Analysis of sex ratio variances and sequences of sex allocation

doi:10.1017/CBO9780511542053.006

Chapter 5 - Analysis of sex ratio variances and sequences of sex allocation

Published online by Cambridge University Press: 06 August 2009

Evert Meelis and

Edited by

Sven Krackow: Affiliation:
Animal Behaviour, Institute of Zoology, University of Zürich-Irchel, Switzerland
Evert Meelis: Affiliation:
Institute of Evolutionary and Ecological Sciences, University of Leiden, The Netherlands
Ian C.W. Hardy: Affiliation:
Lecturer in Animal Population Biology School of Biosciences, University of Nottingham
Ian C. W. Hardy: Affiliation:
University of Nottingham

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Summary

Sex ratio variances can indicate control of sex allocation beyond the production of a certain mean. Furthermore, theory predicts that nonbinomial (nonrandom) offspring-group sex ratio distributions should be selectively favoured in some circumstances. Mechanisms of producing nonbinomial sex ratio variances include the allocation of sex to offspring in fixed or other nonrandom sequences. Variances and sequences are thus linked. In this chapter we review predictions of sex ratio models, consider constraints and expectations arising from particular sex-determination mechanisms and discuss statistical methods for variance and sequence analysis.

Introduction

In Chapters 3 and 4 variance was treated as a consideration necessary to ensure appropriate data analysis. However, variance of offspring-group sex ratios are of interest in themselves both because they may be under selection and because they can indicate parental control of sex allocation. We begin by reviewing predictions of sex ratio models (section 5.3) and considering constraints and expectations arising from particular sex-determination mechanisms (section 5.4). We then introduce sex ratio ‘precision’ and its measurement (section 5.5) and give methods for statistical analysis of sex ratio variance (section 5.6). Sequences of sex allocation, and their relationships with sex ratio variance, are considered in section 5.7.

Variance expectations from optimality theory

Optimal sex-allocation theory makes predictions not just about mean sex ratios but also about variances. When mating opportunities extend throughout large populations (panmixis) the sex ratio within a group of offspring is selectively neutral as long as the population sex ratio remains at equilibrium (Kolman 1960).

Type: Chapter
Information: Sex Ratios
Concepts and Research Methods
, pp. 112 - 131

DOI: https://doi.org/10.1017/CBO9780511542053.006 [Opens in a new window]

Publisher: Cambridge University Press

Print publication year: 2002

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References

Akaike, H (1974) A new look at the statistical model identification. IEEE Transactions on Automatic Control, AC- 19, 716–723CrossRef Google Scholar

Avilés, L, Varas, C & Dyreson, E (1999) Does the African social spider Stegodynus dumicola control the sex of individual offspring?Behavioral Ecology and Sociobiology, 46, 237–243Google Scholar

Avilés, L, McCormack, J, Cutter, A & Bukowski, T (2000) Precise, highly female-biased sex ratios in a social spider. Proceedings of the Royal Society, London, B, 267, 1445–1449CrossRef Google Scholar

Brooks, R J, James, W H & Gray, E (1991) Modelling sub-binomial variation in the frequency of sex combinations in litters of pigs. Biometrics, 47, 403–417CrossRef Google Scholar PubMed

Chow, A & Mackauer, M (1996) Sequential allocation of offspring sexes in the hyperparasitoid wasp, Dendrocerus carpenteri. Animal Behaviour, 51, 859–870CrossRef Google Scholar

Colozza, S & Wajnberg, E (1998) Effects of host egg mass size on sex ratio and oviposition sequence of Trissolcus basalis (Hymenoptera: Scelionidae). Environmental Entomology, 27, 329–336CrossRef Google Scholar

Cooke, F & Harmsen, R (1983) Does sex ratio vary with egg sequence in lesser snow geese?The Auk, 100, 1–8Google Scholar

Craig, S F, Slobodkin, L B, Wray, G A & Biermann, C H (1997) The ‘paradox’ of polyembryony: a review of the cases and a hypothesis for its evolution. Evolutionary Ecology, 11, 127–143CrossRef Google Scholar

Dijkstra, C, Daan, S & Buker, J B (1990) Adaptive seasonal variation in the sex ratio of kestrel broods. Functional Ecology, 4, 143–147CrossRef Google Scholar

Dijkstra, C, Daan, S & Pen, I (1998) Fledging sex ratios in relation to brood size in size-dimorphic altricial birds. Behavioral Ecology, 9, 287–296CrossRef Google Scholar

Edwards, A W F (1958) An analysis of Geissler's data on the human sex ratio. Annals of Human Genetics, 23, 6–15CrossRef Google Scholar PubMed

Edwards, A W F (1960) The meaning of binomial distribution. Nature, 186, 1074CrossRef Google Scholar PubMed

Fiala, K L (1980) On estimating the primary sex ratio from incomplete data. American Naturalist, 115, 442–444CrossRef Google Scholar

Fiala, K L (1981) Sex ratio constancy in the red-winged blackbird. Evolution, 35, 898–910CrossRef Google Scholar PubMed

Frank, S A (1990) Sex allocation theory for birds and mammals. Annual Review of Ecology and Systematics, 21, 13–55CrossRef Google Scholar

Green, R F, Gordh, G & Hawkins, B A (1982) Precise sex ratios in highly inbred parasitic wasps. American Naturalist, 120, 653–665CrossRef Google Scholar

Gutiérrez-Adán, A, Pérez-Garnelo, J, Granados, J J, Garde, M, Pérez-Guzmán, B Pintado & , Fuente J (1999) Relationship between sex ratio and time of insemination according to both time of ovulation and maturational state of oocyte. Zygote, 7, 37–43CrossRef Google Scholar PubMed

Haccou P & Meelis E (1994) Statistical Analysis of Behavioural Data. An Approach Based on Time-Structured Models. Oxford: Oxford University Press

Hamilton, W D (1967) Extraordinary sex ratios. Science, 156, 477–488CrossRef Google Scholar PubMed

Hardy, I C W (1992) Nonbinomial sex allocation and brood sex-ratio variances in the parasitoid Hymenoptera. Oikos, 65, 143–158CrossRef Google Scholar

Hardy, I C W (1997) Possible factors influencing vertebrate sex ratios: an introductory overview. Applied Animal Behaviour Science, 51, 217–241CrossRef Google Scholar

Hardy, I C W & Cook, J M (1995) Brood sex ratio variance, developmental mortality and virginity in a gregarious parasitoid wasp. Oecologia, 103, 162–169CrossRef Google Scholar

Hardy, I C W, Dijkstra, L J, Gillis, J E M & Luft, P A (1998) Patterns of sex ratio, virginity and developmental mortality in gregarious parasitoids. Biological Journal of the Linnean Society, 64, 239–270CrossRef Google Scholar

Harmsen, R & Cooke, F (1983) Binomial sex ratio in the lesser snow goose: a theoretical enigma. American Naturalist, 121, 1–8CrossRef Google Scholar

Hartley, I R, Griffith, S C, Wilson, K, Shepherd, M & Burke, T (1999) Nestling sex ratios in the polygynously breeding Corn Bunting Miliaria calandra. Journal of Avian Biology, 30, 7–14CrossRef Google Scholar

Heinsohn, R, Legge, S & Barry, S (1997) Extreme bias in sex allocation in Eclectus parrots. Proceedings of the Royal Society, London, Series B, 264, 1325–1329CrossRef Google Scholar

Hornig, L E & McClintock, M K (1997) Sex ratios are multiply determined: a reply to James. Animal Behaviour, 54, 467–469CrossRef Google Scholar PubMed

Huck, U W, Seger, J & Lisk, R D (1990) Litter sex ratios in the golden hamster vary with time of mating and litter size and are not binomially distributed. Behavioral Ecology and Sociobiology, 26, 99–109CrossRef Google Scholar

James, W H (1975) The distribution of the combinations of the sexes in mammalian litters. Genetical Research, Cambridge, 26, 45–53CrossRef Google Scholar

James, W H (1998) Hypotheses on mammalian sex ratio variation at birth. Journal of Theoretical Biology, 192, 113–116CrossRef Google Scholar PubMed

Johnson N L, Kotz S & Kemp A W (1992) Univariate Discrete Distributions. New York: John Wiley

Kemeny J G & Snell J L (1976) Finite Markov Chains. New York: Springer-Verlag

Kilner, R (1998) Primary and secondary sex ratio manipulation by zebra finches. Animal Behaviour, 56, 155–164CrossRef Google Scholar PubMed

Kolman, W A (1960) The mechanism of natural selection for sex ratio. American Naturalist, 94, 373–377CrossRef Google Scholar

Krackow, S (1992) Sex ratio manipulation in wild house mice: the effect of fetal resorption in relation to the mode of reproduction. Biology of Reproduction, 47, 541–548CrossRef Google Scholar PubMed

Krackow, S (1995a) The developmental asynchrony hypothesis for sex ratio manipulation. Journal of Theoretical Biology, 176, 273–280CrossRef Google Scholar

Krackow, S (1995b) Potential mechanisms for sex ratio adjustment in mammals and birds. Biological Reviews, Cambridge, 72, 225–241CrossRef Google Scholar

Krackow, S (1997a) Effect of mating dynamics and crowding on sex ratio variance in mice. Journal of Reproduction and Fertility, 110, 87–90CrossRef Google Scholar

Krackow, S (1997b) Further evaluation of the developmental asynchrony hypothesis of sex ratio variation. Applied Animal Behaviour Science, 51, 243–250CrossRef Google Scholar

Krackow S (1999) Avian sex ratio distortions: the myth of maternal control. In: N J Adams & R H Slotow (eds) Proceedings of the 22nd International Ornithological Congress, pp 425–433. Johannesburg: Bird Life South Africa

Krackow, S & Burgoyne, P S (1998) Timing of mating, developmental asynchrony and the sex ratio in mice. Physiology and Behavior, 63, 81–84CrossRef Google Scholar

Krackow, S & Tkadlec, E (2001) Analysis of brood sex ratios: implications of offspring clustering. Behavioral Ecology and Sociobiology, 50, 293–301CrossRef Google Scholar

Lambin, X (1994) Sex-ratio variation in relation to female philopatry in townsend voles. Journal of Animal Ecology, 63, 945–953CrossRef Google Scholar

Lessells, C M, Mateman, A C & Visser, J (1996) Great tit hatchling sex ratios. Journal of Avian Biology, 27, 135–142CrossRef Google Scholar

Manly B F J (1991) Randomization and Monte-Carlo Methods in Biology. London: Chapman & Hall

McCullagh P & Nelder J A (1989) Generalized Linear Models. London: Chapman & Hall

Morgan, D J W & Cook, J M (1994) Extremely precise sex ratios in small clutches of a bethylid wasp. Oikos, 71, 423–430CrossRef Google Scholar

Nagelkerke, C J (1996) Discrete clutch sizes, local mate competition, and the evolution of precise sex allocation. Theoretical Population Biology, 49, 314–343CrossRef Google Scholar PubMed

Nagelkerke, C J & Hardy, I C W (1994) The influence of developmental mortality on optimal sex allocation under local mate competition. Behavioral Ecology, 5, 401–411CrossRef Google Scholar

Nagelkerke, C J & Sabelis, M W (1998) Precise control of sex allocation in pseudo-arrhenotokous phytoseiid mites. Journal of Evolutionary Biology, 11, 649–684CrossRef Google Scholar

Rabinovich, J E, Torres, Jordá M T & Bernstein, C (2000) Local mate competition and precise sex ratios in Telenomus fariai (Hymenoptera: Scelionidae), a parasitoid of triatomine eggs. Behavioral Ecology and Sociobiology, 48, 308–315CrossRef Google Scholar

Ratnieks, F L W & Keller, L (1998) Queen control of egg fertilisation in the honey bee. Behavioral Ecology and Sociobiology, 44, 57–61CrossRef Google Scholar

Robertson, A (1951) The analysis of heterogeneity in the binomial distribution. Annals of Eugenics, 16, 1–15CrossRef Google Scholar PubMed

Siegel S & Castellan N J (1988) Nonparametric Statistics for the Behavioral Sciences. New York: McGraw-Hill

Soede, N M, Nissen, A K & Kemp, B (2000) Timing of insemination relative to ovulation in pigs: effects on sex ratio of offspring. Theriogenology, 53, 1003–1011CrossRef Google Scholar PubMed

Sokal R R & Rohlf F J (1995) Biometry: The Principles and Practice of Statistics in Biological Research. New York: Freeman

Taylor, P D & Sauer, A (1980) The selective advantage of sex-ratio homeostasis. American Naturalist, 116, 305–310CrossRef Google Scholar

Verner, J (1965) Selection for sex ratio. American Naturalist, 99, 419–421CrossRef Google Scholar

Wajnberg, E (1993) Genetic variation in sex allocation in a parasitic wasp: variation in sex pattern within sequence of oviposition. Entomologia Experimentalis et Applicata, 69, 221–229CrossRef Google Scholar

West, S A & Herre, E A (1998) Stabilizing selection and variance in fig wasp sex ratios. Evolution, 52, 475–485CrossRef Google Scholar PubMed

West, S A, Murray, M G, Machado, C A, Griffin, A S & Herre, E A (2001) Testing Hamilton's rule with competition between relatives. Nature, 409, 510–513CrossRef Google Scholar PubMed