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The good genes hypothesis is a theory that explains what a. why more fit individuals are more likely to have more offspring b. why alleles that confer beneficial traits or behaviors are selected for by natural selection c. why some deleterious mutations are maintained in the population d. why individuals of one sex develop impressive ornamental traits.
The correct choice is (a) the genes theory, which explains the mating of a female's special trait with an honest man who can pass on all of her excellent genes to her kids.
Step by Step Solution
genes hypothesis : .
Females pick a partner based on attributes that are excellent and honest indications of the male's potential to pass on genes, according to the good genes hypothesis. They will also improve her offspring's survival and reproductive success.
(a) In biology, the good genes theory explains the mating of a female's special attribute with an honest male who can pass on all of her good genes to her kids. This series of events culminated in the discovery of male features that are both favored and capable of mating by females, implying that mating boosted offspring survival. As a result, fitter people are more likely to have more offspring.
Other options :
(b) In a population, genetic drift explains the random fluctuations in all forms of gene variants. When alleles, which are different versions of a gene, arise, genetic drift occurs. As a result, natural selection favors genotypes that give desirable characteristics or behaviors.
(c) Individuals who inbreed have less genetic variety since their next generation's genomes have more homozygosity. As a result, dangerous mutations continue to exist in the population.
(d) Random mating occurs when an individual is mated an endless number of times, demonstrating the null model, which is important to population genetics. In reality, this is clearly impossible; for example, when each female mates only a finite number of times, the population size is effectively reduced. As a result, one-sex individuals have amazing ornamental characteristics.
Most popular questions for Biology Textbooks
When males and females of a population look or act differently, it is referred to as ________.
a. sexual dimorphism
b. sexual selection
c. diversifying selection
When closely related individuals mate with each other, or inbreed, the offspring are often not as fit as the offspring of two unrelated individuals. Why?
a. Close relatives are genetically incompatible.
b. The DNA of close relatives reacts negatively in the offspring.
c. Inbreeding can bring together rare, deleterious mutations that lead to harmful phenotypes.
d. Inbreeding causes normally silent alleles to be expressed.
Describe a situation in which a population would undergo the bottleneck effect and explain what impact that would have on the population’s gene pool.
Describe natural selection and give an example of natural selection at work in a population.
Population genetics is the study of:
a. how selective forces change the allele frequencies in a population over time
b. the genetic basis of population-wide traits
c. whether traits have a genetic basis
d. the degree of inbreeding in a population
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GOOD GENES HYPOTHESIS
Hypothesis of female mate selection that argues genetic variation in males correlates with success, features of male behaviour provide information about variation, females respond to variation by choosing males with good genes.
- MAPPING OF GENES
- Activation-Synthesis Hypothesis
- Contact Hypothesis
- One Tailed Hypothesis
- FACIAL FEEDBACK HYPOTHESIS
- RELIGIOUS INSTINCT HYPOTHESIS
- PERSEVERATION-CONSOLIDATION HYPOTHESIS
- MENTAL HOUSECLEANING HYPOTHESIS?
- ADAPTIVE HYPOTHESIS
How our Genes Lie: Honest and Dishonest Genes in Sexual Selection
Samuel Gascoigne Lake Forest College Lake Forest, Illinois 60045
Natural selection has been understood for over a hundred years, but the mechanisms by which it works have not been identified. One of the forms it takes is sexual selection. Sexual selection is an evolutionary pressure conferred by the opposite sex of the same species. The good genes hypothesis, posed in the 1930s, attempted to reconcile mate choice and the selection for certain traits. The selfish gene hypothesis, first declared in 1976, attempted to explain mate choice as well as our behaviors. With our modern understanding of genetics and DNA that holds the information, these two hypotheses can be applied to identify the honest and dishonest genes that are passed down generation after generation.
While the molecular basis is unknown, the role of genes in heredity has been common knowledge since the 1930s. The good genes hypothesis proposed that individuals choose mates on certain phenotypes that pose a genetic advantage for the next generation. To apply this to humans, the attractiveness we prescribe to an individual reflects that individual’s genetic superiority. This is an incomplete model given that different people find different individuals attractive. A possible supplement to the model is the selfish gene hypothesis. The selfish gene hypothesis proposes that our mate choice is a result of our interest to pass our genetic code on to the next generation. A human application of this would be that we choose our mates based on that individual’s similarity to our own genome, thereby probabilistically increasing the longevity of our genes. Both hypotheses have merit but fail to independently explain the presence of honest and dishonest genes; but, together, honest and dishonest genes are made inevitable.
When discussing honest and dishonest genes, it is important to clarify that sexual selection works via the selection of phenotypes, not genotypes. Phenotypes are observable characteristics of an organism and these traits are influenced by the organism’s genes. Since genotypes cannot be seen, phenotypes are used for selection as they are an indirect manifestation of the organism’s genes and experiences. An example of this is if a male peacock has a mutation in a gene important in feather development. A result of this mutation is an upregulation of a hormone responsible for feather growth, thereby increasing the relative size of the peacock’s plumage. Since plumage size is a sexually selected trait in peacocks, the mutated peacock would be selected to a greater degree by hens than a wild-type peacock. The disparity in the selection of males with varying secondary-sexual traits, affected by variation in genotype, is the basis of sexual selection contributing to the evolution of the organism. Yet, while advantageous mutations account for an evolutionary change over the course of multiple generations, genes do not independently explain why a trait is sexually selected. For that, genes must manifest into phenotypes that suggest an evolutionary fitness of the organism. Unfortunately, the path from gene to trait is not without its own set of variation.
Environment plays a key role in phenotype and the development of a sexually selected trait. Genotype does not determine phenotype. Genes code for proteins. Phenotypes can be anything from horn allometry, as in Onthophagus beetles, all the way to call syllables, as in bush crickets. What links genes to corresponding proteins are, most often, a suite of developmental and cellular mechanisms. It is this developmental and cellular link between genes and phenotypes that explain the plasticity of phenotypes. Phenotypic plasticity is the phenomenon that multiple phenotypes can arise from a single genotype; one example is the case of monozygotic twins. Imagine a pair of monozygotic twins, Jim and Jeff. Jim frequents a gym regularly and ensures he maintains a balanced diet. Jeff, on the other hand, frequents a buffet regularly and ensures his freezer is filled with his favorite midnight snacks. It would not be a surprise to find out that Jim has a lower body mass index (BMI) than Jeff despite having the exact same genotype. There was nothing that predisposed Jeff to a higher BMI than Jim. What ensured his increased insulation was the environment he experienced. In summary, genes lead to phenotype, but the phenotype is also moderated by the environment.
Honest and Dishonest Genes
What determines the honesty of a gene is how accurately it depicts, via a phenotype, the fitness of the organism. From a sexual selection standpoint, the evolution of honest genes would be favorable. In addition, over the course of multiple generations, the scruples of sexually selective pressures would refine the accuracy of the honest genes as it would lead to a sensitive and more prosperous method of selection. This is a case of resolution. Imagine a doe is searching for a buck for mating. Two bucks, Skip and Skippy, appear with similar size and muscle proportion. The only way they differ are their coats and horns. Skip has a relatively dull coat and small horns relative to body size while Skippy has a full shiny coat with a large ornament rack relative to body size. Skippy is favorably selected by the doe for mating. In this situation, genes that synthesize androgenic hormones and genes involved in insulin/insulin-like growth factor signaling (IIS) are honest genes; androgens are positively correlated with hair development and IIS is positively correlated with rack size. This situation is favorable for the doe and Skippy as they both have an increased probability of passing their genes on to the next generation. Skip, on the other hand, draws the short straw in the field of honest genes. He, therefore, favors a dishonest set of cards.
Imagine the doe and two bucks scenario once again with Skippy still being the more sexually favored. Now include a mutant Skip. This Skip has a mutation in genes involved in IIS that increase IIS and, further downstream, upregulate androgenic hormones. Mutant Skip has a glossy coat and large rack relative to body size which catches the doe’s eyes to a greater extent than Skippy’s features. In turn, mutant Skip is selected instead of Skippy. While the genes involved were originally honest, the mutation in Skip’s genome made the environment insubstantial in affecting the final phenotype and thus lead to dishonest phenotypes. In this scenario, the doe and Skip win. However, the doe wins at a probability of smaller magnitude as the offspring may be less fit than the offspring of an honest mate. The disparity in winning magnitude offers logic toward a selective pressure in does to increase their resolution for sexual selection; the better the does are at discerning honest genes, the more likely their genes will survive to the following generations. However, the presence of dishonest genes in species either supports the idea that dishonest genes are inevitable with random mutation or, more poignantly, the disparity in winning magnitude due to potential filial unfitness is not enough to select against dishonest genes.
The Two Theories
The presence of honest and dishonest genes highlights a sexually divergent initiative in sexual selection. The sexual selector prefers honest genes, while the sexual selectee prefers either honest or dishonest genes – whatever offers an advantage in increasing gene longevity. In turn, a theory of sexual selection must reconcile both initiatives.
Together, the good genes hypothesis and the selfish gene hypothesis explain the honest-dishonest genes phenomenon. The good genes hypothesis explains honest genes. In the good genes hypothesis, genes that accurately illustrate the fitness of the organism are preferably selected above inaccurate genes. This theory explains the disparate winning advantage in dishonest selection and offers a selective pressure against dishonest genes. Evidence for this theory can be found in IIS-dependent traits. Almost all animals use IIS for cellular and physiological development. One of the reasons IIS is so conserved is that IIS is upregulated in high nutrition. Therefore, an organism in high nutrition has full or increased development due in part to high IIS. In turn, it makes sense that sexual selection would work on traits that are insulin sensitive, allowing greater selection accuracy of well fed mates. However, the presence of dishonest genes indicates a second manner of sexual selection at work.
The selfish gene hypothesis explains the presence and longevity of dishonest genes despite the selective pressure against them offered by the good genes hypothesis. In the selfish gene hypothesis, animal behavior, including mate choice, is explained to increase the longevity of an individual organism’s genes. An example of this would be the mutant described above, Skip. The mutant Skip illustrates the presence of a dishonest gene via a mutation. According to the selfish gene hypothesis, what offers a dishonest gene its longevity, in addition to the phenotypic advantage, is the fact that organisms with the same gene tend to mate with one another, thus increasing the probable lifetime of the dishonest gene.
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- 036-037_Gascoigne_NewsViews (PDF)
Conceptual Challenges in Evolutionary Psychology pp 143–178 Cite as
Sexual Selection, Good Genes, and Human Mating
- Steven W. Gangestad 3
Part of the Studies in Cognitive Systems book series (COGS,volume 27)
Sexual selection is selection due to differential access to quantity and quality of mates. One form of it, intersexual selection, is due to differential access to mates driven by the mate preferences of individuals of the other sex. The major question about sexual selection pursued in theoretical investigation during the past two decades is, what accounts for mate preferences that drive intersexual selection? Several plausible models have been developed, one or more of which may apply to any particular species. This chapter has two major aims. First, evolutionary psychologists are interested in the linked tasks of inferring historical selection pressures that shaped psychological adaptations governing behavior, and describing the nature of those adaptations. Williams (1966) proposed that the criterion for inferring selection pressures, and thereby identifying adaptations that resulted, is special design. The logic of Williams’ approach is briefly described. Second, one particular process of interest is good genes sexual selection. This form of sexual selection occurs when members of one sex (I focus here on females) prefer as sexual mates individuals who possess markers of good genes, whose gametes benefit the chooser’s offspring. The criterion of special design applied to good genes sexual selection is: Are there any features of female mate choice that possess special design for choosing mates for their gametes, such that it is unlikely that such features would have evolved were they not designed by selection for this function? After discussing relevant background theory, I present several lines of evidence that are suggestive of such special design.
- Sexual Selection
- Parental Investment
- Fluctuate Asymmetry
- Material Benefit
- Female Orgasm
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Gangestad, S.W. (2001). Sexual Selection, Good Genes, and Human Mating. In: Holcomb, H.R. (eds) Conceptual Challenges in Evolutionary Psychology. Studies in Cognitive Systems, vol 27. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0618-7_6
DOI : https://doi.org/10.1007/978-94-010-0618-7_6
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- v.279(1727); 2012 Jan 22
Fixed and dilutable benefits: female choice for good genes or fertility
Samuel j. tazzyman.
1 CoMPLEX, University College London, Gower Street, London WC1E 6BT, UK
2 The Galton Laboratory, Research Department of Genetics, Environment and Evolution, University College, 4 Stephenson Way, London NW1 2HE, UK
Robert M. Seymour
3 Department of Mathematics, University College London, Gower Street, London, UK
Benefits accruing to females who exercise mate choice have been defined to be either ‘direct’ or ‘indirect’. We suggest an alternative distinction: benefits can be considered ‘fixed’, meaning they are on average equal to all females mating with the same male (e.g. good genes' benefits) or ‘dilutable’, meaning they are shared between females mating with the same male, so that the more mates a male has, the lower the average benefit to each (e.g. fertility benefits or many forms of direct benefit). Using a simple model, we show that this distinction has a major effect on the form of female preference. We predict that mating skew will be far greater in species where the benefits are fixed when compared with those where the benefits are dilutable.
The purpose of female mating preferences for male ornaments has been a subject of debate since Darwin's time [ 1 , 2 ]. Many hypotheses have been put forward which suggest the types of benefit accruing to a female from carefully selecting her mate. These benefits are generally categorized as being either ‘direct’ or ‘indirect’ in nature [ 3 , 4 ]. Examples of direct benefits include getting more or high-quality food or territory from the male, a larger nuptial gift when mating, good parenting skills (for review of these, see [ 2 ]) and high fertilizing efficiency [ 5 , 6 ]. Alternatively, female mating preferences could have direct benefits owing to genes underlying them having beneficial pleiotropic effects elsewhere in the phenotype [ 4 ]. Indirect benefits, on the other hand, are those that give an advantage to the female's offspring rather than directly to her. Examples are having offspring with high genetic viability owing to ‘good genes’ [ 7 ] or ‘compatible genes’ [ 8 ], avoiding the cost of inbreeding [ 9 , 10 ], or having attractive offspring (sometimes called the ‘sexy son’ hypothesis, originally proposed by Fisher [ 11 ]). As the different benefits to females are not mutually exclusive, neither are the hypotheses. After much empirical and theoretical work [ 3 , 12 – 16 ], there is still debate as to the strength of evolutionary force generated by each type of benefit [ 3 , 13 , 17 , 18 ], and difficulty in empirically measuring the strengths of each force [ 19 – 21 ].
Another way in which potential benefits differ that has been overlooked in previous discussions is whether or not benefits can be shared. Consider the difference in this regard between the ‘good genes’ hypothesis [ 22 , 23 ], and the ‘phenotype-linked fertility’ hypothesis [ 5 ]. The ‘good genes’ hypothesis postulates that females select their mates based on genetic quality, so as to have high-viability offspring. A male passes on an equal number of high-viability genes (on average) every time he mates, and so the expected benefit a female gets from mating with a given male is not dependent on the number of copulations he has with other females. A high genetic quality male will pass on high-quality genes in every mating (to first approximation, at least). We call this type of benefit ‘fixed’.
Now consider the ‘phenotype-linked fertility’ hypothesis. This postulates that females select males who have a higher fertilizing ability [ 5 ], to minimize the probability of unfertilized eggs. Fertilizing ability may depend on the number of mates a male has obtained: if males are sperm-limited, those that are preferred and thus mate many times will have a decreased expected ejaculate investment per mating, owing to depletion [ 24 , 25 ]. A highly fertile male may ejaculate a large number of sperm the first time he mates, but this number will decrease as he has more matings [ 6 ]. Thus, the expected fertility benefit a female gets from a given male depends on the number of previous copulations he has had with other females. As the number of other females he mates with increases, the expected benefit to the focal female decreases. This effect will be exacerbated on an evolutionary timescale because there will also be selection for more attractive males to invest fewer sperm per mating [ 26 ]. In this case, the benefits a male confers are ‘dilutable’.
This new distinction is not suggested as a replacement for the old direct/indirect categorization, but rather as an additional factor to consider in the field of mate choice evolution. The fixed/dilutable dichotomy has a bearing upon female behaviour, as we show using a simple model. In turn, this can affect mating skew, affecting the strength of sexual selection. A fresh look at categorizing female preferences may thus provide impetus for new empirical and theoretical investigations, and potentially shed further light on the evolution of mate choice.
To show that this new categorization of female benefits will affect mate choice behaviour, we consider optimal female preference in two idealized circumstances. In the first, females are selecting for good genes, and thus the benefits to be gained from higher quality males are fixed. In the second, females are selecting for high sperm count in ejaculates. Males are assumed to be sperm-limited, and so the benefits to be gained from higher quality males are dilutable. By contrasting these two cases, we show that there is potential for female behaviour to provide evidence of what benefits inform female preferences.
2. The model
We model an idealized species. All females are identical in terms of expected number of matings. The differences in fitness come from the female's preference function, as this leads to differences in realized mating outcomes. By selecting a mate appropriately, a female can acquire benefits, either having more offspring (perhaps because her mate provides fertility benefits), or having more offspring survive to breeding age (perhaps because her mate provides more resources for the offspring, or has good or compatible genes). We assume that females cannot directly assess the benefits they wish to maximize when selecting a mate, but rather make decisions based on some male trait, characterized by a single real variable z . This may be a single male trait, such as tail length, or it may be a combination of several traits, in which case z can be taken to be some suitable weighted average. We assume that there are lower and upper bounds on z , which we denote as a and b , respectively, so that for every male, a ≤ z ≤ b .
For simplicity, we assume that choice is cost-free, so females can examine all possible males before making their decision. We also assume that there is a large density of available males of every trait value, and the duration of copulation is short relative to its frequency, so that copulation with a single male of trait value z does not significantly decrease the number of z -males in the mating pool. Females exhibit preferences based on z . We model female preference as a function p ( z ), defined for a ≤ z ≤ b , and satisfying p ( z ) ≥ 0. Because we are interested in female preference as a relative measure (i.e. the attractiveness of trait value z 1 compared with that of trait value z 2 ), we scale the preference function such that
Thus, the preference function can be regarded as a probability density function describing the probability that a female will mate with a male whose trait value is within a given interval. We now define the expected benefit that accrues to a female depending on her preference function. The form this takes will differ depending upon the nature of the benefit at stake.
(a) Good genes (fixed benefits)
In the first case, females select a mate so as to maximize the genetic quality of their offspring. In this way, they improve the chances of their offspring surviving to breeding age. This is assumed to be dependent on the genetic quality of the male. We define the continuous benefit function, s ( z ). This is the expected benefit accruing to a female should she mate with a male of trait value z . Of course, a male's trait value is a noisy indicator of his actual quality, as trait values are affected by both genetics and environment; in particular, not all males of trait value z will have the same ‘good genes’. However, the female's expected benefit s ( z ) is taken as an average across all z -males.
A female with preference function p ( z ) will then obtain expected benefit
The preference function p that maximizes [ 2 ] will therefore be the function that maximizes female fitness W [ p ] in the ‘good genes’ case.
(b) Fertility (dilutable benefits)
We want the benefit function s ( z , q ) to obey two conditions. First, we assume that the more matings a male gets, the fewer sperm on average he ejaculates per mating:
(i) Condition (i)
For each trait value z , s ( z , q ) is differentiable in the popularity variable q , and
for all q > 0. That is, the benefit function is monotonically decreasing in q , so that for fixed z , the benefit function s ( z , q ) declines as the popularity q of z -males increases. This is because as a male's popularity increases, he will mate more often, and thus the benefits that he confers will be shared between more females, meaning a lower expected share to each female. We also require that s ( z,q ) → 0 as q → ∞, so that, if female preference for a male of trait value z increases indefinitely, then the reward to any particular female from mating with such a male diminishes to insignificance (the male has only a finite sperm reservoir to share among all his female mates).
Second, we also want to assume that males with larger trait values give larger benefits (i.e. more sperm) all else being equal (the phenotype-linked fertility hypothesis [ 5 ]). So the benefit function must also satisfy:
(ii) Condition (ii)
for all q ≥ 0. That is, the benefit function is monotonically increasing in z for fixed q , so that if there are two males of equal popularity, the male with the larger trait value will confer higher benefits.
(c) Difference between the two models
The key difference between the two models is that for fixed benefits, the benefit function is dependent only on a male's ornament. For dilutable benefits, however, the benefit function is dependent both on a male's ornament and also on the mean preference function of the female population. This means different approaches must be used in the analysis of these two models: in the fixed case, we simply use an optimization approach, while in the dilutable case, we require an evolutionarily stable strategy (ESS) approach [ 27 ].
We look for benefit functions p ( z ) that maximize the expected payoff function W [ p ] given by equation (2.2).
An example of female preference for fixed benefits. We show some fixed benefit function s ( z ) plotted against trait value z . This has a unique maximum at z = b . The optimal female preference function q b ( z ) is zero for all z ≠ b , and thus females should reject any male with a trait value in this range. The only trait value for which the preference function is non-zero is z = b , and so females should accept only males with this trait value.
Another example of female preference for fixed benefits. A fixed benefit function s ( z ) is shown plotted against trait value z . It attains its maximum for trait values c ≤ z ≤ b . The optimal female preference function p ( z ) is zero for all z < c , and thus females should reject any male with a trait value in this range. The preference function is constant and non-zero for trait values z ≥ c , and so females should accept any male with trait value in this range. Females are indifferent if given a choice between males with trait sizes larger than c .
In the natural world, then, if preference is for good genes, all females should choose to mate with the same optimal male type (or possibly with males from a set of types conferring approximately equal benefits), who will therefore monopolize all (consensual) matings. Males with genes worse than the optimum (as signalled by their trait values) will be rejected. Given a choice between two males, females should always choose the male with the better genes.
We apply the well-established concept of an ESS; that a population, all of whose members use the same ‘equilibrium strategy’, denoted p *, should be resistant to invasion by a sufficiently small influx of mutants using a different strategy, denoted p. This notion has been extensively developed in the context of finite strategy games [ 27 ]. The situation for games with infinite strategy spaces, such as in the dilutable benefits case considered here, is somewhat more problematic, and more so when payoff functions are nonlinear. Here, we shall require that an ESS be a totally uninvadable strategy [ 28 , 29 ] in the following sense:
for all 0 < ɛ ≤ 1, and all alternative strategies p ≠ p *. This means that, if we begin with an initial population of females who all use the strategy p *, and replace a non-zero fraction of size ɛ of this population with a subpopulation of females who all use an alternative strategy p ≠ p *, then the p *-females have a strictly higher fitness in this mixed population than do the mutant p -females. Further, this holds for any non-zero fraction of invading mutant females. We can show the following results (electronic supplementary material, appendix 2). First, there are no pure strategy equilibria such as the delta function solution given in the fixed benefit case. To see this, suppose that females use a pure strategy; that is, all females in the population mate only with males who have a particular trait value z *. In this case, any such male will be totally depleted, and hence the expected payoff to each female will be zero (since from above, s ( z *, q ) → 0 as q → ∞). However, a mutant female who will mate with a male of trait value z ≠ z * will obtain the positive payoff s ( z , 0). This shows that mating only with z *-males cannot be an equilibrium strategy.
Second, there is a unique equilibrium female preference function p *( z ), which is an ESS in the above sense. This function is continuous on [ a , b ], and there is a threshold trait value c with a ≤ c < b , such that s ( z,p *( z )) = w * (a non-zero constant) for c ≤ z ≤ b while p *( z ) = 0 and s ( z,p *( z )) = s ( z ,0) < w * for z < c (applicable only if c > a ). Finally, for all z ∈ [ c,b ], p *( z ) is monotonically increasing.
In nature, then, this means that males with larger trait values, who would give larger fertility benefits if female preference were uniform, will get more matings than those with smaller ornaments, but they will not have a monopoly on matings. Instead, expected number of matings will decline as ornament size decreases. It may be that all males achieve some matings (so that the threshold value c = a ), or it may be that some threshold is reached, below which males will receive no (consensual) matings at all (so that the threshold value c > a ). Interestingly, given a choice between a male with a higher and a male with a lower trait value, females will not always choose to mate with the bearer of the higher trait. Rather, there will be some probability of choosing each, with more females choosing the bearer of the higher trait value, who will therefore obtain more matings overall, but some choosing the bearer of the lower trait value, who will receive fewer matings overall. This is because the higher trait value male will obtain more matings and hence will be subject to greater sperm depletion relative to the lower trait value male. In effect, the female is negotiating a trade-off between a more attractive, but more depleted male, against a less attractive, but less depleted male. The equilibrium female preferences would be expected to result in the expected benefit from a mating with each male being identical ( figure 3 ).
An example of female preference for dilutable benefits. The dashed horizontal line represents the preference function where females consider all males equally attractive, p 0 ( z ) = 1/( b − a ). The corresponding benefit function s ( z , p 0 ( z )) is shown by the other dashed line. Note that it is increasing in z , as per condition (ii) of the main text. The optimal preference function p * is shown by the solid line. This is zero for z ≤ c and linearly increasing thereafter. Females will reject all males with trait values z ≤ c . Males with trait values z > c will be accepted with increasing likelihood as their trait size increases. The corresponding benefit function s ( z,p *( z )) is shown by the other solid line. Males with trait values z > c will all give the same average benefit, while those with trait values z ≤ c will give average benefits less than this (and hence are not worth mating with).
The evolution of female mate choice has been broadly characterized as being due either to ‘direct’ or ‘indirect’ benefits [ 30 ]. We propose another way to characterize the benefits females obtain from mate choice, in terms of whether they are ‘dilutable’ or ‘fixed’. As we have shown in the model above, this distinction will affect female preference. If females are selecting for fixed benefits, they should only mate with males who provide them with the largest payoff, rejecting all others. On the other hand, if females are selecting for dilutable benefits, their mating pattern will follow a probability distribution so that the best males (those with the highest trait values) get more matings, but do not have a monopoly.
We have modelled explicitly for the cases of good genes (fixed) and fertility benefits (dilutable), but our model could equally apply to other hypotheses for female mate choice, as we now consider. Most types of indirect benefits will be fixed, as characteristics inherited genetically will benefit offspring from all matings equally. This logic applies both for benefits to viability and attractiveness. Where genetic benefits arise from genetic compatibility, they are contingent on complementarity between the parents and so will not flow equally to all females. But they are not dilutable, as the gain of one female is independent of others' choices (in this case, each female's optimal preference function would be different, but would correspond to that for a fixed benefit).
Generally, direct benefits will be dilutable. Parenting ability, for example, seems likely to decrease in most cases as the number of offspring with different mothers increases (see the polygyny threshold model [ 31 , 32 ]; although there can be benefits to polygyny too [ 32 , 33 ]). However, there are many exceptions where direct benefits are likely to be fixed. A possible example could be where females choose mates for good parenting, and form socially monogamous pairs. Then paternal care is not diluted, as the male only provides care for his social partner's offspring. Even if the father sires offspring through extra-pair copulations, the benefits he provides are likely to be fixed to first order, unless the time he spends seeking extra-pair matings impedes his provision of parental care [ 34 ]. Another example is the case of prey items acting as nuptial gifts. Then the benefit is direct, but it is not dilutable, as it is consumed entirely by a single female. Nuptial gifts such as spermatophores may be somewhat dilutable, however, if the male's ability to produce a large spermatophore is affected by frequent copulation.
The different potential benefits to female choice are not mutually exclusive, so evolution will favour combinations of dilutable and fixed benefits. A hypothetical example is a species where females select males for their size and strength, because large, strong males can defend better territory. In this instance, the benefit to females is direct, as they gain better territory, and dilutable since sharing the male with other females means each female gets a smaller share of the rewards from the territory. However, if the male's size and strength are genetic, the females will also gain fixed, indirect benefits through her offspring inheriting their father's genetic quality. This model shows that female mate choice can itself offer some clues as to the relative strength of the forces underlying its evolution.
Of course, our model makes a number of simplifying assumptions, and in reality, female choice is likely to be a much more complicated affair. For example, we assume that females are able to accurately assess and compare all potential mates, having no time constraints or costs of mate choice. This is unlikely to be the case, and indeed the time taken to make a decision may itself be costly [ 38 ]. If females are not time-constrained, the ability to compare a large number of potential mates may be beyond the cognitive abilities of many species. Even if females have a limited selection of males from which to choose, qualitatively similar results will be obtained, although the evolutionary dynamics will be slower (initial simulation results). This is something we intend to investigate further in future work.
Different preference functions may also have different associated costs, or females may accept males of certain trait sizes with conditional probability based on time and cost constraints [ 39 , 40 ]. We chose not to assess the effects of cost of choice (other than by constraining the set from which the choice is made). While we of course accept that such costs would affect the evolution of mate choice, these effects will depend to a large degree on the nature and size of the costs. This is certainly an important area for future investigations, but in this paper we have aimed to analyse the effects of fixed and dilutable benefits upon mate choice in an idealized setting, and this is more simply and clearly done without considering the many different ways in which a cost could be applied to choice. Nevertheless, it is certainly the case that a non-uniform distribution of costs of mating with different males can potentially moderate the all-or-nothing conclusion that it is always optimal to mate with the ‘best’ males in the fixed benefits case.
In addition, we assume that there is a reliable link between ornament and benefit. This will be justified in cases where the trait has a functional role in determining the benefits females will receive. If the benefit is number of sperm, for example, then testes size could be such an indicator. It can also be justified by recourse to the handicap principle in which male investment in the ornament is correlated with the traits which determine the benefits females receive because of condition-dependent costs [ 41 ]. The phenotype-limited fertility hypothesis suggests that females choose males based on their fertilizing ability [ 5 ]; for this to be possible, females must be able to assess the fertilizing abilities of males using some trait or combination of traits. We simply assume for simplicity that such assessments are reliable, in the sense that paying attention to the trait value achieves, on average, greater benefits for the female than not paying attention. The effect of signal unreliability is worth investigating in the future; we expect that it will slow down the evolution of preference functions of the predicted type, but that qualitatively, the results will be the same. However, in this paper we are concerned only with exploring the effects of the conceptual difference between fixed and dilutable benefits, and for this our simplifying assumptions are sufficient.
Something else we have not addressed is the possibility of polyandry, where females mate with more than one male within a breeding season. This could come about in either fixed or dilutable benefits cases if constraints mean that the females cannot achieve the optimal choice. In the fixed benefit case, a female selecting the best male available to her at a given time may later come across better males and thus wish to ‘trade up’. In the dilutable benefit case, the same could occur if females are constrained so that the resultant benefit function is not one that means all males give the same benefits. However, as extra-pair copulations would themselves cause further dilution of the benefits provided by males, this may be less likely.
Once we accept that benefits accruing to a female from a given male can depend on the number of other females he mates with, there is also the possibility that the more mates a male has, the higher the expected benefit to each: the opposite of the dilutable benefits scenario considered here. In some species, it is thought that increased polygyny may in fact benefit females. For example, in birds, breeding in the same territory as other females may decrease the chances of nest predation [ 32 ]. This could be modelled by considering a benefit function s ( z , q ) that is increasing with increasing popularity q , rather than decreasing as we have assumed in this paper. Although we have chosen not to consider this case here, note that under these circumstances, the ESS strategy could be one where all females will choose males of the same trait value x , if s ( z,q z ( z )) < s ( x,q x ( x )) for all z ≠ x and delta functions q z and q x . However, the exact solution is likely to be highly dependent upon the way s ( z , q ) varies with z , giving several possibilities.
A female who mates with a male bearing a trait value preferred by other females in the population may gain some benefit by having ‘sexy sons’ [ 11 , 42 ]. This could be covered by the last framework, with the benefit accruing to a female for mating with a male of a given trait value increasing if more females in the population have a preference for that value. It is therefore interesting to note the similarity of the result in this case (that all females have the same preference) to Fisher's runaway process. It is also notable that female choice for dilutable benefits in our formulation gives a similar result to the polygyny threshold model [ 2 , 31 , 32 ], with females balancing the trade-off between attractiveness and sperm depletion, so as to make the expected benefit from each (acceptable) male identical. If the benefit function s ( z,p ) declines linearly with increasing p , the resulting preference function will resemble an ideal-free distribution, with males' popularity being proportional to s ( z ,0), which could be seen as the total amount of resources they have to give to females. Thus, although our formalism is simple and intuitive, it encompasses a wide spectrum of possible patterns of female choice, and uncovers previously unrealized relationships between them. While it is not intended to replace the old direct/indirect benefits distinction, it does provide an additional way of considering the evolution of female choice, which could be of use in stimulating new empirical studies that will hopefully unravel the complexity surrounding this area of evolutionary theory.
We would like to thank Max Reuter for helpful discussions. ST was supported by a CoMPLEX PhD studentship and PhD+ award from the Engineering and Physical Sciences Research Council, AP by Natural Environment Research Council (NE/G00563X/1) and Engineering and Physical Sciences Research Council (EP/F500351/1).