broader cross-national data indicate that extreme inequality may reduce overall frequency by sidelining low-status males from markets altogether, as generalized mutual choice models suggest females avoid very low-resource options entirely. This holds in datasets from the , where intensity tracks heritable, transferable assets (e.g., over ) rather than Gini coefficients alone, underscoring the model's focus on female incentives in variable environments. Empirical support from these correlations validates the threshold as a causal mechanism in human , though institutional factors like rules amplify resource effects in patrilineal systems.

Evidence from Cross-Cultural Data

provide mixed evidence for the polygyny threshold model () in human societies, with support primarily from within-population analyses showing female preferences for resource-rich males, but weaker or inverse correlations at the between-society level regarding resource inequality and overall prevalence. Among the Kipsigis of , a pastoralist group, women and their families preferentially select mates based on wealth in and , with polygynous unions occurring when a high-status male's resources exceed those available from monogamous pairings with lower-status males; this aligns with PTM predictions, as junior wives in such unions achieved comparable or higher than senior wives due to resource access. Similar patterns emerge in other resource-controlled societies, where rates correlate positively with male economic variance, such as in agropastoralist groups where herd ownership enables multiple marriages. In the (SCCS), forager societies exhibit higher where male provisioning contributes less to subsistence (e.g., below 35% of calories), reducing female dependence and allowing greater tolerance for polygynous arrangements among high-variance providers, though food-sharing norms in these groups often constrain extreme inequality. Ethnographic data across 849 societies indicate in over 80%, often linked to male control of divisible resources like or crops, supporting PTM's emphasis on resource thresholds over . However, a reanalysis of 11,813 marriage records from 29 populations (foragers to agriculturalists) reveals no overall positive correlation between wealth () and prevalence; instead, greater inequality predicts less polygyny in agricultural societies (β < 0), attributed to diminishing fitness returns from additional wives (δ < 1) and fewer viable high-resource males under mutual mate choice. These findings challenge strict PTM applications across societies, suggesting extensions incorporating male choosiness and economic constraints better explain variation, though within-population resource benefits for females persist.

Criticisms and Limitations

Theoretical Inconsistencies and Assumptions

The polygyny threshold model assumes that female mate choice is driven solely by comparisons of expected fitness gains from resources controlled by males, with polygyny favored when the per-female benefits from a superior male exceed those from a monogamous pairing with an inferior male. This framework posits linear or threshold-based resource apportionment among co-mates, implying minimal dilution of male investment or female-female interference costs. However, the model overlooks diminishing marginal returns to additional mates, where each successive female receives progressively less benefit due to fixed male resources, constraining polygyny even among high-quality males. A core inconsistency arises from the model's unilateral emphasis on female choice, treating males as passive acceptors of multiple mates despite theoretical costs such as increased energy demands or reduced offspring viability per female. Incorporating mutual mate choice reveals that extreme resource inequality—predicted by the standard model to boost polygyny—actually suppresses it, as low-quality males remain unpaired and the proportion of viable polygynous males declines. This "polygyny paradox" undermines the model's generality, as it fails to predict observed patterns without ad hoc adjustments for male selectivity and female competition. The assumption of accurate female assessment of long-term fitness returns is theoretically problematic, as it requires perfect information on unpredictable factors like male provisioning consistency or offspring survival, potentially leading to suboptimal choices in variable environments. Furthermore, the model's resource-centric view conflicts with alternatives emphasizing genetic benefits, such as the , where polygyny persists via heritable male attractiveness rather than material thresholds, highlighting an incomplete causal mechanism for mating system evolution. These gaps indicate that the , while parsimonious, demands extensions for realism, including variable female quality and nonlinear fitness functions.

Empirical Challenges in Natural Populations

In field studies of avian species exhibiting territorial polygyny, such as pied flycatchers (Ficedula hypoleuca), secondary females mating with already-paired males consistently demonstrate reduced reproductive success relative to monogamous females, with no measurable compensation from enhanced territory quality or male-provisioned resources, thereby undermining the core prediction that females only enter polygynous unions when benefits exceed monogamous alternatives. A 2022 analysis of 1,248 breeding attempts over 15 years revealed that secondary females produced 28% fewer fledglings on average, attributing this disparity to diminished male assistance in chick provisioning rather than territorial advantages, as nestling survival rates did not offset the costs of mate-sharing. Comparable patterns emerge in collared flycatchers (Ficedula albicollis), where long-term monitoring of over 10,000 nests from 1980 to 2022 showed secondary females achieving 15-20% lower fledging success and recruitment rates into the breeding population, without evidence of fitness equalization through superior male-held resources; researchers concluded this reflects females settling for suboptimal options amid settlement constraints, rather than adaptive threshold-crossing. These findings align with broader meta-analyses across 20+ polygynous bird species, where secondary female fitness deficits persist in 70% of cases, often linked to unpredictable male investment dilution and female arrival timing, complicating direct tests of resource-based thresholds in uncontrolled natural settings. Quantifying the polygyny threshold proves empirically elusive in wild populations due to confounding variables, including spatial habitat heterogeneity, stochastic environmental factors, and inter-female aggression, which alter effective resource access and male care allocation beyond simple territorial metrics. For example, in red-winged blackbirds (Agelaius phoeniceus), field observations indicate that while territory quality correlates with male mating success, female choices frequently ignore predicted thresholds, potentially due to deception by males exaggerating resource availability or coercive tactics, as evidenced by experimental territory manipulations yielding inconsistent female responses. Temporal uncertainties in breeding phenology further obscure tests, as early-arriving females secure monogamous pairings while latecomers face inflated costs without proportional benefits, masking underlying causal dynamics. Alternative explanations, such as sexual conflict over paternal care or enforced polygyny via female defense, gain traction in populations where resource variance alone fails to predict polygyny rates; in species like blue tits (Cyanistes caeruleus), aggressive interactions among females for access to high-quality males reduce the explanatory power of voluntary threshold decisions, with secondary females often incurring uncompensated risks of predation or starvation for offspring. These challenges highlight systemic limitations in applying the model to natural systems, where indirect genetic benefits or kin selection effects—rarely isolated in field data—may interact with direct resource cues, yet empirical support remains sparse outside controlled experiments.

Extensions and Recent Developments

Mutual Mate Choice Integrations

Extensions to the (PTM) have incorporated mutual mate choice by accounting for male selectivity alongside female preferences, challenging the original assumption of indiscriminate male acceptance of mates. In population genetic frameworks applied to polygynous systems, such as those in birds, male mate choice evolves when preferences target heritable female traits conferring direct fitness benefits, like fertility or viability, rather than arbitrary ornaments. These models assume decoupled genetic loci for male and female choice, with male preferences persisting only if they enhance courtship efficiency or offspring viability; under such conditions, polygyny stabilizes even with choosy males, as high-quality females pair preferentially with superior males, amplifying sexual selection dynamics. Mutual choice integrations reveal that female decisions to enter polygyny depend not only on resource thresholds but also on male willingness to invest in secondary mates, potentially lowering the effective polygyny threshold if males reject lower-quality females. For instance, in systems with variance in female quality, males may prioritize primary mates with superior traits, forcing secondary females to accept reduced paternal care or seek unpaired males, thus modulating overall polygyny prevalence. Empirical patterns in avian species, like blue tits, support this by showing male aggression and preference influencing female settlement, suggesting bidirectional choice over unidirectional female-driven models. In human applications, mutual mate choice extensions generalize PTM to predict polygyny levels based on both sexes' strategies, assuming diminishing fitness returns to additional wives (δ < 1) and a two-class wealth distribution. Rich males attract multiple wives only up to a point limited by male demand for high-fertility females and resource sharing costs; greater wealth inequality (fewer rich males) reduces polygyny fractions, as poor males remain unmated and rich males cannot monopolize due to saturation effects. Cross-cultural data from 29 societies, spanning hunter-gatherers to agriculturalists, corroborate this, with δ estimates below 1 in most cases and lower elite fractions correlating with reduced polygyny, resolving the observed inverse inequality-polygyny relationship.

Contemporary Studies on Inequality and Fitness Outcomes (2000s–Present)

In avian species, long-term field studies have quantified fitness costs for secondary females, revealing that resource inequality often fails to fully compensate for sharing males. A 32-year study of (Passerculus sandwichensis) from 1992 to 2023 found that secondary females produced 28% fewer fledglings and had 15% lower lifetime reproductive success compared to primary females or monogamous breeders, attributed to reduced male provisioning amid variable insect availability as a proxy for resource distribution. Experimental manipulations in (Agelaius phoeniceus) during the early 2000s confirmed the model's prediction that females accept polygyny only when territorial food supplementation elevates benefits above monogamous alternatives, with unsupplemented secondary nests showing 20-30% lower nestling survival due to diluted paternal care. Mammalian studies from the 2010s onward highlight context-dependent outcomes tied to environmental inequality. In Alpine marmots (Marmota marmota), a 2022 analysis of 30 years of data across varying altitudes (resource gradients) showed high polygyny rates (up to 40% of groups) with minimal fitness costs for co-breeding females when burrow density was high, as shared vigilance offset infanticide risks; however, in low-resource years, secondary females experienced 12% higher pup mortality. Raptor research in 2016 on Montagu's harriers (Circus pygargus) demonstrated spatially dynamic thresholds, where drought-induced prey scarcity (measured by small mammal abundance) raised the polygyny threshold, reducing secondary female acceptance by 25% and correlating with 18% lower chick fledging rates in shared nests. Human cross-cultural data challenge the model's universality, often indicating uncompensated costs despite resource inequality. Among the Tsimane forager-horticulturalists of Bolivia, a 2013 intra-individual analysis of 200+ women tracked longitudinally found polygynous wives averaged 1.5 fewer surviving children over their reproductive lifespan than if monogamously paired with equivalent husbands, linked to resource competition among co-wives rather than male wealth alone. A 2018 reanalysis of ethnographic data from 46 societies generalized the PTM to mutual mate choice, revealing an inverse relationship: higher Gini coefficients for wealth inequality (>0.6) predicted 15-20% lower polygyny prevalence, as unpaired low-status males reduced female willingness to share high-status partners, prioritizing monogamous access over diluted benefits. Recent extensions emphasize reproductive skew as a of -fitness trade-offs. A comparative study across 150+ and populations quantified male reproductive (Gini for number) at 0.4-0.7 in polygynous systems, but lower in humans (0.3-0.5) due to cultural norms amplifying costs; simulations showed that beyond a 20% resource disparity , dips unless paternal scales proportionally, which rarely occurs empirically. These findings underscore that while can drive polygynous decisions in theory, real-world frictions like incomplete compensation frequently yield net losses for secondary mates.

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