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Kin Recognition and the Evolution of Altruism Aneil F doi 10.1098/rspb.2001.1611 Kin recognition and the evolution of altruism Aneil F. Agrawal Department of Biology and Center for the Integrative Study of Animal Behavior, Indiana University, 1001 East 3rd Street, Bloomington, IN 47405-3700, USA ([email protected]) In 1964, Hamilton formalized the idea of kin selection to explain the evolution of altruistic behaviours. Since then, numerous examples from a diverse array of taxa have shown that seemingly altruistic actions towards close relatives are a common phenomenon. Although many species use kin recognition to direct altruistic behaviours preferentially towards relatives, this important aspect of social biology is less well understood theoretically. I extend Hamilton’s classic work by de¢ning the conditions for the evolution of kin-directed altruism when recognizers are permitted to make acceptance (type I) and rejection (type II) errors in the identi¢cation of social partners with respect to kinship. The e¡ect of errors in recognition on the evolution of kin-directed altruism depends on whether the population initially consists of uncondi- tional altruists or non-altruists (i.e. alternative forms of non-recognizers). Factors a¡ecting the level of these error rates themselves, their evolution and their long-term stability are discussed. Keywords: altruism; kin recognition; Hamilton’s rule; recognition errors the null hypothesis is wrongly accepted. In kin recogni- 1. INTRODUCTION tion, an acceptance error (type I error) occurs when an Although various exceptions to Hamilton’s (1964a,b) rule individual identi¢es a social partner as kin when it is non- have been noted when the simplifying assumptions of the kin, whereas a rejection error (type II error) occurs when theory are violated (e.g. Charlesworth 1978; Uyenoyama an individual identi¢es a social partner as non-kin when it & Feldman 1982; Karlin & Matessi 1983), it remains a is kin. With acceptance errors, altruism is bestowed on cornerstone of behavioural biology and social evolution non-relatives, whereas with rejection errors altruism is (Grafen 1991; Queller 1992a,b; Frank 1998). Consistent withheld from relatives. with the predictions of Hamilton’s rule, altruistic beha- As with type I and type II errors in statistics, there is viours tend to be directed towards close relatives. In some some inherent degree of trade-o¡ in minimizing both systems, individuals predominantly interact with their kin types of errors in kin recognition. When the function as a by-product of spatial structure, but in many other constraining the relationship between acceptance-error systems individuals interact with both kin and non-kin, and rejection-error rates was speci¢ed, Reeve (1989) was and preferentially direct altruistic behaviours towards the able to solve for the optimal balance between type I and former (Fletcher & Michener 1987; Hepper 1991), using type II errors under a variety of di¡erent social condi- environmental and/or genetic cues to identify kin tions. In contrast, the purpose of the model presented (reviewed in Sherman et al. 1997). Despite some earlier here is to quantify how imperfect kin recognition changes skepticism (Grafen 1990), the existence of kin recognition the conditions for the evolution of an altruistic behaviour. has now been demonstrated in a wide variety of taxa I do not assume that the error rates are at their evolu- including mammals (e.g. Manning et al. 1992; Mateo & tionary optima or that they are evolving to be so; rather, Johnston 2000), birds (e.g. Komdeur & Hatchwell (1999), I treat these error rates as constants. I extend Hamilton’s and references therein), amphibians (e.g. Masters & (1964a,b) work by outlining when a population of uncon- Forester 1995; Pfennig 1999), ¢shes (e.g. Olsen et al. 1998), ditionally non-altruistic alleles can be invaded by an ascidians (Grosberg & Quinn 1986), spiders (e.g. Evans (imperfect) kin-recognizing altruistic allele. In particular, 1998, 1999), Hymenoptera (e.g. Moritz & Hillesheim 1990; I show how the two types of error rates modify Hamil- Gamboa et al. 1996) and other insects (e.g. Joseph et al. ton’s rule. I then model an alternative situation by 1999; Loeb et al. 2000). Although Hamilton discussed the outlining when a population of unconditionally altruistic possible importance of kin recognition in his classic work alleles can be invaded by an (imperfect) kin-recognizing on the evolution of altruism (Hamilton 1964a,b), at the altruistic allele. I show that the relative importance of time he did not believe kin recognition to be as widespread acceptance errors versus rejection errors changes in these as the empirical evidence now suggests (Hamilton 1987). di¡erent situations. It is clear from kin-selection theory that altruism should evolve more readily in those animals that can accurately 2. EVOLUTION OF KIN-DIRECTED ALTRUISM AMONG identify kin and direct their altruistic acts exclusively NON-ALTRUISTS towards them. However, most recognition systems have some degree of error, and kin recognition is no exception I use a haploid model because this analysis provides (Keller 1997; Sherman et al. 1997). In kin recognition, two the same result as would a game-theoretical approach. di¡erent types of error can occur; these errors are analo- Consider a haploid organism with a kin-recognition locus gous to type I and type II errors in statistics (Reeve 1989). having two alternative alleles. Individuals with the kUNA In statistics, a type I error occurs when the null hypothesis allele do not discriminate between individuals and never is wrongly rejected, whereas a type II error occurs when act altruistically with respect to the behaviour of interest Proc. R. Soc. Lond. B (2001) 268, 1099^1104 1099 © 2001 The Royal Society Received 11 October 2000 Accepted 9 February 2001 1100 A. F. Agrawal Kin recognition and altruism (i.e. they are unconditionally non-altruistic, UNA). Indi- (a) viduals with the K allele perform kin-directed altruistic behaviours (i.e. they act altruistically but only towards f = 0.7 individuals identi¢ed as kin). The altruistic action provides a ¢tness bene¢t, B, to the recipient but there is a ¢tness cost, C, incurred by the donor. Acceptance (type 0.4 I) errors and rejection (type II) errors occur with prob- maximum 1 cost–benefit a 0.2 0.8 , abilities ¬ and ­ , respectively. I assume that a constant ratio te a r fraction, f, of social interactions occur between kin. The 0 0.6 r 0 o rr conditional probability that the kin of a K individual will r0.2e e jec 0.4 e tio0.4 c also have genotype K is pK K. The conditional probability n er n j ro0.6r ta ra 0.2 p that the kin of a kUNA individual will have genotype K is te e , b0.8 c 0 c p K kUNA . The global frequency of K individuals is p. a jUsing these parameters, the ¢tnesses of the genotypes are given by (b) W(kUNA) 1 f (1 ­ )( pK kUNA B) (1 f )¬pB (1) f = 0.3 ˆ ‡ ¡ j ‡ ¡ and W(K) 1 f (1 ­ )( pK K B C) (1 f )¬(pB C). (2) ˆ ‡ ¡ j ¡ ‡ ¡ ¡ 0.4 1 maximum a The second term in each equation is a result of inter- cost–benefit 0.2 , 0.8 te ratio a actions that occur with kin while the third term is a result r 0 0.6 r of interactions with non-kin. For altruism to be favoured, ro 0 r 0.2 e K individuals should derive higher ¢tness from interacting reje 0.4 e ctio0.4 c n n with their kin than kUNA individuals will derive from err 0.6 ta or 0.2 p rat e interacting with their kin (i.e. the second term in equa- e, b0.8 c 0 c tion (2) should be greater than the second term in equa- a tion (1)). However, K individuals will derive lower ¢tness Figure 1. The maximum cost^bene¢t ratio permitting the from interacting with non-kin than will kUNA individuals evolution of kin-directed altruism in a population of (i.e. the third term in equation (2) will be less than the unconditionally non-altruistic individuals. The maximum third term in equation (1)). Kin-directed altruism evolves cost depends on the accuracy of kin recognition, measured through natural selection when the ¢tness of K indivi- by the rates of acceptance errors, ¬, and rejection errors, ­ . duals is greater than the ¢tness of kUNA individuals, i.e. The greater the space under the surface, the easier it is for W(K) 4 W(kUNA). This condition is met when kin recognition to evolve. This plot assumes that the kin are full-sibs so that r 0.5; (a) 70% of social interactions occur ˆ f (1 ­ ) between kin, f 0.7; and (b) 30% of social interactions occur ¡ r4C=B, (3) ˆ ¬(1 f ) f (1 ­ ) between kin, f 0.3. ¡ ‡ ¡ ˆ where r is the probability of identity by descent. The probability that the kin of a K individual will also have inaccurate (high values of ¬ and ­ ) then an uncondition- the K allele is equal to the probability of identity by ally altruistic behaviour may be favoured over a beha- descent plus the probability of identity by chance (not viour based on kin recognition. descent), i.e. pK K r (17r)p. The probability that the The extent to which a particular combination of ¬ and j ˆ ‡ kin of a kUNA individual will have the K allele is equal to ­ expands or contracts the conditions for the evolution of the probability of non-identity by chance, i.e. altruism using a kin-directed strategy relative to the p K k (17r)p.
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