Rensch's rule

Rensch's rule is a biological rule on allometrics, concerning the relationship between the extent of sexual size dimorphism and which sex is larger. Across species within a lineage, size dimorphism increases with increasing body size when the male is the larger sex, and decreases with increasing average body size when the female is the larger sex. The rule was proposed by the evolutionary biologist Bernhard Rensch in 1950.[1]

After controlling for confounding factors such as evolutionary history, an increase in average body size makes the difference in body size larger if the species has larger males, and smaller if it has larger females.[2] Some studies propose that this is due to sexual bimaturism, which causes male traits to diverge faster and develop for a longer period of time.[3] The correlation between sexual size dimorphism and body size is hypothesized to be a result of an increase in male-male competition in larger species,[4] a result of limited environmental resources, fuelling aggression between males over access to breeding territories[5] and mating partners.[2]

Phylogenetic lineages that appear to follow this rule include primates, pinnipeds, and artiodactyls.[6]

This rule have rarely been tested on parasites. A recent study showed that Philopterid and Menoponid lice comply with it, while Ricinid lice exhibit a reversed pattern.[7]

References

Rensch, B. (1950). Die Abhängigkeit der relativen Sexualdifferenz von der Körpergrösse. Bonner Zoologische Beiträge 1:58-69.
Dale, James; Dunn, Peter O.; Figuerola, Jordi; Lislevand, Terje; Székely, Tamás; Whittingham, Linda A. (2007-12-07). "Sexual selection explains Rensch's rule of allometry for sexual size dimorphism". Proceedings of the Royal Society of London B: Biological Sciences. 274 (1628): 2971–2979. doi:10.1098/rspb.2007.1043. ISSN 0962-8452. PMC 2211517. PMID 17878139.
Blanckenhorn, Wolf; Dixon, A. "Proximate Causes of Rensch's Rule: Does Sexual Size Dimorphism in Arthropods Result from Differences in Development Time?". University of Zurich. University of Zurich.
Székely, Tamás; Freckleton, Robert P.; Reynolds, John D. (2004-08-17). "Sexual selection explains Rensch's rule of size dimorphism in shorebirds". Proceedings of the National Academy of Sciences of the United States of America. 101 (33): 12224–12227. doi:10.1073/pnas.0404503101. ISSN 0027-8424. PMC 514460. PMID 15304645.
Lengkeek, W.; Didderen, K.; Côté, I. M.; van der Zee, E. M.; Snoek, R. C.; Reynolds, J. D. (2008-10-01). "Plasticity in sexual size dimorphism and Rensch's rule in Mediterranean blennies (Blenniidae)". Canadian Journal of Zoology. 86 (10): 1173–1178. doi:10.1139/z08-103. ISSN 0008-4301.
Fairbairn, D.J. (1997). "Allometry for Sexual Size Dimorphism: Pattern and Process in the Coevolution of Body Size in Males and Females". Annu. Rev. Ecol. Syst. 28 (1): 659–687. doi:10.1146/annurev.ecolsys.28.1.659.
Piross, I.S.; Harnos, A.; Rozsa, L. (2019). "Rensch's rule in avian lice: contradictory allometric trends for sexual size dimorphism". Scientific Reports. 9: 7908. doi:10.1038/s41598-019-44370-5.

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[1] Rensch, B. (1950). Die Abhängigkeit der relativen Sexualdifferenz von der Körpergrösse. Bonner Zoologische Beiträge 1:58-69.

[:2-2] Dale, James; Dunn, Peter O.; Figuerola, Jordi; Lislevand, Terje; Székely, Tamás; Whittingham, Linda A. (2007-12-07). "Sexual selection explains Rensch's rule of allometry for sexual size dimorphism". Proceedings of the Royal Society of London B: Biological Sciences. 274 (1628): 2971–2979. doi:10.1098/rspb.2007.1043. ISSN 0962-8452. PMC 2211517. PMID 17878139.

[3] Blanckenhorn, Wolf; Dixon, A. "Proximate Causes of Rensch's Rule: Does Sexual Size Dimorphism in Arthropods Result from Differences in Development Time?". University of Zurich. University of Zurich.

[:3-4] Székely, Tamás; Freckleton, Robert P.; Reynolds, John D. (2004-08-17). "Sexual selection explains Rensch's rule of size dimorphism in shorebirds". Proceedings of the National Academy of Sciences of the United States of America. 101 (33): 12224–12227. doi:10.1073/pnas.0404503101. ISSN 0027-8424. PMC 514460. PMID 15304645.

[:0-5] Lengkeek, W.; Didderen, K.; Côté, I. M.; van der Zee, E. M.; Snoek, R. C.; Reynolds, J. D. (2008-10-01). "Plasticity in sexual size dimorphism and Rensch's rule in Mediterranean blennies (Blenniidae)". Canadian Journal of Zoology. 86 (10): 1173–1178. doi:10.1139/z08-103. ISSN 0008-4301.

[6] Fairbairn, D.J. (1997). "Allometry for Sexual Size Dimorphism: Pattern and Process in the Coevolution of Body Size in Males and Females". Annu. Rev. Ecol. Syst. 28 (1): 659–687. doi:10.1146/annurev.ecolsys.28.1.659.

[7] Piross, I.S.; Harnos, A.; Rozsa, L. (2019). "Rensch's rule in avian lice: contradictory allometric trends for sexual size dimorphism". Scientific Reports. 9: 7908. doi:10.1038/s41598-019-44370-5.

Biological rules
Rules	Allen's rule Shorter appendages in colder climates Bateson's rule Extra limbs mirror their neighbours Bergmann's rule Larger bodies in colder climates Cope's rule Bodies get larger over time Deep-sea gigantism Larger bodies in deep-sea animals Dollo's law Loss of complex traits is irreversible Eichler's rule Parasites co-vary with their hosts Emery's rule Insect social parasites are often in same genus as their hosts Fahrenholz's rule Host and parasite phylogenies become congruent Foster's rule (Insular gigantism, Insular dwarfism) Small species get larger, large species smaller, after colonizing islands Gause's law Complete competitors cannot coexist Gloger's rule Lighter coloration in colder, drier climates Haldane's rule Hybrid sexes that are absent, rare, or sterile, are heterogamic Harrison's rule Parasites co-vary in size with their hosts Hamilton's rule Genes increase in frequency when relatedness of recipient to actor times benefit to recipient exceeds reproductive cost to actor Hennig's progression rule In cladistics, the most primitive species are found in earliest, central, part of group's area Jarman-Bell principle The correlation between the size of an animal and its diet quality; larger animals can consume lower quality diet Jordan's rule Inverse relationship between water temperature and no. of fin rays, vertebrae Lack's principle Birds lay only as many eggs as they can provide food for Rapoport's rule Latitudinal range increases with latitude Rensch's rule Sexual size dimorphism increases with size when males are larger, decreases with size when females are larger Rosa's rule Groups evolve from character variation in primitive species to a fixed character state in advanced ones Schmalhausen's law A population at limit of tolerance in one aspect is vulnerable to small differences in any other aspect Thorson's rule No. of eggs of benthic marine invertebrates decreases with latitude Van Valen's law Probability of extinction of a group is constant over time von Baer's laws Embryos start from a common form and develop into increasingly specialised forms Williston's law Parts in an organism become reduced in number and specialized in function
Related	Countergradient variation Where genetics opposes environment as a factor Gigantothermy Large ectothermic animals more easily maintain constant body temperature