Encyclopedia of Animal Cognition and Behavior

Living Edition
| Editors: Jennifer Vonk, Todd Shackelford

Polygyny Threshold Model

  • Gaute GrønstølEmail author
Living reference work entry
DOI: https://doi.org/10.1007/978-3-319-47829-6_460-1



The polygyny threshold model is a framework proposed to describe optimal female mate choice in resource defense polygyny systems. The polygyny threshold is defined as the increase in breeding resources required to offset costs of sharing a territory with another female.


Until the 1960s, polygyny was largely considered a result of an excess of female to male breeders (Searcy and Yasukawa 1989). This explanation was found inadequate as it became clear that it is fairly common to see territorial males remaining unmated despite courtship efforts, while neighboring males mate polygynously. In the mid-1960s, the polygyny threshold model (hereafter the PTM) was proposed as an adaptive explanation to this phenomenon (Orians 1969; Verner 1964; Verner and Willson 1966).

Since its inception, the PTM has been applied on a wide range of organisms that exhibit social resource defense polygamy, including birds, mammals, fishes, reptiles, amphibians, and invertebrates. The threshold mechanism in the PTM is identical for polyandrous and polygynous systems, so the “Polygamy Threshold Model” would be a more appropriate term (Gowaty 1981), but because the model initially was proposed for polygynous birds, and because social polygyny is far more common than social polyandry, the term “Polygyny Threshold Model” has been most widely used.

How the PTM Works

The PTM describes the mating pattern in resource defense polygyny systems. Unlike in lek polygyny, female defense polygyny, and scramble polygyny, males in resource defense polygyny systems provide breeding resources to the female and offspring. They defend breeding territories which often hold food or other valuable resources, and they often take part in parental activities like food provisioning, incubation, and defense against predators. The breeding territories are typically aggregated in clusters, and females have the opportunity to evaluate several males before making their mate choice.

In the PTM the breeding resources offered by individual males are thought to vary, and to maximize reproductive success (i.e., number of offspring raised), a female should settle with the male breeder that offers the most. Male breeding resources are typically finite (e.g., food resources on the territory, or time spent by male incubating or feeding young), and monogamous females may take advantage of all resources the male offers. Females in polygynous dyads, however, have to share the breeding resources and experience sharing costs in the form of loss of breeding resources to the other female. Therefore, when a female considers settling as a secondary female, she should subtract the expected sharing costs from the overall resources offered by the male. If she finds that the territory still yields more breeding resources than available bachelor-held territories, the polygyny threshold is exceeded and she should prefer polygyny over monogamy (Orians 1969; Verner 1964; Verner and Willson 1966). All females that settle in a breeding cluster are expected to make this calculation for the available breeding territories before making their mate choice, and female settlement should follow an ideal free distribution with the most resourceful males becoming polygynous and the poorest males either having to settle for monogamy or remaining unmated.

Early variants of the PTM used aspects of territory quality (denoted as environmental quality in Fig. 1) as predictors of female mate choice. In time, it became clear that offspring survival was also affected by male parental effort and male skills (e.g., breeding experience, competitive skills, foraging skills, and skills and resolve to defend against predators) (Davies et al. 2012; Webster 1991). Male attractiveness was also proposed to be a genetic trait that the offspring might benefit from inheriting (Weatherhead and Robertson 1979). This identified the problem of how to decide on which traits mate-prospecting females find most valuable and base their mate choice on – male characteristics, territory characteristics, or a mix of both. Territory quality (or environmental quality) was therefore substituted with the term male “Breeding Situation Quality” (BSQ), which represents the sum of resources offered by males that affect the breeding outcome, and ultimately the reproductive fitness of females (Wittenberger 1981). Instead of trying to pinpoint which cues females use to choose a mate, the assumption is then made that females choose the best males available at the time of their settlement. The first chosen male in a breeding cluster is considered to have the highest BSQ, BSQ then declines over the colonization order, and males that are chosen last or remain unmated are assigned the lowest BSQ (Searcy and Yasukawa 1989).
Fig. 1

A graphical representation of the PTM modified from Orians (1969). The upper diagonal line gives the expected reproductive success for a monogamous female and the lower line for bigamous females. The dotted lines denote the environmental quality or Breeding Situation Quality (BSQ) of territories (a) and (b). The vertical short-dashed line between the diagonals indicates the sharing costs for bigamous females on the best territory (b) in terms of reduced reproductive success. The horizontal long-dashed line between the diagonals indicates the increase in BSQ needed to offset these costs, i.e., the polygyny threshold. As the threshold balances the costs of sharing, the monogamous female on territory (a) has equal prospects of reproductive success to a bigamous female on territory (b). A larger difference in BSQ favors bigamy, and a smaller difference favors monogamy

Assumptions of the PTM

The PTM rests on the following assumptions:
  • Females experience costs associated with sharing a mate.

  • There is variation in male BSQ across the breeding population.

  • Females can accurately assess BSQ of the males in the system.

  • Females value BSQ on a similar scale.

  • Females prefer breeding territories that offer the highest amount of BSQ.

  • Females are equal in quality and distribute according to offered BSQ in an ideally free fashion (i.e., after settlement, the number of breeders on the territories is proportional to the amount of resources available on the territories).

A critical requirement for the PTM is that females experience a cost associated with sharing a territory with another female breeder. If not, no threshold needs to be compensated and other mechanisms may better explain the dynamics of the mating system (Pribil 2000; Searcy and Yasukawa 1989).

Predictions Derived from the PTM

A number of predictions may be derived from the PTM, but some of the main ones are related to settlement order, reproductive success for females, and male attractiveness.
  • Settlement order: Using the settlement order as a proxy for BSQ, the first settled territories should have highest BSQ and reach polygynous status first, and:
    • Primary polygynous females should precede monogamous females in the settlement order.

    • There should be a positive correlation between BSQ and harem size.

  • Reproductive success: If secondary females are compensated for costs associated with sharing a breeding territory, they should on average have access to as much BSQ as simultaneously settling monogamous females, and:
    • Secondary females should have similar reproductive success to contemporary monogamous breeders.

  • Male attractiveness: Using harem size as a female preference criterion, polygynous males should be preferred as genetic sires over monogamous males:
    • The proportion of genetic paternity loss should be lower for polygynous males than for monogamous males.

Tests of the PTM Predictions

Species-specific life-history constraints and varying ecological factors have shaped variants of resource defense polygyny which to some extent differ in cost–benefit trade-offs, and over the years modifications have been made to the PTM to tailor it to specific variants (Andersson 1994; Davies et al. 2012; Garson et al. 1981; Grønstøl et al. 2003; Leonard 1990; Searcy and Yasukawa 1989; Slagsvold and Lifjeld 1994). Since the 1960s, numerous studies have tested the predictions of the PTM listed above, and the overall conclusions are: (1) harem size does not overall correlate with settlement order, (2) monogamous females tend to breed earlier in the settlement order than predicted by the PTM, (3) monogamous females perform on average better than secondary females in terms of offspring production, and (4) polygynous males do not suffer less cuckoldry than monogamous males. All of these conclusions are contrary to expectations from the PTM.

There have been many suggestions for how to explain the lacking empirical support of the PTM predictions. These include sexy-son effects, i.e., that reproductive fitness benefits of polygyny may be genetic and manifested as quality rather than quantity of offspring, an excess of breeding females to breeding males, and maladaptive female choice because (1) males deceive females into believing that they are unmated, (2) mate sampling may be costly and the opportunities to engage in mate sampling may be restricted, or (3) the environment is unpredictable and females may be unable to foresee unfortunate changes that may occur after they have made their mate choice. Although some of these explanations may be relevant in some mating populations, neither of them seems likely to provide a general explanation for why predictions are not met (Davies 1989; Grønstøl et al. 2003).

Revisiting the PTM Assumptions

So, empirical results indicate that the PTM does not accurately describe the settlement dynamics in resource defense polygyny systems. For instance, empirical results place monogamous females earlier in the breeding order than expected. Why so? After all it seems reasonable to assume that the earliest female settlers choose the best available males, and that subsequent settlers also consider these as premium territories, resulting in these earliest settled territories becoming polygynous. Could it be that some early settling females remain monogamous because it is in their interest to do so, and that they are able to enforce monogamy by denying access for subsequent female mate prospectors despite male courtship attempts?

Common for most studies modeling variants of the PTM is the underlying assumption that females are equally resourceful and introduced sequentially to choose a mate in a system with a seasonal decline in reproductive success, in a manner conforming to the ideal free distribution. If females settle with mates in an ideally free fashion, it should in essence be a zero-sum game for the females, but what if it is not? When PTM was proposed and onwards for quite some time, research on mate choice and sexual selection was very much focused on variation in male quality and in the expression of male sexual ornaments considered attractive by females. Female traits and strategies to influence the mating outcome was not so much the focus of attention (Rosenqvist and Berglund 1992). Since then, however, a bulk of studies have shown that females differ individually, much like males do, and that females act in their own interests to maximize their reproductive fitness. This gives reason to question the validity of the equal-female assumption.

Sexual Conflict and the PTM

What are the female interests in resource defense polygyny? When there is a cost associated with sharing a male, resident females experience a reduction in BSQ with the addition of a secondary female on the territory. This should motivate resident females to oppose polygyny and try to enforce monogamy. Males, however, are likely to increase the number of offspring they produce if able to attract more mates, so they should strive for polygyny. This highlights a sexual conflict – a conflict of interests between the male and female in a pair-bond over how males should allocate their breeding resources (Davies 1989; Davies et al. 2012; Parker 1979; Trivers 1972).

Some authors realized decades ago that the PTM did not accommodate this sexual conflict. In one of their papers on Dunnocks (Prunella modularis), Davies and Houston (1986) commented that: “there is a more general reason for why the [polygyny threshold] model is likely to fail in predicting observed mating systems – namely, it largely ignores conflicts of interests between individuals,” and Krebs and Davies (1993) stated in their textbook on Behavioral Ecology that “The assumptions of the PTM are like those of ‘the ideal free distribution’” … [and] … “that ideal free conditions rarely hold in nature because dominant individuals attempt to grab more than their fair share of resources.”

Division of BSQ on Polygynous Territories

The original PTM assumes that females sharing a polygynous territory divide the BSQ evenly. This is probably not the case because BSQ appears to be economically defendable units that females compete over (Emlen and Oring 1977). It has been pointed out that different rules for sharing costs between primary and secondary female will yield different PTM-predictions (e.g., secondary females bearing 50% of the sharing costs vs. being forced to bear up to 100% of the costs) (Altmann et al. 1977; Davies 1989). Several factors are likely to contribute to a nonequal sharing of BSQ.

Individual Differences in Female Competitive Strength

It is quite common to see resident females behaving aggressively towards secondary mate prospectors, and many studies have found that females vary in competitive strength. It seems reasonable to interpret this aggression as attempts to monopolize their male, or to gain more than their fair share of the BSQ (Davies 1989; Slagsvold and Lifjeld 1994; Wittenberger and Tilson 1980).

Degree of Synchrony Between Females in Polygynous Dyads

The competition over the BSQ increases with increasing temporal overlap between the primary and secondary female (Leonard 1990; Slagsvold and Lifjeld 1994). Birds in general seem to have a reproductive fitness premium on breeding early (Perrins 1970), and the optimal timing of breeding is probably determined by a trade-off between costs and reproductive benefits of early breeding. Individuals able to handle the adverse effects of weather and sparse food early in the season generally do better than individuals that breed late. The optimal time of breeding onset is likely to be condition-dependent, and superior individuals may have earlier optima than poorer individuals (Drent and Daan 1980). The early breeders thus enjoy first pick of territory and take advantage of a longer chick growth season, whereas later breeders do the best of a bad job breeding as early as their condition permits. If prospects of reproductive success had not diminished with delayed breeding, secondary females would probably benefit from breeding later relatively to primary females, which would minimize the temporal overlap. But, as it is, females prospecting for secondary mating status probably cannot afford to delay their breeding to reduce the overlap.

Division of Paternal Effort Between the Primary and Secondary Female

In passerine birds, polygynous males often invest more paternal effort in the brood of the primary female than in the brood of the secondary female, and the extent of this inequality often increases with increased asynchrony between primary and secondary females (Slagsvold and Lifjeld 1994; Webster 1991). There are, however, examples of later breeding secondary females not being disfavored by males. It seems sound to assume that males should allocate their paternal effort in a manner that maximizes the return per unit invested. If early chicks have higher reproductive value and count as greater (reproductive fitness) losses than later chicks, the polygynous males might do best prioritizing their primary female. However, if the male could rely on a resourceful primary female to raise the offspring reasonably successfully without assistance, whereas a less resourceful, less experienced secondary female would face a larger risk of failure without male assistance, the male would probably raise more offspring if contributing more help to his secondary female than to his primary female (Grønstøl 2003). The more paternal care a resident female stands to lose to a secondary female, the higher her motivation should be to try to monopolize the BSQ and behave aggressively towards female mate prospectors.

Male Interference to Mitigate Female Attempts at Monopolizing Breeding Resources

In cases where resident females attack females prospecting for secondary mating status, males are sometimes seen to attack the aggressor in what looks like efforts to dissuade the resident females from chasing away the newcomers. This behavior has by several researchers been interpreted as male efforts to facilitate settlement of the female mate prospector. If the prospector is able to settle as a secondary female, recurrent skirmishes may occur with the primary females attacking the secondary females in what gives the impression of being attempts to monopolize as much BSQ as possible. How successful males are in facilitating settlement of secondary females probably depends on their strength and tenacity compared to that of their resident females. Females are sometimes successful in enforcing their interests, whereas the males’ interests prevail at other times (Davies et al. 2012).

Incorporating Varying Female Competitive Strength in the PTM

It seems plausible that ability to monopolize BSQ correlates with female competitive strength. It also seems reasonable to expect female competitive strength to vary individually in a breeding cluster. Therefore, in order to portray the polygynous settlement as accurately as possible, female despotism should be included when modeling resource defense polygyny. Introducing variation in female competitive strength to the PTM requires a revision of the assumptions. One might keep four of the original assumptions:
  • Females experience costs of sharing a mate.

  • Females can accurately assess BSQ of the males in the system.

  • Females value BSQ on a similar scale.

  • Females prefer breeding territories that offer the highest amount of BSQ.

And add some new assumptions:
  • Females differ in competitive strength.

  • Females can assess the competitive strength of other females relative to their own.

  • Females benefit from nesting as early as their condition permits.

  • Competitive strength decreases from first to last settled female.

  • Strong females monopolize resources at the cost of weaker females to a degree determined by the relative difference in competitive strength between the female antagonists.

Running this framework in a simulation where individual differences in female competitive strength are set to approximately match BSQ-differences between males produces a settlement pattern where some of the early females remain monogamous due to successful deterrence of mate prospectors (Grønstøl et al. 2003). From the simulation results, the following can be extracted: (1) harem size does not correlate with settlement order; (2) the settlement order of monogamous females is similar to that of primary females, and monogamous females settle earlier than secondary females; (3) in terms of reproductive success, monogamous females perform equally as well as primary females and better than secondary females; and (4) because some monogamous males are among the earliest breeders, polygynous males should not (by default) be considered more attractive than monogamous males. All these new predictions match previous empirical findings well: (1) field studies show that monogamous females are found earlier in the settlement order than expected from the original PTM; (2) overall, studies have failed to document that settlement order significantly predicts harem size; (3) monogamous females are in general found to have higher reproductive success than secondary females, instead of similar success which is predicted by the original PTM; and (4) paternity studies reveal that polygynous males are not cuckolded less than monogamous males, which they should according to the original PTM.

Concluding Remarks

The new predictions generated from a PTM-model that incorporates a variation in female competitive strength match the accumulated empirical results well (Grønstøl et al. 2003), which strengthens the hypothesis that strong females may be able to impose their own interests in the sexual conflict over parental care by enforcing monogamy and monopolizing the breeding resources of their mate.

The simulation results placed monogamous males at both the high and the low end of the BSQ scale. This implies that it is not appropriate to use harem size as a proxy for male attractiveness (or BSQ) in resource defense polygyny systems without accompanying evidence demonstrating that such a link between harem size and male quality does exist. One might speculate that some of the most attractive males perhaps may do better breeding monogamously if they are confident that they will be preferred as extra-pair sires by neighboring females. They would then parasitize the parental effort of neighboring males instead of splitting their own parental care over more females (i.e., a strategy of social monogamy and genetic polygyny for the most attractive males). This might even cause these males to be less resistant to social monogamy and easier to monopolize by their (strong) females.

In natural systems of resource defense polygyny there probably exist additional variables that play a part in the shaping of polygynous settlement patterns, which so far have not been included in the testing framework. An interesting effect that may alleviate sharing costs (and thereby reduce the polygyny threshold) is relatedness between female breeders that share a territory. If females on a polygynous territory are related, costs associated with sharing a territory may be lessened by indirect reproductive fitness benefits of kin selection, i.e., helping a relative to reproduce returns a reproductive fitness gain proportional to the relatedness (also termed inclusive fitness) (Hamilton 1964). Benefits from mutualistic behavior (or reciprocal helping), such as communal defense, may then increase and the resistance to sharing a territory should be lower than for unrelated females (Grønstøl et al. 2015).

An assumption that all variants of the PTM share is that females agree on how attractive the available males are, and that all females, given the chance, would choose the same male. This assumption might to some extent be challenged by research done on mate choice of complementary genotypes. Results have been presented indicating that females in some species prefer to mate with males with a MHC-genotype that is different from, or complementary to, their own MHC-genotype. This is thought to increase the heterogeneity of MHC in the offspring, which should increase the efficiency of the immune system (Mays and Hill 2004). As females are expected to vary with regard to MHC-genotypes, this effect would introduce an element of disagreement over which males are considered the most attractive. The strength of this objection will depend on how well the males’ attractiveness as social mates correlates with their attractiveness as genetic sires. Females might prefer to form social bonds with males that offer the most BSQ and covertly seek out more MHC-compatible males as extra-pair mates. Future research will probably establish how strong the effect of selection for complementary genotypes is compared to the preference for male traits that females agree on.

Theoretical models are not better than the foundation they rest on, and it is necessary to revisit, identify, evaluate, and explicitly state assumptions when applying them to natural systems. New insights might call for corresponding revisions of the PTM.



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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Natural History MuseumUniversity of OsloOsloNorway

Section editors and affiliations

  • David Hanbury
    • 1
  1. 1.Averett UniversityDanvilleUSA