zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Heavy-tailedness and threshold sex determination. (English) Zbl 1154.62084
Summary: This paper studies the properties of the sex ratio in two-period models of threshold (e.g., polygenic or temperature-dependent) sex determination under heavy-tailedness in the framework of possibly skewed stable distributions and their convolutions. We show that if the initial distribution of the sex determining trait in such settings is moderately heavy-tailed and has a finite first moment, then an excess of males (females) in the first period leads to the same pattern in the second period. Thus, the excess of one sex over the other one accumulates over two generations and the sex ratio in the total alive population in the second period cannot stabilize at the balanced sex ratio value of 1/2. These properties are reversed for extremely heavy-tailed initial distributions of sex determining traits with infinite first moments. In such settings, the sex ratio of the offspring oscillates around the balanced sex ratio value and an excess of males (females) in the first period leads to an excess of females (males) in the second period. In addition, the sex ratio in the total living population in the second period can stabilize at 1/2 for some extremely heavy-tailed initial distributions of the sex determining trait. The results in the paper are shown to also hold for bounded sex determining phenotypes.

MSC:
62P10Applications of statistics to biology and medical sciences
62G32Statistics of extreme values; tail inference
WorldCat.org
Full Text: DOI
References:
[1] An, M. Y.: Logconcavity versus logconvexity: A complete characterization. Journal of economic theory 80, 350-369 (1998) · Zbl 0911.90071
[2] Bacci, G.: Sex determination. (1965)
[3] Beirlant, J.; Goegebeur, Y.; Segers, J.; Teugels, J.: Statistics of extremes. Theory and applications. (2004) · Zbl 1070.62036
[4] Bull, J. J.: Evolution of environmental sex determination from genotypic sex determination. Heredity 47, 173-184 (1981)
[5] Bull, J. J.; Charnov, E. L.: Enigmatic reptilian sex ratios. Evolution 43, 1561-1566 (1989)
[6] Bulmer, M. G.; Bull, J. J.: Models of polygenic sex determination and sex ratio control. Evolution 36, 13-26 (1982)
[7] Cherfas, J.; Gribbin, J.: The redundant male. (1985)
[8] Edlund, L.: Son preference, sex ratios, and marriage patterns. Journal of political economy 107, 1275-1302 (1999)
[9] Embrechts, P.; Kl├╝ppelberg, C.; Mikosch, T.: Modelling extremal events for insurance and finance. (1997)
[10] Gabaix, X., Ibragimov, R., 2007. Rank-1/2: a simple way to improve the OLS estimation of tail exponents. Harvard Institute of Economic Research Discussion Paper No. 2106. Available at http://www.economics.harvard.edu/faculty/ibragimov/files/LogLogRevised2.pdf
[11] Grant, V. J.: Sex determination and the maternal dominance hypothesis. Human reproduction 11, 2371-2375 (1996)
[12] Ibragimov, R., 2005. New majorization theory in economics and martingale convergence results in econometrics. Ph.D. dissertation, Yale University. Available at http://www.economics.harvard.edu/faculty/ibragimov/files/Dissertation.pdf
[13] Ibragimov, R.: Efficiency of linear estimators under heavy-tailedness: convolutions of ${\alpha}$-symmetric distributions. Econometric theory 23, 501-517 (2007) · Zbl 1237.62042
[14] Ibragimov, R.: Thou shalt not diversity: why two of every sort?. Journal of applied probability 44, 58-70 (2007) · Zbl 1136.60010
[15] Ibragimov, R.; Walden, J.: The limits of diversification when losses May be large. Journal of banking and finance 31, 2551-2569 (2007)
[16] James, W. H.: Parental dominance/social status, hormone levels, and sex ratio of offspring. Reproductive and interpersonal aspects of dominance and status 2, 63-74 (1994)
[17] James, W. H.: What stabilizes the sex ratio?. Annals of human genetics 59, 243-249 (1995)
[18] James, W. H.: Evidence that mammalian sex ratios at birth are partially controlled by parental hormone levels at the time of conception. Journal of theoretical biology 180, 271-286 (1996)
[19] James, W. H.: A potential mechanism for sex ratio variation in mammals. Journal of theoretical biology 189, 253-255 (1997)
[20] Janzen, F. J.; Paukstis, G. L.: Environmental sex determination in reptiles: ecology, evolution, and experimental design. The quarterly review of biology 66, 149-179 (1991)
[21] Karlin, S.: Mathematical models, problems, and controversies of evolutionary theory. American mathematical society. Bulletin. new series 10, 221-274 (1984) · Zbl 0552.92013
[22] Karlin, S.: Stochastic comparisons between means and medians for i.i.d. Random variables. The art of statistical science. A tribute to G. S. Watson (1992)
[23] Karlin, S.; Lessard, S.: Theoretical studies on sex ratio evolution. (1986)
[24] Marshall, A. W.; Olkin, I.: Inequalities: theory of majorization and its applications. (1979) · Zbl 0437.26007
[25] Oster, E.: Hepatitis B and the case of the missing women. Journal of political economy 113, 1163-1216 (2005)
[26] Zolotarev, V. M.: One-dimensional stable distributions. (1986) · Zbl 0589.60015