OIKOS 30: 89-89. Copenhagen 1978
Is the female biased sex ratio in wood lemming Myopus schisticolor maintained by cyclic inbreeding?
Nils Chr. Stenseth
Zoological Institute, University of Oslo
Stenseth, N. C. 1978. Is the female biased sex ratio in wood lemming Myopus schisticolor maintained by cyclic inbreeding?- Oikos 30: 83-89.
The hypothesis is developed where the female biased sex ratio in wood lemming Myopus schisticolor (Lillj.), a cyclic microtine, is maintained through evolutionary time by recurrent inbreeding. If the effects, with respect to sex ratio, of inbreeding are stronger than the effects of outbreeding, then the optimal strategy (being favour ed by individual selection) would be to produce as many females as possible; the condition is that a sufficient number of males are present to ensure fertilization of all (or most) daughters. This is ensured by producing enough sons and/or by fathers mating with daughters. Some evidence supporting the occurrence of cyclic inbreeding (both sister-brother and daughter-father matings) during large fractions of microtine cycles in general, is outlined. Female biased sex ratio is predicted to be more common among exaggerated cyclic microtines than appreciated at present. One known case that seems to be similar to the situation in the wood lemming is briefly discussed: The arctic lemming Dicrostonyx torquatus (Pall.) in arctic USS R and North America. Studies aimed at producing data for testing the hypothesized occurrence of in breeding are sorely needed: Microtines should be studied with respect to breeding structure during low and early increase phases. In addition, breeding experiments for analysing the genetic mechanism are needed.
N. C. Stenseth, Zoological Institute, P. 0. Box 1050, Blindern, Oslo 3, Norway.
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{ L i 11 j . ) 1 c Ll,l1K.JeCJ CH TaJOKe HaJ1e KOJlJ.{'!eCTBa CaM.J.OB1 .QOCTaTOtiHOro tJ:TOCbJ 05eCOetrn1 onno .riOTBOpeHHe acex ( H11H 6onw.el1 pal1oHax CCCP H Cea • M£pHKH. Heooxo,I:�,HM: Hccne.n.oBaHHH c UeJlb"' npo,I: .D.aH� )l1 onpe,neneHI15I rHOOTeTHt.IeCJ Accepted 23 August 1977 © OIKOS OIKOS 30:1 (1978) 83 6• 1976), the observations of Wachtel and his co-workers 1. Introduction indicate that the Y-gene(s) either is (are) absent, or not The wood lemming Myopus schisticolor (Lilljeborg), a operating in XY females. cyclic microtine (cf. Krebs and Myers 1974), has been Fredga and his co-workers hypothesized that (1) reported to have a female biased sex ratio (20 to 30% there is an X-linked factor (or gene, called X* whene ver males) under both laboratory and field conditions (Ka necessary in the following) which represses the male lela and Oksala 1966, Frank 1966, Fredga et al. 1976, determining effect of the Y -chromosome; (2) this 1977). Breeding experiments in the laboratory show X-linked factor is transferred by the XY -females to all that a significant proportion of the females produce only of their eggs, presumably by the operation of a meiotic daughters. There is some indication that this sex ratio drive (Sandler and Novitski 1957) causing mainly distortion may be ancient (cf. Fredga et al. 1976) and X-carrying eggs to be produced. Thus mainly (or only, if consequently evolutionarily stable. However, from Fis the meiotic drive is 100% effective) female offspring her (1930) an approximately 1:1 sex ratio is, under result. Clearly, a population where X* has gone to fixa. most circumstances, expected to be the only evolution tion is dead; there will be no male in such a population. arily stable ratio. I contend that the Fisherian argument Thus, a polymorphism is expected. does not apply to the wood lemming. It should be pointed out that Fredga and his co-work. Specifically, the purpose of this paper is to present, in ers do not show any evidence, other than circumstantial, qualitative terms, an evolutionary mechanism for the for the existence of a mutant X gene. Thus, the mutant maintenance of this female biased sex ratio (Sect. 3). gene suppressing the male determining genes on they Only circumstantial evidence for the validity of the hy chromosome might equally well be on an autosomal pothesis is presented. (Sect. 4). However, based on the chromosome. However, Bengtsson (1977) gives strong analysis of Maynard Smith and Stenseth (1978) I con reasons to believe that the mutant gene is unlikely to be sider the hypothesis a plausible one for the wood lem an autosomal one. Thus, Bengtsson (1977: 339) de ming. monstrates that an autosomal sex reversal gene, A* will Secondly, I present a general hypothesis stating that always be selected against and will disappear from the cyclic microtines may be expected to have female biased population under the condition that the sex reversed sex ratios at birth. However, I do not maintain that the animals have lower fertility than other animals. What specific genetic mechanism seen in wood lemmings will happen if such a reduced fertility is not connected (Sect. 2; leading to extreme sex ratio distortions) is a with sex reversal remains to be analyzed. The general general one. hypothesis presented below, for the evolutionary Thirdly, I point out some important, but poorly un maintenance of the female biased sex ratios applies derstood aspects of micro tine population biology. As whether the sex reversing gene is autosomal or not. done by Krebs and Myers (1974), the following discus In a population with X*, X, and Y, three types of sion points to the importance of studying cyclic microti matings are possible: nes also when they are rare. XX S?x XY d giving 1 S? : 1 cJ X*X S?x XY d giving 3 S?S?: 1cJ' 2. Genetic mechanism X*Y S?x XY d giving only � � Fredga et al. (1976, 1977) have recently reported that some females, producing mainly female offspring, had Bengtsson (1977) has shown that in a random mating an XY chromosome constitution. Otherwise both XX population the frequencies of the four different geno· and XY females seem to be phenotypically indistin types X*X, XX, X*Y, and XY all are expected to be guishable. No difference in litter size was found. Kalela close to 0.25. Thus, there will be approximately 25% and Oksala (1966) report observations from laboratory males in the population. Simulations indicate that this experiments that can be interpreted as XY females result does not depend on whether or not inbreeding · having a mean litter size equal to 3.94 ± 0.18 (based on occurs (Maynard Smith and Stenseth 1978); the only 89 litters from 18 different females) whereas the other condition is that all females are potentially mated. This · females (i.e.XX which actually may be of two genetic latter condition is likely to be valid, an inference ba sed ally different types, see below) had a mean litter size on the observed greater home range of males compa red 1 equal to 4.00 ± 0.16 (based on 111 litters from 26 with females in many microtine species (e.g. Myllymiiki different females). 1975). Furthermore, Skaren (1964) observed 100% • Furthermore, Wachtel et al. (1976) have demon pregnancy among wild caught wood lemmings. Thus, strated that XY females are H-Y antigen negative while Fredga and his co-workers' hypothesis may be conclud· · XY males are H-Y antigen positive ( cf. Silvers and ed to result in an ecologically stable system in a global Wachtel 1977). Presuming that the H-Y antigen is the sense. This is an important property of a genetic system gene product of the Y chromosome, responsible for ini to operate in cyclic fluctuating species like the wood · tiating testicular differentiation and male development lemming: The frequencies of the different genotypes Ii: (cf. Bmgger and Aagenres 1964, Crew 1965, Ohno a population may be radically changed due to migratien 84 OIKOS 30:1 (19.1$) (the tendency to disperse seems to be unevenly distri and genes determining the sex of the individual, will buted over different genotypes (cf. Krebs et al. 1973)), tend to produce a 1:1 sex ratio at birth. The only genes or due to drift and founder effects (which might be of distorting sex ratio, which would at first be selected, are great importance just after the crash). those on the X and Y chromosome of the heterogametic However, it should be emphasized that the hypothesis sex (Maynard Smith 1978, Maynard Smith and Stenseth of Fredga and his co-workers treats the genetic mecha unpubl.). However, mutants suppressing these latter nism underlying the observations on wood lemmings genes may always be expected as selected in a random only. They did not consider the evolutionary stability of mating population. the postulated system. If the Fisherian argument ap Hamilton (1967) pointed out that the Fisherian ar plies, modifiers suppressing the X linked gene would be gument fails under inbreeding: In such situations it is expected to be selected. individually beneficial to produce as many daughters as The model presented by Bengtsson (1977) demon possible. Thus, Hamilton's argument and the one pre strates only the ecological stability of the genetic system sented in this paper only need to assume the operation suggested by Fredga and his co-workers. To me it seems of individual selection. In addition, a sparse patchily that Bengtsson's model is insufficient to explain evoluti distributed population may be presumed to have group onary stability. The ecological stability of the system is a selective advantages of female biased sex ratio. Hamil necessary but insufficient condition for stability in evo ton's argument does not depend on arrhenotoky, i.e. a lutionary time. In order to study the evolutionary stabi sex determining mechanism in which fertilized diploid lity of a system it is necessary to consider what happens eggs develop as females and unfertilized haploid eggs as in the case of new genetic material being introduced males (cf. Maynard Smith and Stenseth 1978, unpubl.): into a population consisting of X*, X, and Y. Bengtsson Hamilton's arguments are likely to apply whenever (1977) does this for a panmictic population and May genes (autosomal or not) in the gametophyte can influ nard Smith and Stenseth (1978) for a population with ence the sex ratio. The condition for optimizing the different degrees of inbreeding. For the system to be strategy of producing as many daughters as possible is stable or "unbeatable" in evolutionary time, it must re that enough males are present to ensure fertilization of sist the introduction of mutants tending to normalize the all (or most) daughters. This is ensured by producing an sex ratio: Bengtsson (1977: 341) and Maynard Smith adequate number of sons, possibly in combination with and Stenseth (1978) demonstrate that genes suppres fathers mating with daughters, or sons with their sing the X* - gene are likely to be established in a mothers. panmictic population. Based on Hamilton's original suggestion I hypothesize that the peculiar sex ratio seen in wood lemmings is maintained through evolutionary time by recurrent in 3. A hypothesis for the evolutionary stability of the breeding (i.e. mating between close relatives) during most female biased sex ratio of the cyclic periods. Inbreeding results from extremely Tactically, the Fisherian argument for a 1:1 sex ratio low densities and patchy distribution during the low assumes that mating is random (panmictic). No other phases. restrictions with respect to the mating system (e.g. mo Several features of the situation discussed by Fisher nogamy or not) seem necessary (cf. Maynard Smith and and Hamilton differ from the wood lemming case, parti Ridpath 1972). The Fisherian argument goes as follows cularly with respect to the genetic system assumed in the case of equal expenditure on both sexes until (Sect. 2): The Fisher-Hamilton arguments were origin weaning (cf. MacArthur 1965) (J. Maynard Smith pers. ally put forth for (autosomal) genes determining the sex comm.) : Let s d d : 1 '¥ '¥ be the existing sex ratio in ratio of the offspring, and not for genes determining sex the population. That is, s : 1 is the expected sex ratio at in the individual carrying it. Hamilton's model assumes birth (or weaning) for any individual in the population. that an autosomal gene (m, say) may, if it operates in If s > 1, it will pay (in an evolutionary sense) to produce males, cause (through the operation of a meiotic drive) females, because females have more offspring; i.e. if s > fewer sperms carrying a Y chromosome than an X 1, an individual producing daughters will have more chromosome to be produced, but all XY individuals are grandchildren. Thus, if s > 1 selection will reduce s. By males. Alternatively, if the gene, m, operates in the fe similar arguments, if s < 1, selection will increase it. males, she may be able to differentiate between Only s = s* = 1 is an evolutionarily stable strategy, or "XY-embryos" and "XX-embryos" and cause more of an ESS ( cf. Maynard Smith 1972, Lawlor and Maynard the latter type to be implanted. This would be a form of Smith 1976). Maynard Smith and Stenseth (unpubl.) differential parental care, but without any significant show that this argument can be made genetically correct cost (due to the early operation). for, at least, autosomal genes: Thus, if the production of However, Maynard Smith and Stenseth (1978) de males and females is genetically determined by autoso monstrate that Hamilton's argument is also applicable mal genes, in a random mating popultion, the ESS will to a genetic mechanism as hypothesized by Fredga and be found to be s* = 1. All genes in the homogametic his co-workers; that is, where a gene exists that both parent, autosomal genes in the heterogametic parent, determines the sex ratio at birth and the sex itself. OIKOS 30:1 (1978) 85 Ecologically, my hypothesis is also somewhat differ available when the weanlings mature at an age of ent from Hamilton's: I have hypothesized mating to oc approximately one month (limen and Lahti 1968), cur between close relatives like brothers and sisters, or thus ensuring their fertilization. daughters and fathers. Hamilton, on the other hand, (3) New demes may also be formed by the weanlings. supposed that the population consisted of groups of n An open question is whether or not these new de m families whose members mated randomly. A female es tend to be established by close relatives (e.g. then has a probability of lin of mating with her brother. brothers and sisters). No relevant data from free-living microtines seem to exist. Preli Hamilton obtained s* = (n-1 )/2n. Maynard Smith and minary Stenseth (unpubl.) demonstrate that this result is gene (unpu bl.) analysis of a current experiment with rally applicable for brother-sister mating in diploids, i.e. freely-growing confined root vole populations for the situation hypothesized in this paper. Microtus oeconomus (Pall.) indicates that siblings An important point of great theoretical implication tend to stay where they were born, or else move concerning the discussion of sex and optimal sex ratios together to another place in the population ca ge. in wild populations is apparent: The problems of Similar observations on the Norwegian lemming breeding structure and grades of relationship between Lemmus lemmus (L.) have been made by A. mating individuals. This has most often been neglected Semb-Johansson (pers. comm.). by proponents of both group selection and individual If sisters only establish a new deme, then repro selection when discussing optimal sex ratios (cf. Willi duction may not occur. Thus there would be a te n ams (1971, ch. 4), but see Hamilton (1975)). Although dency to produce, in effect, non-reproductive off the existence of a non-random breeding structure has spring. I contend that this effect is slight. Particu vaguely been appreciated by field biologists, they have, larly may this be assumed to result from the greater unfortunately, given the problem too little considera mobility of males compared to that of females (cf. tion. Myllymaki 1975): By their greater mobility, males are likely to find any females that are within reasonable distances. 4. Inbreeding in cyclic microtine populations (4) The average low density in the habitat dictates that I have been unable to locate data to test the hypothe the probability is low for an individual emigrating sized occurrence of inbreeding directly. Studies aimed from one deme into another established deme. This at producing such data are sorely needed: Microtines probability would be further reduced since re si should be studied with respect to their breeding struc dents repel strangers (Lidicker 1975). ture during low and early increase phases. (5) From any of the three mating types in the system In the following I will briefly outline some evidence hypothesized by Fredga and his co-workers for the supporting the occurrence of cyclic inbreeding during wood lemming, males will sooner or later be bo rn. the greater part of microtine cycles (i.e. low and in Thus, any group may be quite likely to contain at crease phases) in general: least one male. Based on information collected and interpreted by Stenseth et al. ( 1977: Sect. 7), these (1) After a crash of cyclic microtines, a meta population males may be assumed to be driven away at their (cf. Levins 1970) is presumed to exist in survival age of maturation, unless the old male should die. pockets (Lidicker 1973) consisting of only a few This, presumably general tendency further assures individuals which may be closely related. the fertilization of all females. (2) In increasing populations selective pressures exist (6) In cases of low density, these young dispersing for allocating as many resources as possible to in males may be likely to find their mothers who creasing the current reproductive output (see Pian dispersed earlier when pregnant. This further con· ka and Parker 1975). Thus there is a tendency for a tributes to the degree of inbreeding. pregnant female, with a newly weaned litter to mi grate to another place prior to giving birth (Sten Consequently, during the low phase, inbreeding in the seth 1978). Empirical evidence suggests that many metapopulation may be extensive. In particular, it fol rodent species display this behaviour (Lidicker lows from the above circumstantial evidence that 1975). The offspring (possibly only daughters) are daughters are unlikely to be inseminated by non-relate d likely to continue to reside in the proximity of their males in most cases. During the peak phase, the likeli · birthplace. This is particularly true for the hood for outbreeding increases. Thus the crux is how daughters. Lloyd and Christian (1967: 268) work will the effects of inbreeding and outbreeding balance? ing with the house mouse Mus musculus L. observ The structure of the metapopulation facilitating in· ed that "litters tended to remain together in nest breeding is, however, likely to exist for 2/3 or more of · sites long after weaning and after subsequent litters the whole cyclic period: Micro tines are only observed as : had been born". This tendency was common at low common every third or fourth year. densities. Since pregnancy (of the mother) occurred It might be argued, that since microtines exhibit den• at- all, a reproductively active male is likely to be sity cycles and are extremely abundant every third oi 86 OIKOS 30:1 (1978) fourth year, these species ought to exhibit little in one class of such strategies, i.e. those suppressing the breeding compared with other "stable" populations , effect of the X*-mutant. Then, what I have suggested is being fairly rare all the time. This I do not believe is a that strong inbreeding will prevent such suppressor gen valid criticism of the hypothesis. Thus, A. Myllymaki es being established in the population. I have disregard (pers. comm.) has data for the field vole Microtus agre ed strategies due to "hitch-hiking" with other advanta stis (L.) which indicate a relatively close demic structure geous genes. I contend that this is not of major import (and presumably some inbreeding) even at peak densi ance because, as I have pointed out in Sect. 3, individual ties. Rasmussen (1964) found extensive inbreeding in selection will, in the case of inbreeding favour a female fairly dense populations of deer mouse Peromyscus ma biased sex ratio. Thus it might be argued that selective niculatus Wagner. Thus there is, I belive, no reason to pressure favours a decoupling of the two genes. Much expect the degree of inbreeding to be less in cyclic further work is certainly needed at this point. microtines. Inbreeding often results in excessive homozygosity and may therefore result in reduced individual fitness. Inbreeding is therefore likely to be fairly rare in nature, a presumption supported by empirical information ( cf. 5. Conclusion and discussion Wilson 1975: 79, Jacquard 1974). Nevertheless, during My arguments can be summarised as follows: periods of low density and for certain spatial distribu tions, inbreeding may be a "statistical necessity": The (1) Fisher's (1930) argument for the selection of a 1:1 only individuals around may be close relatives and a sex ratio has panmixis as a prerequisite. given individual may have the choice between not re (2) Hamilton (1967) has shown that inbreeding leads producing at all, or mating with a close relative like one to selection of female biased sex ratios. This biased of its parents or a sibling. This I believe is just the situa sex ratio is evolutionarily stable. This is true if the tion in many cyclic microtine species and in the wood genes determining the sex ratio are autosomal lemming in particular. In such a system, deleterious (Hamilton 1967, Maynard Smith and Stenseth un genes are likely to have been strongly selected against. publ.) or sex linked (Maynard Smith and Stenseth But if inbreeding overrides outbreeding with respect 1978). to sex ratio, then why are female biased sex ratios not (3) Fredga et al. (1976) have hypothesized on the basis observed in more cyclic microtine populations? First, as of observations that the genetic basis for the female stated above, I contend that the lower the density dur biased sex ratio in wood lemmings is sex linked. ing a cyclic low, the greater the likelihood will be of (4) I have, by means of examples, substantiated the extensive inbreeding, causing a sex ratio distortion. hypothesis that inbreeding may be fairly common in Thus, it should be noted that the wood lemming exhibits cyclic microtines in general and in wood lemmings density cycles which are even more exaggerated than in particular. those of the legendary Norwegian lemming (Kalela and (5) I propose therefore that a contributing factor to the Oksala 1966). However, as is apparent from the discus evolutionary stability of the observed female biased sion in Sect. 4, whether or not this happens depends on sex ratio in wood lemmings is extensive inbreeding, the particular behaviour and population dynamics of the presumably during the low phases of the density species being considered. cycle. Secondly, sex ratio distortions among small rodents are not extensively sought after. Nevertheless, a few A few words about stability are necessary at this point to cases resembling the female dominance in the wood avoid confusion. (I am indebted to B. 0. Bengtsson for lemming apparently exist among other microtines: pointing out some of the difficulties to me.) I have used Fredga et al. (1976) cites Gileva and Lobanova's (1974) the term "evolutionary stability" in the following observations on the arctic lemming Dicrostonyx torqu meaning: Given a complete description of all strategies atus (Pallas) in the arctic tundra of USSR. Similar ob (genotypes/phenotypes) constituting the "fitness set" servations are reported for the arctic lemming in Alaska (cf. Levins 1968), the strategy maximizing individual (Rausch and Rausch 1972). Another possibly similar fitness will represent an evolutionarily stable, or un situation may be found in the root vole in Alaska (R. L. beatable, strategy; that is an ESS in the terminology of Rausch, cited from Whitney 1973: 221). This female Maynard Smith (1972). Defined thus, an ESS is that biased sex ratio may, however, hot be evolutionary strategy which, if adopted by all individuals in the po stable (cf. Maynard Smith and Stenseth 1978). I predict pulation, is proof against further evolution (for a given that female biased sex ratios (possibly with different long-term consistent environmental pattern) because genetic basis) are likely to be observed in other microti any mutant would be less fit than the remaining mem ne populations exhibiting exaggerated styles. Field and bers of the population (e.g. Leon 1976). However, to laboratory studies testing this prediction are badly ne describe all possible strategies is an impossible task. eded. Realizing this, one has to restrict oneself to a subset of Two general problems ought to be investigated in the possible strategies. In this paper I have had in mind connection with the hypothesis discussed in this paper OIKOS 30:1 (1978) 87 1967. (both with respect to the wood lemming in particular Hamilton, W. D. Extraordinary sex ratios. -Science 156: 477-488. and with respect to microtines in general): - 1975. Gamblers since life began: barnacles, aphids, elms. Quart. Rev. Bioi. 50: 175-180. (1) Genetic analysis of the offspring from different limen, M. and Lahti, S. 1968. Reproduction, growth and wood types of matings in order to investigate the genetic behaviour in the captive lemming, Myopus schisti· color (Lilljeb.). - Ann. Zoo!. Fennici 5: 207-219. mechanism (Sect. 2), and Jacquard, A. 1974. The genetic structure of populations._ (2) The mating structure of the population in order to Springer, Berlin. investigate the occurrence of inbreeding; i.e. stud Kalela, 0. and Oksala, T. 1966. Sex ratio in the wood !em. ies of the social organization, breeding biology and ming, Myopus schisticolor (Lilljeb.), in nature and in capti vity.- Ann. Univ. Turkuensis, Ser. All 37: 1-24. movement patterns, particularly during the low Krebs, C. J. and Myers, J. H. 197 4. Population cycles in small phases of microtine cycles. mammals.- Adv. Ecol. Res. 8: 269-399. - , Gaines, M.S., Keller, B. L., Myers, J. H., Tamarin, R. H. The latter issue might be investigated by the occurrence 1973. Population cycles in small rodents. -Science 179: of different genotypes ( cf. Rasmussen 1964) within a 35-41. Lawlor, L. R. and Maynard Smith, J. 1976. The coevolution geographical area: If, for instance, a shortage of hetero and stability of competing species.- Am. Nat. 110: 79 99. zygous individuals is observed, and this shortage cannot Le6n, J. A. 1976. Life histories as adaptive strategies. - J. be accounted for by differential survival, inbreeding is theoret. Bioi. 60: 301-335. likely to occur. Particularly, if the genetic variability Levins, R. 1968. Evolution in changing environments.- Prin ceton Univ. Press, Princeton, N.J. within groups is significantly smaller than the genetic - 1970. Extinction. - In: Cowan, J. D. (ed.), Some mathe variability between groups, inbreeding is likely to occur matical questions in biology. Lectures on mathematics in in a metapopulation. The application of blood protein the life sciences. Am. Math. Soc. 2: 75-108. as markers seems to be the obvious device. Lidicker, W. Z., Jr. 1973. Regulation of numbers in an island population of the California vole: a problem in community dynamics. - Ecol. Monogr. 43: 271-302. 1975. The role of dispersal in the demography of small Acknowledgements - This paper owes a great deal to �?any mammals.-In: Golley, F. B., Petrusewicz, K., and Rysz. stimulating and clarifying discussions with J. MaynardSm Ith at kowski, L. (ed. ), Small mammals: their productivity and . the University of Sussex. Without his encouragement, this pa population dynamics. Camb. Univ. Press, New York, pp. per might never have materialized. B. 0. Bengtsso , T. Fen � . 103-128. chel, K. Fredga, and A. L0v!ie are thanked for their detailed Lloyd, J. A. and Christian, J. J. 1967. Relationship of activity reviews of an earlier draft to this paper. B. 0. Bengtsson (who and aggression to density in two confined populations of is very critical towards my argument about inbreeding), K. house mice (Mus musculus).- J. Mammal. 48: 262-269. Fredga, W. D. Hamilton, L. Hansson, J. Maynard Smith, A. MacArthur, R. H. 1965. Ecological consequences of natural _ Myllymaki and A. Semb Johansson are thanked for shanng selection. - In: Waterman, T. H. and Morowitz, H. J. (ed.), their ideas with me and/or for making unpublished manu Theoretical and mathematical biology. Blaisdell, New scripts and data available to me. A grant from the British York, pp. 388-397. Council, making it possible for me to work in the Population Maynard Smith, J. 1972. On evolution. - Edinburgh Univ. and Developmental Biology Group at the University of Sussex Press, Edinburgh. is gratefully acknowledged. M. Espeland, R. Wiger and L. - 1978. Sex and evolution. -Cambridge Univ. Press, Cam· Wold are thanked for improving the language. bridge. (in press) - and Ridpath, M. G. 1972. Wife sharing in the Tasmanian , native hen, Tribonyx mortierii: a case of kin selection?- :. Am. Nat. 106: 447-452. References - and Stenseth, N. C. 1978. On the evolutionary stability of • Bengtsson, B. 0. 1977. 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