Sex ratio and male sexual characters in a population of blue tits, Parus caeruleus

Sex allocation theory proposes that parents should bias thesex ratio of their offspring if the reproductive value of onesex is greater than that of the other. In the monogamous bluetit (Parus caeruleus), males have a greater variance in reproductivesuccess than females, and high-quality males have higher reproductivesuccess than high-quality females due to extrapair paternity.Consequently, females mating with attractive males are expectedto produce broods biased toward sons, as sons benefit more thandaughters from inheriting their father's characteristics. Songand plumage color in birds are secondary sexual characters indicatingmale quality and involved in female choice. We used these malesexual traits in blue tits to investigate adaptive sex ratiomanipulation by females. We did not find any relationship betweenmale color ornamentation and brood sex ratio, contrary to previousstudies. On the other hand, the length of the strophe bout (i.e.,the mean number of strophes per strophe bout) of fathers waspositively related with the proportion of sons in their broods.The length of the strophe bout is supposed to reflect male qualityin terms of neuromuscular performance. We further showed thatsons produced in experimentally enlarged broods had shorterstrophe bouts than sons raised in reduced broods. These resultsare consistent with the hypothesis that females adjust the sexratio of their broods in response to the phenotype of theirmate.     

Sex allocation in black-capped chickadees Poecile atricapilla

Optimal sex allocation for individuals can be predicted from a number of different hypotheses. Fisherian models of sex allocation predict equal investment in males and females up to the end of parental care and predict brood compositions based on the relative costs of producing males and females. The Trivers-Willard hypothesis predicts that individual females should alter the sex ratio of their broods based on their own condition if it has a differential impact on the lifetime reproductive success of their sons and daughters. The Charnov model of sex allocation predicts that females should alter sex allocation based on paternal attributes that may differentially benefit sons versus daughters. Because females are the heterogametic sex in birds, many recent studies have focussed on primary sex ratio biases. In black-capped chickadees Poecile atricapilla , males are larger than females suggesting they may be more costly to raise than females. Female condition affects competitive ability in contests for mates, and thus may be related to variance in fecundity. Females prefer high-ranking males as both social and extrapair partners. These observations suggest that females might vary the sex ratio of their broods based on the predictions of any of the above models. Here, we report on the results of PCR based sex determination of 1093 nestlings in 175 broods sampled from 1992 to 2001. Population-wide, we found a mean brood sex ratio of 0.525±0.016, with no significant deviation from a predicted binomial distribution. We found no effect of clutch size, female condition, hatch date, parental rank or paternity. Our results reject the idea that female black-capped chickadees systematically vary sex allocation in their broods.     

Brood sex ratio in the Kentish plover

How and why do the mating opportunities of males and femalesdiffer in natural population of animals? Previously we showedthat females have higher mating opportunities than males inthe Kentish plover Charadrius alexandrinus. Both parents incubatethe eggs, and males provide more brood care than females; thusit is not obvious why the females find new mates sooner thanthe males. In this study we investigated whether the sex-biasedmating opportunities stem from biased offspring sex ratios.We determined the sex of newly hatched, precocial chicks usingCHD gene markers. Among fully sexed broods, 0.461 ± 0.024(SE) of chicks (454 chicks in 158 broods) were male, and thissex ratio was not significantly different from unity. The proportionof males at hatching decreased significantly over the breedingseason, which occurred consistently in all 3 years of the study.Large chicks were more likely to be males than females. Neitherparental age nor body size of male and female parents was relatedto brood sex ratio. We also sexed a number of chicks that werecaught after they left their nest (range of estimated ages 0–17days) and found that the proportion of males increased withbrood age. This relationship remained highly significant whencontrolling statistically for hatching date. As brood size decreaseddue to mortality after the chicks left their nest, these resultssuggest that the mortality of daughters was higher than thatof the sons shortly after hatching. Taken together, our resultsshow that the female-biased mating opportunities in the Kentishplover are not due to biased brood sex ratio at hatching but,at least in part, are due to female-biased chick mortality soonafter hatching.     

Offspring sex ratio produced by female guppies in the wild correlates with sexual ornaments of their sons

The attractiveness hypothesis predicts that females produce broods with male-biased sex ratios when they mate with attractive males. This hypothesis presumes that sons in broods with male-biased sex ratios sired by attractive males have high reproductive success, whereas the reproductive success of daughters is relatively constant, regardless of the attractiveness of their sires. However, there is little direct evidence for this assumption. We have examined the relationships between offspring sex ratios and (1) sexual ornamentation of sons and (2) body size of daughters in broods from wild female guppies Poecilia reticulata. Wild pregnant females were collected and allowed to give birth in the laboratory. Body size and sexual ornamentation of offspring were measured at maturity. Our analysis revealed a significant positive correlation between offspring sex ratios (the proportion of sons per brood) and the total length as well as the area of orange spots of sons, two attributes that influence female mating preferences in guppies. The sex ratio was not associated with the body size of daughters. These results suggest that by performing adaptive sex allocation according to the expected reproductive success of sons and daughters, female guppies can enhance the overall fitness of their offspring.     

Maternal influences on brood sex ratios: an experimental study in tree swallows

When the reproductive value of sons and daughters differ, parents are expected to adjust the sex ratio of their offspring to produce more of the sex that provides greater fitness returns. The body condition of females or environmental factors, such as food abundance and mate quality, may influence these expected fitness returns. In a previous study of tree swallows (Tachycineta bicolor), we found that females produced more sons in their broods when they were in better body condition (mass corrected for size). We tested this relationship by experimentally clipping some flight feathers to reduce female body condition. As predicted, we found that females with clipped feathers had a lower proportion of sons in their broods and poorer body condition. However, female body condition alone was not a significant predictor of brood sex ratio in our experiment. We suggest that brood sex ratio is causally related to some other factor that covaries with body condition, most likely the foraging ability of females. The hypothesis that brood sex ratios are influenced by individual differences in female foraging ability is supported by a high repeatability of brood sex ratio for individual females. Thus, maternal effects may have a strong influence on the sex ratios of offspring.     

Pair bond duration influences paternal provisioning and the primary sex ratio of brown thornbill broods

Parents should vary their level of investment in sons and daughters in response to the fitness costs and benefits accrued through male and female offspring. I investigated brood sex ratio biases and parental provisioning behaviour in the brown thornbill, Acanthiza pusilla, a sexually dimorphic Australian passserine. Parents delivered more food to male-biased than female-biased broods. However, factors determining parental provisioning rates differed between the sexes. Female provisioning rates were related to brood sex ratio in both natural and experimental broods with manipulated sex ratios. In contrast, male provisioning rates were not affected by brood sex ratio in either natural or experimental broods. However, males in established pairs provisioned at a higher rate than males in new pairs. Data on the sex ratio of 109 broods suggest that female brown thornbills adjust their primary sex ratio in response to pair bond duration. Females in new pairs produced broods with significantly fewer sons than females in established pairs. This pattern would be beneficial to females if the costs of rearing sons were higher for females in new than established pairs. This may be the case since females in new pairs provisioned experimental all-male broods at elevated rates. The condition of nestlings also tended to decline more in these all-male broods than in other experimental broods. This will have additional fitness consequences because nestling mass influences recruitment in thornbills. Female thornbills may therefore obtain significant fitness benefits from adjusting their brood sex ratio in response to the status of their pair bond. Copyright 2002 The Association for the Study of Animal Behaviour. Published by Elsevier Science Ltd. All rights reserved.     

Offspring sex ratios in tree swallows: females in better condition produce more sons

Organisms are expected to adjust the sex ratio of their offspring in relation to the relative fitness benefits of sons and daughters. We used a molecular sexing technique that amplifies an intron of the CHD1 gene in birds to examine the sex ratio at egg-laying in socially monogamous tree swallows (Tachycineta bicolor). We examined all individuals in 40 broods (210 young), including all unhatched eggs and nestlings. Thus, the sex ratio we measured was the same as the sex ratio at laying. Overall, the mean sex ratio per brood (+/- SD) was biased significantly towards males (57 +/- 2% male). Within broods, male-biased sex ratios were associated with females in better body condition, and these females were more likely to produce sons in better condition. Tree swallows have one of the highest known levels of extra-pair paternity in birds (38-76% extra-pair young), and, as a consequence, variance in male reproductive success is greater than that of females. Thus, in tree swallows, investment in sons has the potential for higher fitness returns than investment in daughters, assuming that sons in better condition have greater reproductive success.     

Sex ratio in relation to timing of breeding, and laying sequence in a dimorphic seabird

When the cost of rearing sons and daughters differs and the subsequent survival and reproductive success of one sex is more dependent than the other, on the amount of parental investment, adult females tend to produce more chicks of the more dependent sex if the females are in good condition themselves. One method of varying the total investment in each sex is through modifying the sex ratio of offspring produced. This study shows that in broods of European Shags Phalacrocorax aristotelis , the sex ratio varied with laying date. Presumably in this species, the lifetime reproductive success of males is more dependent on the level of parental investment. Early breeders are in better condition, the brood sex ratio of early broods was male biased (0.63), while that of late broods was female biased (0.36). The overall difference in sex ratio found between early and late nests could be attributed to manipulation of sex in the first laid egg. In early broods, 77% of the first hatched chicks were male but only 30% of the first hatched chicks in late broods were male. The sex combination of the first two chicks in a brood significantly affected growth as measured by asymptotic mass.     

Nestling sex ratio is associated with both male and female attractiveness in rock sparrows

According to theory, in species in which male variance in reproductive success exceeds that of the females, sons are more costly to produce; females mated with high quality males or those in better condition should produce more sons. In monogamous species, however, the variance in the reproductive success of the two sexes is often similar and mate choice is often mutual, making predictions regarding sex allocation more difficult. In the rock sparrow Petronia petronia, both males and females have a sexually selected yellow patch on the breast, whose size correlates with individual body condition. We investigated whether the brood sex ratio co‐varies with the size of the yellow patch of the father and the mother in a sample of 173 broods (818 chicks) over 8 breeding seasons. While the size of the yellow patch of the mother and the father did not predict per se a deviation from the expected 1:1 sex ratio, brood sex ratios were predicted by the interaction of male and female yellow patch size. This result is surprising, as the ornament is sexually selected by both males and females as an indicator of quality in both sexes and should therefore be inherited by all offspring irrespective of their sex. It indirectly suggests that other sex‐specific traits associated with patch size (e.g. polygyny in males and fecundity in females) may explain the sex allocation bias observed in rock sparrows. Thus, female individual quality alone, as expressed through the size of the yellow patch, was not associated with the biases in sex ratios reported in this study. Our results rather suggest that sex allocation occurs in response to male attractiveness in interaction with female attractiveness. In other words, females tend to preferentially allocate towards the sex of the parent with more developed ornament within the pair.     

Evidence for Strategic Sex Allocation in the Guppy (Poecilia reticulata): Brood Sex Ratio and Size Predict Subsequent Adult Male Mating Success

Sex allocation theory predicts that females should produce more sons when the reproductive success of sons is expected to be high, whereas they should produce more daughters, not daughters when the reproductive success of sons is expected to be low. The guppy (Poecilia reticulata) is a live‐bearing fish, and female guppies are known to produce broods with biased sex ratios. In this study, we examined the relationship between brood sex ratio and reproductive success of sons and daughters, to determine whether female guppies benefit from producing broods with biased sex ratios. We found that sons in male‐biased broods had greater mating success at maturity than sons in female‐biased broods when brood sizes were larger. On the other hand, the reproductive output of daughters was not significantly affected by brood sizes and sex ratios. Our results suggest that female guppies benefit from producing large, male‐biased brood when the reproductive success of sons is expected to be high.     

The Influence of Maternal Quality on Brood Sex Allocation in the Small Carpenter Bee,Ceratina calcarata

In the twig‐nesting carpenter bee, Ceratina calcarata, body size is an important component of maternal quality, smaller mothers producing significantly fewer and smaller offspring than larger mothers. As mothers precisely control the sex and size of each offspring, smaller mothers might compensate by preferentially allocating their investment towards sons. We investigated whether variation in maternal quality leads to variation in sex allocation patterns. At the population level, the numerical sex ratio was 57% male‐biased (1.31 M/F), but the investment between the sexes was balanced (1.02 M/F), because females are 38% larger than males (1.28 F/M). Maternal body size explained both sex allocation pattern and size variation among offspring: larger mothers invested more in individual progeny and produced more female offspring than smaller mothers. Maternal investment in offspring of both sexes decreased throughout the season, probably as a result of increasing maternal wear and age. The exception to this pattern was the curious production of dwarf females in the first two brood cell positions. We suggest that the sex ratio distribution reflects the maternal body size distribution and a constraint on small mothers to produce small broods. This leads to male‐biased allocation by small females, to which large mothers respond by biasing their allocation towards daughters.     

Facultative Adjustment of Brood Sex Ratio in Response to Indirect Manipulation of Behaviour

Sex allocation theory states that parents should adjust their offspring sex ratio according to the expected fitness returns from sons and daughters. Several recent studies indicate that such adaptive manipulation of offspring sex ratio is achievable, and that it may be influenced by e.g. morphological characters. Here we manipulate behaviour through interspecific cross-fostering of great tits ( Parus major ) and blue tits ( Cyanistes caeruleus ), and investigate its effect on the offspring sex ratio of adults that were themselves cross-fostered as chicks. The experience of being raised by a different species has previously been shown to result in aberrant species assortative behaviour and song, and a lowered dominance status during winter. Brood sex ratios of conspecifically breeding pairs with and without cross-fostered members were compared. Broods with at least one cross-fostered parent contained significantly more males than did control broods. Sex of cross-fostered parents did not influence the brood sex ratio. We conclude that female great tits and blue tits seem to be able to adjust the sex ratio of their broods, and that changes in their own or their partners' behaviour may elicit such adjustments.     

Hatching sex ratio and sex specific chick mortality in common terns Sterna hirundo

Bias in sex ratios at hatching and sex specific post hatching mortality in size dimorphic species has been frequently detected, and is usually skewed towards the production and survival of the smaller sex. Since common terns Sterna hirundo show a limited sexual size dimorphism, with males being only about 1–6% larger than females in a few measurements, we would expect to find small or no differences in production and survival of sons and daughters. To test this prediction, we carried out a 2-year observational study on sex ratio variation in common terns at hatching and on sex specific post hatching mortality. Sons and daughters hatched from eggs of similar volume. Post hatching mortality was heavily influenced by hatching sequence. In addition, we detected a sex specific mortality bias towards sons. Overall, hatching sex ratio and sex specific mortality resulted in fledging sex ratios 8% biased towards females. Thus, other reasons than body size may be influencing the costs of rearing sons. Son mortality was not homogeneous between brood sizes, but greater for two-chick broods. Since adults rearing two-chick broods were younger, lighter and bred consistently later than those rearing three-chick broods, it is suggested that lower capacity of two-chick brood parents adversely affected offspring survival of sons. Though not significantly, two-chick broods tended to be female biased at hatching, perhaps to counteract the greater male-biased nestling mortality. Thus, population bias in secondary sex ratio is not limited to strongly size dimorphic species, but species with a slight sexual size dimorphism can also show sex ratio bias through a combination of differential production and mortality of sons and daughters.     

Male-biased brood sex ratio depresses average phenotypic quality of barn swallow nestlings under experimentally harsh conditions

Sex allocation strategies are believed to evolve in response to variation in fitness costs and benefits arising from the production of either sex and can be influenced by the differential susceptibility of sons and daughters to environmental conditions. We tested the effects of manipulating brood size and the sex ratio of the nestmates and the effect of sex on the phenotypic quality of individual barn swallow (Hirundo rustica) nestlings. Brood enlargement, which results in harsh rearing conditions, negatively affected the morphology and immunity of the nestlings. However, the negative consequences of brood enlargement were more marked among male than female offspring. In enlarged but not reduced broods, high proportions of male nestmates resulted in lowered individual body mass, body condition and feather growth. Thus, the consequences of a harsh environment on individual nestlings differed between the sexes and depended on the sex ratio among the other nestlings in the brood. The evolution of sex allocation strategies may therefore depend on the sex of individual nestlings but also on an interaction between environment and progeny sex ratio.     

Offspring sex ratio is related to male body size in the great tit (Parus major)

Sex allocation theory predicts that the allocation of resourcesto male and female function should depend on potential fitnessgain realized through investment in either sex. In the greattit (Parus major), a monogamous passerine bird, male resourceholdingpotential (RHP) and fertilization success both depend on malebody size (e.g., tarsus length) and plumage traits (e.g., breaststripe size). It is predicted that the proportion of sons ina brood should increase both with male body size and plumage traits,assuming that these traits show a father—offspring correlation. Thiswas confirmed in our study: the proportion of sons in the brood increasedsignificantly with male tarsus length and also, though not significantly,with the size of the breast stripe. A sex ratio bias in relationto male tarsus length was already present in the eggs because(1) the bias was similar among broods with and without mortalitybefore the nestlings' sex was determined, and (2) the bias remainedsignificant when the proportion of sons in the clutch was conservativelyestimated, assuming that differential mortality before sex determinationcaused the bias. The bias was still present among recruits.The assumption of a father—offspring correlation was confirmedfor tarsus length. Given that both RHP and fertilization successof male great tits depend on body size, and size of father andoffspring is correlated, the sex ratio bias may be adaptive.     

Reproductive success of polygynous male corn buntings (Miliaria calandra) as confirmed by DNA fingerprinting

Despite a sex ratio approximating to unity, female corn buntingswere not equally distributed among males. In 1989 and 1990,41.2% of 50 males were monogamously paired, 29.4% were polygynous,and 23.5% were unpaired. Polygynous males usually paired withtwo females, although in 1990 three males were trigamous. Polygynousmales fledged more offspring from their territories than didmonogamous males, mainly because they had more mates. The fledgingsuccess per nesting female was slightly higher in territoriesof polygynous males, but not significantly so. DNA fingerprintingwas used to confirm the true paternity of 44 offspring from15 broods and the true maternity of 50 offspring from 16 broods.A further 12 offspring from three broods for which neither putativeparent was available were also fingerprinted. Actual reproductivesuccess of parents was close to that inferred from observationsof number of young raised. There was only one brood, containingtwo chicks (4.5% of offspring, or in 6.7% of broods), wherethe chicks were not fathered by the male defending the territory.However, this nest was close to the territory boundary, andthe defending male may have been assigned incorrectly. Therewere no cases of intraspecific brood parasitism (n = 16 broods).The copulation rate was low, and extrapair copulation attemptswere rare, probably because of the poor chances of sneakingonto a neighbor's territory undetected and the costs of leavinga territory unguarded.     

Within‐female plasticity in sex allocation is associated with a behavioural polyphenism in house wrens

Sex allocation theory assumes individual plasticity in maternal strategies, but few studies have investigated within‐individual changes across environments. In house wrens, differences between nests in the degree of hatching synchrony of eggs represent a behavioural polyphenism in females, and its expression varies with seasonal changes in the environment. Between‐nest differences in hatching asynchrony also create different environments for offspring, and sons are more strongly affected than daughters by sibling competition when hatching occurs asynchronously over several days. Here, we examined variation in hatching asynchrony and sex allocation, and its consequences for offspring fitness. The number and condition of fledglings declined seasonally, and the frequency of asynchronous hatching increased. In broods hatched asynchronously, sons, which are over‐represented in the earlier‐laid eggs, were in better condition than daughters, which are over‐represented in the later‐laid eggs. Nonetheless, asynchronous broods were more productive later within seasons. The proportion of sons in asynchronous broods increased seasonally, whereas there was a seasonal increase in the production of daughters by mothers hatching their eggs synchronously, which was characterized by within‐female changes in offspring sex and not by sex‐biased mortality. As adults, sons from asynchronous broods were in better condition and produced more broods of their own than males from synchronous broods, and both males and females from asynchronous broods had higher lifetime reproductive success than those from synchronous broods. In conclusion, hatching patterns are under maternal control, representing distinct strategies for allocating offspring within broods, and are associated with offspring sex ratios and differences in offspring reproductive success.     

Brood-size and sex-ratio variation in field populations of three species of solitary aphid parasitoids (Hymenoptera: Braconidae, Aphidiinae)

Solitary parasitoids of colony-forming hosts may produce quasi-gregarious broods, which favours sibmating on the natal patch and local mate competition (LMC). We examined seasonal variations in brood size and sex ratio in three species of solitary parasitoids of aphids associated with trophobiotic ants. Adialytus arvicola, a parasitoid of Sipha agropyrella on grasses, had the smallest broods (mean=4.2, maximum 19), while Lysiphlebus hirticornis, a parasitoid of Metopeurum fuscoviride on tansy, had the largest broods (mean=32.0, maximum 265). In Pauesia pini, a parasitoid of Cinara piceicola on Norway spruce, broods comprised an average of 5.8 (maximum 41) individuals; brood size increased during early summer when hosts became more available but remained the same later in the season. In all three species the sex ratio at eclosion was female-biased, with broods containing approximately two daughters for each son in both A. arvicola and L. hirticornis; the degree of female-bias was least in P. pini. The sex ratio did not vary with brood size. In A. arvicola, the variance of the number of sons declined with an increase in brood size, consistent with "precise" sex allocation. In contrast, in L. hirticornis, the overall sex-ratio variance was greater than its binomial expectation, while it did not differ from binomial in P. pini. A large proportion of broods contained only sons or only daughters, especially in A. arvicola. An excess of male-only broods is expected if constrained females (which can produce only sons) contribute offspring prior to mating. The number of male-only broods, however, did not differ from the number expected if all females are mated and allocate offspring sexes binomially, except in P. pini. In the latter species, broods with two daughters (as opposed to two sons) exceeded binomial expectations. We propose that P. pini is largely outbreeding, while the strongly female-biased sex ratio in A. arvicola and L. hirticornis is consistent with partial sibmating and LMC. Ant-parasitoid interactions could account for a different population mating structure in the three parasitoid species. Both A. arvicola and L. hirticornis mimic the epicuticular hydrocarbon pattern of their aphid hosts. Eclosing wasps are ignored by honeydew-collecting ants and hence can mate and forage on the natal patch. In contrast, P. pini generally depart the mummy area to avoid attacks by trophobiotic ants and mate off patch.     

Sex ratio variation among broods of great reed warblers Acrocephalus arundinaceus

The sex of 746 great reed warbler fledglings (from 175 broods) was determined by the use of single primer polymerase chain reaction. The reliability of the technique was confirmed as 104 of the fledglings were subsequently recorded as adults of known sex. The overall sex ratio did not differ from unity. Variation in sex ratios between broods was larger than expected from a binomial distribution. Female identity explained some of the variation of brood sex ratio indicating that certain females consistently produced sex ratios that departed from the average value in the population. The theory of sex allocation predicts that parents should adjust the sex ratio of their brood to the relative value of sons and daughters and this may vary in relation to the quality of the parents or to the time of breeding. In the great reed warbler, the proportion of sons was not related to time of breeding, or to any of five female variables. Of five male variables, males with early arrival date tended to produce more daughters. The sex ratio of fledglings that were a result of extra-pair fertilizations did not differ from that of legitimate fledglings. Hence, there is currently no evidence of that female great reed warblers invest in a higher proportion of sons when mated with attractive males.     

Sex ratio and maternal investment in the multivoltine large carpenter bee Xylocopa sulcatipes (Apoideh: Anthophoridae)

Abstract. 1. Females of the multivoltine carpenter bee Xylocopa sulcutipes (Maa) (Hymenoptera: Anthophoridae) usually excavate a straight tunnel in dead twigs and mass provision a linear array of up to ten brood cells with pollen and nectar. An egg is deposited upon each food mass within one cell.
2. Female offspring generally receive a higher provisioning mass (0.180 ± 0.048 g) than males, a significant difference ( P > 0.001). There are, however, male larvae that receive as much food or more as their sisters or female larvae reared in another nest.
3. There is a close positive association between the size of a mother and the weight of provisions for individual daughters, but not for sons.
4. Female offspring are positioned in the innermost brood cells (Gositions 1, 2 and 3). The sex ratio of the outer cells is either significantly male biased (positions 4–6) or skewed towards males (positions 8 and 9). Positions 7 and 10 are in equilibrium.
5. Solitary females produce a significantly female biased sex ratio ( P < 0.01). Sex ratio in social nests is skewed toward females, but not significantly so ( P < 0.2). There is no significant difference between the sex ratio of solitary and social nests ( P = 0.361). The population sex ratio (pooled sex ratio of all broods produced) is significantly female biased ( P = 0.003).
6. Females kept in the laboratory produced female biased sex ratios whilst unmated females produced all-male broods indicating that insemination and ovarian development are not causally related.
7. The expected sex ratio (ESR) under equal investment, calculated as 1/CR (CR = mean male provision weight/mean female provision weight), is 137.5:117.5 (males:females), and differs significantly from that observed, 104:151 (males:females) ( P < 0.001). The 'Local Resource Enhlancement' hypothesis best explains the female biased sex ratio found in X.sulcatipes and its maintenance in the population.