adaptive for stressed mammals to produce a male-biased offspring sex ratio. His ... the unqualified term "stress" in the context of sex allocation. Although ...
V o l . 1 2 7 .N o . 6
The American Naturalist
June 1986
NOTES AND COMMENTS
BIASED SEX RATIOS IN STRESSED ANIMALS McGinley (1984)recently drew attention to circumstancesin which it could be adaptive for stressed mammals to produce a male-biased offspring sex ratio. His argument, which applies to species that have small litters, is based on (1) the prediction by Trivers and Willard (1973) that, in a polygynous mating system, mothers should invest in male offspring when their ability to invest in individual offspring is high, (2) the analysis by Smith and Fretwell (1974) of the optimal balance between offspring size and number, and (3) the problem of what parents should do with the surplus when their investment ability falls between what is neededfor two litter sizes(first discussedin Ricklefs 1968in relation to bird clutch sizeslimited by food availability). McGinley, suggestingthat the fractional surplus should be invested in large male offspring, predicted that (l) male-biasedoffspring sex ratios may be produced by stressedfemales when the litter size is reduced, and (2) male-biased offspring sex ratios should be more common in smaller-thanaveragelitters. He cited a number of studies,particularly Verme's (1969)work on white-tailed deer (Odocoileus virginianus), that produced results consistent with these predictions. My main aims here are to draw attention to Williams' (1979) discussion of the same subject and to point out that although the phenomena referred to by McGinley may be used to explain some results in the literature, they are not sufficient to predict whether offspring sex ratios will be biased in favor of males or females. To do this, we also need precise measures of parentalinvestment (PI) ability, the relative costs of male and female offspring, and the effects on subsequent reproductive success of intrasexual variation in neonatal si ze. Before discussingthese issues it is worth mentioning a minor problem in using the unqualifiedterm "stress" in the context of sex allocation. Although McGinley clearly intended to refer to nutritional stress,the term is more commonly used to connote the behavioral and physiological syndrome caused by adrenal responses to such factors as pain, aggressiveinteractions, and overcrowding (recently reviewed in Lee and MacDonald 1985). There is the potential for confusion here because parents could allocate resources to offspring of different sexes in relation to social (frequency-dependent) factors as well as to resource availability. This ambiguity can be avoided if the independent variable used in considering a mother's investment in offspring of differing size, number, and sex is simply Am. Nat. 1986.Vol. 121,pp.89l-896. BritishCrownCopyright1986.
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variation in PI ability, when PI is any investment that increasesan offspring's reproductive successat the cost of the parent's ability to invest in future offspring (Trivers 1972). When the component of PI under discussion is the ability of a female mammal to nourish her offspring, the principal variable that should be considered(although not the only one) is the portion of the mother's nutrient or fat reserves that can be apportioned to each offspring (Gosling and Petrie l98l; G os ling 1986) . More important, McGinley also considered stress (or declining PI ability) in a way that casts doubt on the generality of his case. He argued that a mother with more PI ability than necessary for one offspring, but not enough for a litter of two, should produce one large offspring. Under these circumstancesshe should produce a male, since large males achieve high reproductive successin a polygynous mating system. He then argued that such mothers are stressed,going on to generalizethat stressedmothers should produce male-biasedprogenies. In fact, McGinley used "stressed" in the very specialized sense of a mother whose PI ability is reduced below that needed to produce a litter of n average-sizedoffspring, but which is still above that needed to produce a litter of n - I offspring. In the conventional senseof the term stress,a mother whose PI ability is reduced to below that neededfor n - | offspring should be even more stressed.But if the mother can still produce smaller-than-averageoffspring, the Trivers and Willard hypothesis would then predict a female-biasedratio, since in a polygynous system, small females might do almost as well as large femalesbut small males would do much worse than large males. McGinley mentioned that this could occur in the case of yearling female white-tailed deer, which produce female-biasedoffspring, but did not explain why all mothers should not do the same when sufficiently s t r es s ed. McGinley's second main prediction, that male-biased offspring sex ratios should be more common in smaller-than-averagelitter sizes, would have general validity in the case of white-tailed deer (for which the mean litter size is between one and two) only if mothers could not produce any young when their investment ability falls below that needed for a single male offspring. If females could still produce one small offspring, the prediction is that the offspring of these highly stressed mothers would be biased toward females. Similarly, in the illustration used by McGinley in which a female has the capacity to produce 1.8 "notional offspring units," why should she not invest in two small females rather than one large male? Theoretically, this should depend on the relative costs of producing male and female neonatesof various body size and on the part of the variation in s ubs equentr ep ro d u c ti v es u c c e s sth a t d e p e n dson the mother' s i ni ti al i nvestment. Not any of these data are available for deer. These argumentsare not intended to suggest that the stress hypothesis does not successfully explain Verme's main body of data on the sex ratio of white-tailed deer on high- and low-plane diets (Verme 1969).Rather, they intend to show that the prediction succeedsbecauseit considers only a part of the range in PI ability in a specieswith a particular range of litter sizes. The generalization that stressedfemales with small litters should produce a male-biasedprogeny cannot be sustainedexcept under limited circumstances.The studiesof wolves (Canis lupus) and red-wingedblackbirds (Agelaius
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phoenic'ezs)cited as evidence for male-biasedsex ratios in stressedmothers do not resolve PI ability finely enough to determine whether or not females are stre ss edin t he s pe c i a l i z e ds e n s eu s e d b y Mc G i n l ey. Williams (1979)previously outlined the expected adaptive responseby mothers that can produce more than one offspring, depending on variation in their ability to invest, if they can control the sex of the offspring within a litter. In fact, becauseWilliams' illustration of sex-ratio optimization usesfemales that produce up to three offspring. it is particularly applicable to white-tailed deer. Thus, from the lowest level of PI ability at which it is possible to produce an offspring, mo th er s s hould pr o d u c e a fe m a l e (F ); a n d a t successi vel yhi gher l evel s, they sh o uld pr oduc e one m a l e (M), th e n l i tte rs o f F F , M F, MM, and fi nal l y FFF. It can easily be seen in this series how female-biased progenies could result from mothers that produced smaller-than-averagelitters, given the selectionof particul a r l ev els of P I . T hi s mo d e l a s s u me sth a t th e re a r e l .l cost uni ts for a son and 1.0 for a daughter and that mothers try to maximize their total parental investment in relation to their own reproductive value. However, the assumptionsof the model are restrictive, and it has also been suggestedthat females may expend less than the maximum possible reproductive effort in producing one litter, probably because they can thus maximize their fitness over their entire reproductive lifetime (Ch a r nov and K r eb s 1 9 7 4 ).In c a s e si n w h i c h fe mal esproduce a seri esof l i tters. the investment in any one litter may detract from the resourcesavailablefor other litters and may also reduce the chance of surviving to produce them. Females could thus maximize their lifetime total number of offspring, by producing litters smaller than the maximum possible at any one time or by increasingthe interval between litters. Thus, a female could have nutrients to spare when producing any one litter, and selection could favor the ability to use this surplus to respond to changing circumstances during her reproductive life; for example, she could produce different combinations of sons and daughters in responseto changes in the operational sex ratio (assumingthat facultative determinationof offspring sex is physiologically possible). Williams' model could also be extended in another way to consider intrasexual variation in offspring size (and potential reproductive su cc es s ) .I t is pos s i b l e to e n v i s a g e d e mo g ra phi c ci rcumstancesi n w hi ch thi s variation might give an advantage to females that produced fewer offspring than expected from the average unit costs of males and females. For example, when average-sizedmales are common in a population or social group, mothers might increase their fitness by reducing the litter size and producing a small number of very large sons. If mothers can vary their offspring production in this way, it would be even more difficult to predict offspring sex biasesthan envisagedin the e a rl i er dis c us s ion. However, even assuming the simplest hypothesis-namely, that females maximize some product of offspring number and size at each littering event and that their ability to do this is limited by the resources available to them-a practical difficulty arises from Williams' and McGinley's ideas. The absenceof information about PI ability and the costs of male and female offspring create the opportunity for a Panglossianinterpretation of every offspring sex-ratio result. Each increasing notch on the scale of maternal ability to invest has a unique sex-ratio predic-
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tion, and every result that differs significantly from unity can thus be given an adaptive interpretation. However, this difficulty is reducedwhen there is a precise determination of PI ability in relation to offspring sex and quality (usually size). McGinley's note is valuable in drawing attention to this requirement in future studies of facultative variation in offspring sex ratio. ACKNOWLEDGMENTS
I am gratefulto M. Petrie, M. A. McGinley, and two anonymousreferees, whosecommentsimprovedan earlierdraft. LITERATURE CITED
C h a r n o ' . ' ,E . L . , a n d J . R . K r e b s . 1 9 7 4 .O n c l u t c h - s i z ea n d f i t n e s s .l b i s l l 6 : 2 1 7 - 2 1 9 . Gosling, L. M. 1986. Selective abortion of entire litters in the coypu: adaptive control of offspring production in relation to quality and sex. Am. Nat. 127:772-795. G o s l i n g , L . M . , a n d M . P e t r i e . 1 9 8 1 .T h e e c o n o m i c s o f s o c i a l o r g a n i s a t i o n .P a g e s3 1 5 - 3 4 5 i n C . R . Townsend and P. Calow, eds. Physiological ecology: an evolutionary approach to resource use. Blackwell, Oxford. L e e , A . K . , a n d I . R . M a c D o n a l d . 1 9 8 5 .S t r e s s a n d p o p u l a t i o n r e g u l a t i o n i n s m a l l m a m m a l s . O x f o r d Rev. Reprod. Biol. 7:261-304. M c G i n l e y , M . A . 1 9 8 4 .T h e a d a p t i v e v a l u e o f m a l e - b i a s e ds e x r a t i o s a m o n g s t r e s s e dm a m m a l s . A m . Nat. 124:597-599. R i c k l e f s , R . E . 1 9 6 8 . O n t h e l i m i t a t i o n o f b r o o d s i z e i n p a s s e r i n eb i r d s b y t h e a b i l i t y o f a d u l t s t o nourish their young. Proc. Narl. Acad. Sci. USA 6l:847-851. S m i t h , C . C . , a n d S . D . F r e t w e l l . 1 9 7 4 .T h e o p t i m a l b a l a n c e b e t w e e n s i z e a n d n u m b e r o f o f f s p r i n g . Am. Nat. 108:499-506. T r i v e r s , R . L . 1 9 7 2 .P a r e n t a l i n v e s t m e n t a n d s e x u a l s e l e c t i o n .P a g e s 5 9 7 - 5 9 9 i n B . G . C a m p b e l l , e d . S e x u a l s e l e c t i o na n d t h e d e s c e n t o f m a n , l 8 7 l - 1 9 7 1 . A l d i n e , C h i c a g o . T r i v e r s , R . L . , a n d D . E . W i l l a r d . 1 9 7 3 .N a t u r a l s e l e c t i o n o f p a r e n t a l a b i l i t y t o v a r y t h e s e x r a t i o o f offspring. Science (Wash., D.C.) 179:90-92. Verme, L. L 1969. Reproductive patterns of white-tailed deer related to nutritional plane. J. Wildl. Manage. 47:573-582. Williams, G. C. 1979.The question of adaptive variation in sex ratio in outcrossed vertebrates. Proc. R. Soc. Lond. B. Biol. Sci.. 205:567-580.
L. M. Gosl rN c Coypu REsenncsLnsoRnrony MtNrsrny oF AcRICULTURE, FtsHERIgs, ANDFooo JuprrERRonp Nonwrcs NR66sP UNlruo KlNcool,t Submitted April 22, 1985;Accepted October 15, 1985
