Model:

We consider a population in which interactions occur within “groups” ofn individuals each and affect phenotypic values of individuals. In classical quantitative genetic theory, the phenotypic trait value of an individual,P, is the sum of a heritable component,A, referred to as “breeding value” and a residual component,E, referred to as “environment”:P =A +E. With interactions amongn individuals, however, the observed phenotypic trait value of an individual is due to two unobserved phenotypic effects: a direct effect originating from the focal individual and the sum of the associative effects originating from of each of itsn − 1 group members (Griffing 1967). Associative effects may be interpreted as heritable environmental effects provided by associates to the focal individual (Wolf 2003). Both phenotypic direct and associative effects are the sum of a heritable component (A) and a nonheritable component (E), so that the observed phenotypic trait value of an individual is given by

(1)

(Griffing 1967), in whichi denotes the focal individual andj one of its associates (i.e., group members). The first two terms inEquation 1 represent effects due to the focal individual; the last two terms represent the effects due to itsn − 1 associates. The effect is the direct breeding value (DBV) andE_D,i is the direct nonheritable value of individuali, whereas is the associative breeding value (SBV) andE_S,j the associative nonheritable value of associatej. The DBV and the SBV represent the heritable components underlying the observed phenotypes.

Note that nonheritable associative effects, indicated by inEquation 1, may contribute to the observed phenotype. This is because the full associative effect of an individual is a phenotypic effect, which may contain both heritable and nonheritable components. The genes of an individual do notdirectly affect the associates; the associates experience a phenotype. We emphasize those nonheritable associative effects, because they modify the statistical model required to obtain unbiased estimates of genetic parameters (see below).

Heritable variation:

Because each individual interacts withn − 1 associates, the total heritable impact of an individual on the population mean, referred to as its total breeding value (TBV), equals the sum of its DBV andn − 1 times its SBV: TBV_i = DBV_i + (n − 1)SBV_i. Response to selection equals the change per generation of the TBV. Hence, the TBV is a generalization of the classical breeding value, to account for interactions. The total heritable variation available for response to selection, therefore, equals the variance of the TBV,

(2)

(Bijmaet al. 2007), in which is the variance of DBV, is the variance of SBV, and is the covariance between DBV and SBV. The sign of the covariance between DBV and SBV is a measure of competitionvs. cooperation. Negative may be interpreted as “heritable competition,” in the sense that individuals with positive breeding values for their own phenotype (DBV) have on average a negative heritable impact on the phenotypes of their associates (SBV). Conversely, positive may be interpreted as “heritable cooperation.”

Classical quantitative genetic methodology to estimate additive genetic variances of traits rests on similarity of phenotypes' relatives. Associative breeding values of individuals, however, are not expressed in their own phenotypes, but in the phenotypes of their associates. Thus only the variance of DBV surfaces in classical analyses; the remaining part of the full heritable variance,, is hidden. Depending on group size and the heritability of interactions, this hidden heritable variance may be substantially larger than the variance of DBVs. In those cases, classical methods will substantially underestimate the total heritable variation. With specific family structures, the SBV may also be confounded with the DBV (seediscussion andWolf 2003), which would make the result of classical analyses an inaccurate estimate of even the direct genetic variance. The total heritable variation (Equation 2) does not depend on relatedness among associates. This is because all components of the TBV of an individual refer to its own genes. (SeeBijmaet al. 2007 for the effect of population structure.)

Response to selection:

In classical quantitative genetic theory, response to selection is in the same direction as selection pressure; heritability is merely a scaling factor affecting the magnitude of response, not its direction. With interactions among individuals, however, not only the magnitude, but also the direction of response depend on the genetic parameters (Griffing 1967;Kirkpatrick and Lande 1989;Mooreet al. 1997). To illustrate this phenomenon, we consider response to selection among unrelated individuals, which follows from substitutingr =g = 0 intoEquation 5 ofBijmaet al. (2007), giving, in which is the selection gradient. (See alsoGriffing 1976a.) This result shows that the direction of response depends on the covariance between DBV and SBV (). Strong competition,i.e., large and negative, will yield response in the direction opposite to the direction of selection. With interactions, therefore, the genetic parameters play a key role in the outcome of selection; they are no longer merely a scaling factor.

Derivations:

This section describes the derivations ofEquations 4 and5. Consider two individuals,i with group members denoted byj andk with group members denoted byl. The covariance between phenotypes ofi andk follows from substitutingEquation 1 for bothP_i andP_k, giving, which consists of a genetic and an environmental component. Analogous to the basic animal model, we account for the genetic components by including direct and associative breeding values in the model, together with their covariance structure. This yieldsEquation 4. For example, inEquation 4, theith element ofy corresponds toP_i, theith element ofZ_Da_D corresponds toA_D,i, theith element ofZ_Sa_S corresponds to, and theith element ofe corresponds to. As usual in an animal model, we account for covariances between breeding values ina_D anda_S by incorporating the relatedness matrixA in the statistical analyses. (See below and the mixed-model equations inMuir 2005.)

What remains to be done is the covariance structure of the vector of residualse. The covariance between residuals ine originates from the environmental component of the covariance between observations and can be partitioned into. As usual in quantitative genetics, we assume thatE-terms of distinct individuals are independent. (Environmental effects common to multiple individuals are accounted for by the fixed effectsXb.) Thus a nonzero residual covariance occurs only when it involves the same individual, which happens either wheni andk are the same individual or wheni andk are group members. Wheni andk are the same individual,, which is the residual variance. The first term is due to the direct effect of the individual itself, and the second term is due to itsn − 1 group members. Wheni andk are group members, their residuals are correlated for two reasons. First, for groups larger than two,i andk will haven − 2 group members in common, and thus they haven − 2 identical associative effects in their phenotype, giving. Second, the direct effect ofi is expressed in its own phenotype, whereas the associative effect ofi is expressed in the phenotype ofk, and vice versa fork. As with any two traits of a single individual, the direct and associative effect originating from a single individual may be correlated Walsh (Lynch and Walsh 1998), giving. Thus the full covariance between residuals of group members equals. The represents the nonheritable relationship between the direct and associative effect of an individual and is a nonheritable measure of competitionvs. cooperation (analogous to, see above). A negative may, for example, arise from variation in the juvenile environment experienced by individuals. Individuals having experienced good (bad) environments may be more (less) competitive, in which case they will have higher (lower) phenotypic values at the expense (to the advantage) of their associates. InEquation 5, we accounted for the nongenetic covariance between group members by fitting the correlation ρ between records of group members.

Experimental design for application:

The use ofEquations 4 and5 does not require a specific experimental design; groups may be composed of any combination of related and/or unrelated individuals and may vary in size. To calculate the relationship matrixA, information on at least one generation of family relationships will be required, so that one can distinguish full sibs, half sibs, and unrelated individuals. Information on more generations of pedigree, which provides information on more distant relationships, will add to the accuracy of results, but is not required for application. With groups of equal size, there will be no information in the data to separate and, because different combinations of those two parameters may yield an identical residual correlation. The inability to estimate and with equal group size is no problem, because the residual correlation itself, which included these components as part of a ratio, is estimable and sufficient in the analysis to avoid bias in the estimates of the genetic parameters. There are population structures from which the parameters of interest cannot be estimated. (Seediscussion on the work ofWolf 2003).

We used Monte Carlo simulations to validate our statistical methodology (appendix).Table 1 shows that estimated genetic parameters obtained from simulated data are unbiased; true values of genetic parameters are within ±3 standard errors of mean estimated values in all cases. These results confirm thatEquations 4 and5 correspond to the covariance structure that arises fromEquation 1 and that there is no need for a specific structure of the family relationships within and between groups.

Material:

The methodology presented above was applied to analyze mortality in a commercial population of layer chickens. Field data on this population were provided by Hendrix Genetics and consisted of observations on survival days of a single generation of 3800 hens bred from 36 sires and 287 dams, which had been mated at random. Each sire had been mated to ∼8 dams, and each dam contributed on average 13.2 female offspring. Five generations of pedigree were included in the calculation of the matrix of relatedness (A).

Mortality in commercial chicken populations is largely due to cannibalistic pecking behavior (e.g.,Craig and Muir 1996). The direct effect of an individual is, therefore, related to its ability to survive by avoiding being pecked, whereas its associative effect measures its effect on survival of its cage members, which is closely related to its own pecking behavior. In commercial egg production, individuals are frequently beak trimmed, to reduce mortality due to pecking behavior. In this data set, however, individuals had not been beak trimmed, which will be obligatory in the European Union from 2011 onward.

Data consisted of four age groups of approximately equal numbers of hens, differing by 2 weeks of age each. At an age of 20 weeks, individuals were allocated randomly to 950 standard commercial battery cages, four individuals per cage. Due to chance, some cages contained full or half sibs, but most cages contained unrelated individuals only. Facilities consisted of eight rows of cages. Each row was 40 cages long and consisted of 3 cages on top of each other, giving 120 cages per row. The eight rows were grouped into four double rows; both rows of a double row were put with the backs against each other. Each age group was allocated to a single double row. Back fences of cages consisted of latticework allowing limited contact between “backdoor neighbors,”i.e., between the individuals of two corresponding cages, each in one of the two rows of a double row. Adjacent cages in the same row were separated by a closed fence fully preventing contact. Individuals were kept 60 weeks and culled at an age of 80 weeks. Survival (0/1) was recorded daily on all individuals. For each individual, survival days were defined as age at death in days. Individuals surviving until 80 weeks of age had 80 × 7 = 560 survival days. Fifty-four percent of individuals survived until 80 weeks of age. Mean survival time was 454 days, with a standard deviation of 122 days. Inspection of dead hens showed that the vast majority of chickens had died due to being pecked. This observation was supported by previous data on beak-trimmed individuals of the same line kept in the same facilities, which showed substantially lower mortality (<10%). Thus the absence of beak trimming substantially amplified the consequences of social interactions.

Data were analyzed withEquations 4 and5 as a model, using restricted maximum likelihood (REML) (Patterson and Thompson 1971) as implemented in the ASReml software package (Gilmouret al. 2002). The model included a fixed effect for each combination of row (1 through 8) and level (top, middle, and bottom) of the cage and for the number of surviving birds in the back cage, to account for a possible associative effect due to the backdoor neighbors. As usual with an animal model, this analysis directly yields estimates of the parameters of interest and utilizes the full data.

Results:

When using a conventional model without associative effects, estimated heritability for survival days in the chicken line was 6.7%, which is in the range common for survival traits in livestock (Table 2;Beaumontet al. 1997;Carlenet al. 2005;Gitterleet al. 2005). The total heritable variance estimated from the full model (Equations 2,4, and5), however, was 2742 days², which corresponds to 20% of the phenotypic variance. This result indicates a “heritability” threefold greater than that obtained using classical methods,i.e., 20%vs. 6.7%. Two-thirds of the heritable variation, therefore, is due to social interactions among individuals and is hidden from classical analyses.

At first glance, one might expect direct and associative effects for mortality due to pecking behavior to be negatively correlated, because dominant individuals may kill others and survive themselves. However, we found a small but nonsignificant positive correlation of +0.28 (P = 0.016), suggesting that individuals benefit from not harming others. In this population, there seems to be mutual benefit of behaving peacefully and a mutual cost of behaving aggressively. A positive covariance between DBV and SBV increases the total heritable variation (Equation 2) and therefore increases the potential of the population to respond to selection.

Figure 1 shows predicted responses to multilevel selection applied to the chicken population, using equations presented inBijmaet al. (2007). (Details and an example of calculation are in theappendix.) InFigure 1, the strength of multilevel selection is indicated by a factorg, whereg = 0 represents selection among individuals,g = 1 represents selection among groups, and values ofg between 0 and 1 represent a mix of selection among individuals and groups (Bijmaet al. 2007). Classical theory suggests a response of only 7.8 days of survival. Predictions accounting for heritable interactions, however, yield substantially higher responses. Selection among individuals applied to a population composed of groups of unrelated individuals yields an expected response of ∼11 days of survival (g = 0,r = 0). Mild multilevel selection applied to a population composed of groups of full sibs more than doubles the predicted response (g ≥ 0.3,). The maximum response that can be obtained equals 23 days (g = 0.6–0.8 and), which is nearly threefold greater than suggested by classical theory. (Clones do not occur in reality.) The lines inFigure 1 are curved, which indicates that a degree of between-group selection (g) that maximizes response exists, which was also observed by Griffing. This value ofg may be applied in artificial breeding programs, where the aim is to maximize response to selection. Note that results inFigure 1 are specific to the chicken population and to the environment in which it was kept, such as the density of housing; other populations may have other genetic parameters and other relationships among relatedness, multilevel selection, and response. Results inFigure 1 should, therefore, not be taken to conclude that relatedness has a bigger impact than multilevel selection in general.

Monte Carlo simulation used for Table 1:

A population of five discrete generations was simulated. First, a base generation of 250 sires and 500 dams was generated. DBVs of base individuals were sampled from and nongenetic direct effects from. Associative effects of individuals were simulated conditional on their direct effects; the SBV of theith individual of the base generation was sampled as, in whichr_A is the correlation between DBV and SBV, andz is a random variable taken from a standard normal distribution,. Nongenetic indirect effects were sampled as, in whichr_E is the nongenetic correlation between direct and associative effects. Phenotypes were created according toEquation 1 and parents for the next generation were taken at random from the base generation.

Second, four additional generations were generated. DBVs of individuals in those generations were sampled as and SBVs as, in which MS denotes Mendelian sampling components of breeding values, which were sampled as and. Nongenetic effects were sampled in the same way as in the base generation. Phenotypic values from the fifth generation were used to estimate variance components, and all five generations were included in the calculation of the relatedness matrix (A). Fifty replicates were simulated for each set of genetic parameters and estimates were averaged over replicates.

Example of calculation of response to selection for the chicken line:

Estimated genetic parameters for the chicken line were,,,, and ρ = 0.09. In the data, groups consisted of four unrelated individuals, so that the phenotypic variance equals (Table 2).

In the following, we give an example of calculation of response to selection for a population consisting of groups composed of four full sibs (n = 4,r =), with substantial selection pressure given to group performance (g = 0.8), and for an intensity of selection of 1 unit (ι = 1). The general expression for response to selection is, in whichC denotes the selection criterion,, andg the relative emphasis given to group performance in the selection criterion (Bijmaet al. 2007). Thus, calculation of response to selection requires calculating the variance of the total breeding values,, the covariance between phenotypic values and TBVs of individuals,, and the selection gradient,. We start with the selection gradient and subsequently calculate and.

The denominator of the selection gradient, the standard deviation of the selection criterion,, depends on the phenotypic variance,, and on the covariance between phenotypes of group members,. The general expression for the phenotypic variance follows fromEquation 1, giving. The covariance between phenotypes of associates also follows fromEquation 1,. Next, it follows from that. Thus the selection gradient equals.

The variance of the total breeding value equals (Equation 2). The covariance between phenotypic values and TBVs of individuals equals (Bijmaet al. 2007). Finally, response to selection follows from.

Expected sire and dam covariances in the design of Wolf (2003):

In the experimental setup ofWolf (2003), flies were kept in pairs of two individuals that were full sibs, half sibs, or unrelated. With unrelated individuals, the same two half-sib families were always combined in a pair. Dams were nested within sires; each sire was mated to exactly two dams and each dam to a single sire only.

Investigation of the expectations of sire and dam variances presented inWolf (2003) shows that they are incomplete. Consider, for example, the case where tube members are half sibs. In this case, the sire covariance between two individuals in different groups (tubes) equals, instead of as listed inTable 1 ofWolf (2003),i.e., a difference of. This extra originates from the full-sib relationship that exists between a focal individual and the tube member of a half sib of the focal individual, which is not accounted for inWolf (2003). When each sire is mated to exactly two dams, the group member of a half sib of the focal individual must be a full sib of the focal individual (in the case where tube members are half sibs). Note that is not a variance, but a covariance. For example, if estimates presented inWolf (2003) would have been the true values, so that,, and, then the expected sire variance would equal −2666,i.e., a negative value. Hence, a sire plus dam-within-sire model is inappropriate, because the expected sire variance may be negative for combinations of direct and indirect genetic variances that are biologically possible.

To investigate whether direct and associative genetic variances can be estimated from the data structure used inWolf (2003), we derive general expressions for expectations of sire and dam covariances. We distinguish between (i) covariances between individuals in the same group and (ii) covariances between individuals in different groups. The expected covariance between two individuals,i andj, in the same group is

(A1)

and in different groups is

(A2)

in which is relatedness betweeni andj, is relatedness betweeni and the group member ofj, is relatedness betweenj and the group member ofi, and is relatedness between the group members ofi andj.Table A1 shows expected covariances between full sibs, half sibs, and unrelated individuals for each of the three tube compositions used inWolf (2003). The expectations of sire and dam covariances given in Table 3 differ from those presented inWolf (2003), primarily because covariances due to group members of full and half sibs are incomplete inWolf (2003).

TABLE A1.

Expectations of full- and half-sib covariances in the data structure used in Wolf (2003)

	Tube composition
Covariance	Full-sib pairs	Half-sib pairs	Unrelated pairs
FS same		NO	NO
FS diff.			a orbc
HS same	NO		NO
HS diff.			b orac
Unrelated same	NO	NO
Unrelated diff.	0	0	0

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FS, full sibs; HS, half sibs; same, in the same group; diff., in different groups; NO, this combination does not occur.

^a

When the group members of both individuals are full sibs.

^b

When the group members of both individuals are half sibs.

^c

Only those two covariances provide information to separate the direct and the indirect genetic variance.

It follows fromEquations A1 andA2 that and can be separated only when. Thus the information in the data to separate and depends on whether and how frequently occurs. It follows fromTable A1 that occurs only in the situation where groups consist of two unrelated individuals and only when relatedness between the two group members of both individuals differs from that between both individuals considered. (seeTable A1 footnote). Whether or not that situation occurs in the data depends on details of the experimental implementation that are not described inWolf (2003). Thus, the data structure used inWolf (2003) provides either very little or no information at all to separate the direct and the associative heritable variance.

To validate this theoretical result we performed Monte Carlo simulation of the data structure used inWolf (2003), where, in the case of groups consisting of unrelated individuals, group members of full sibs were full sibs as well, and group members of half sibs were half sibs as well. Hence, theoretically this data structure should not contain any information to separate and. Statistical analyses of the simulated data usingEquations 4 and5 as a model showed that the matrix of second derivatives of the likelihood (Fisher's information matrix) was singular, indicating that there are an infinite number of combinations of parameters that yield the identical maximum likelihood. Indeed identical maximum likelihoods were observed for multiple combinations of and, which confirms the theoretical result derived above.

1. Beaumont, C., N. Millet, E. LeBihanDuval, A. Kipi and V. Dupuy, 1997. Genetic parameters of survival to the different stages of embryonic death in laying hens. Poult. Sci. 76: 1193–1196. [DOI] [PubMed] [Google Scholar]
2. Bijma, P., W. M. Muir and J. A. M. Van Arendonk, 2007. Multilevel selection 1: quantitative genetics of inheritance and response to selection. Genetics 175: 277–288. [DOI] [PMC free article] [PubMed]
3. Carlen, E., M. D. Schneider and E. Strandberg, 2005. Comparison between linear models and survival analysis for genetic evaluation of clinical mastitis in dairy cattle. J. Dairy Sci. 88: 797–803. [DOI] [PubMed] [Google Scholar]
4. Clutton-Brock, T., 2002. Behavioral ecology—breeding together: kin selection and mutualism in cooperative vertebrates. Science 296: 69–72. [DOI] [PubMed] [Google Scholar]
5. Craig, J. V., and W. M. Muir, 1996. Group selection for adaptation to multiple-hen cages: beak-related mortality, feathering, and body weight responses. Poult. Sci. 75: 294–302. [DOI] [PubMed] [Google Scholar]
6. Dawkins, M., 1982.The Extended Phenotype. W. H. Freeman, San Francisco.
7. Denison, R. F., E. T. Kiers and S. A. West, 2003. Darwinian agriculture: When can humans find solutions beyond the reach of natural selection? Q. Rev. Biol. 78: 145–168. [DOI] [PubMed] [Google Scholar]
8. Gilmour, A. R., B. J. Gogel, B. R. Cullis, S. J. Welham and R. Thompson, 2002.ASReml User Guide Release 1.0. VSN International, Hemel Hempstead, UK (http://www.vsn-intl.com/).
9. Gitterle, T., M. Rye, D. Salte, J. Cock, H. Johansenet al., 2005. Genetic (co)variation in harvest body weight and survival in Penaeus (Litopenaeus) vannamei under standard commercial conditions. Aquaculture 243: 83–92. [Google Scholar]
10. Goodnight, C. J., 2005. Multilevel selection: the evolution of cooperation in non-kin groups. Popul. Ecol. 47: 3–12. [Google Scholar]
11. Goodnight, C. J., and L. Stevens, 1997. Experimental studies of group selection: What do they tell us about group selection in nature? Am. Nat. 150: S59–S79. [DOI] [PubMed] [Google Scholar]
12. Griffing, B., 1967. Selection in reference to biological groups. I. Individual and group selection applied to populations of unordered groups. Aust. J. Biol. Sci. 20: 127. [PubMed] [Google Scholar]
13. Griffing, B., 1968. a Selection in reference to biological groups. II. Consequences of selection in groups of one size when evaluated in groups of a different size. Aust. J. Biol. Sci. 21: 1163. [DOI] [PubMed] [Google Scholar]
14. Griffing, B., 1968. b Selection in reference to biological groups. III. Generalized results of individual and group selection in terms of parent-offspring covariances. Aust. J. Biol. Sci. 21: 1171. [DOI] [PubMed] [Google Scholar]
15. Griffing, B., 1969. Selection in reference to biological groups. IV. Application of selection index theory. Aust. J. Biol. Sci. 22: 131. [PubMed] [Google Scholar]
16. Griffing, B., 1976. a Selection in reference to biological groups. V. Analysis of full-sib groups. Genetics 82: 703–722. [DOI] [PMC free article] [PubMed] [Google Scholar]
17. Griffing, B., 1976. b Selection in reference to biological groups. VI. Use of extreme forms of nonrandom groups to increase selection efficiency. Genetics 82: 723–731. [DOI] [PMC free article] [PubMed] [Google Scholar]
18. Griffing, B., 1981. a A theory of natural-selection incorporating interaction among individuals. I. The modeling process. J. Theor. Biol. 89: 635–658. [DOI] [PubMed] [Google Scholar]
19. Griffing, B., 1981. b A theory of natural-selection incorporating interaction among individuals. II. Use of related groups. J. Theor. Biol. 89: 659–677. [DOI] [PubMed] [Google Scholar]
20. Hamilton, W. D., 1963. Evolution of altruistic behavior. Am. Nat. 97: 354. [Google Scholar]
21. Hamilton, W. D., 1964. a Genetical evolution of social behaviour I. J. Theor. Biol. 7: 1. [DOI] [PubMed]
22. Hamilton, W. D., 1964. b Genetical evolution of social behaviour 2. J. Theor. Biol. 7: 17. [DOI] [PubMed] [Google Scholar]
23. Henderson, C. R., 1950. Estimation of genetic parameters. Ann. Math. Stat. 21: 309–310. [Google Scholar]
24. Keller, L., 1999.Levels of Selection in Evolution. Princeton University Press, Princeton, NJ.
25. Kirkpatrick, M., and R. Lande, 1989. The evolution of maternal characters. Evolution 43: 485–503. [DOI] [PubMed] [Google Scholar]
26. Kruuk, L. E. B., 2004. Estimating genetic parameters in natural populations using the ‘animal model’. Philos. Trans. R. Soc. Lond. Ser. B Biol. Sci. 359: 873–890. [DOI] [PMC free article] [PubMed] [Google Scholar]
27. Kruuk, L. E. B., J. Merila and B. C. Sheldon, 2001. Phenotypic selection on a heritable size trait revisited. Am. Nat. 158: 557–571. [DOI] [PubMed] [Google Scholar]
28. Kruuk, L. E. B., J. Merila and B. C. Sheldon, 2003. When environmental variation short-circuits natural selection. Trends Ecol. Evol. 18: 207–209. [Google Scholar]
29. Lynch, M., and B. Walsh, 1998.Genetics and Analysis of Quantitative Traits. Sinauer, Sunderland, MA.
30. Maynard-Smith, J., 1974. Theory of games and evolution of animal conflicts. J. Theor. Biol. 47: 209–221. [DOI] [PubMed] [Google Scholar]
31. Moore, A. J., and C. R. B. Boake, 1994. Optimality and evolutionary genetics—complementary procedures for evolutionary analysis in behavioral ecology. Trends Ecol. Evol. 9: 69–72. [DOI] [PubMed] [Google Scholar]
32. Moore, A. J., E. D. Brodie and J. B. Wolf, 1997. Interacting phenotypes and the evolutionary process. 1. Direct and indirect genetic effects of social interactions. Evolution 51: 1352–1362. [DOI] [PubMed] [Google Scholar]
33. Muir, W. M., 1996. Group selection for adaptation to multiple-hen cages: selection program and direct responses. Poult. Sci. 75: 447–458. [DOI] [PubMed] [Google Scholar]
34. Muir, W. M., 2003. Indirect selection for improvement of animal well-being, pp. 247–256 inPoultry Genetics, Breeding and Biotechnology, edited by W. M. Muir and S. Aggrey. CABI Press, Cambridge, MA.
35. Muir, W. M., 2005. Incorporation of competitive effects in forest tree or animal breeding programs. Genetics 170: 1247–1259. [DOI] [PMC free article] [PubMed] [Google Scholar]
36. Patterson, H. D., and R. Thompson, 1971. Recovery of inter-block information when block sizes are unequal. Biometrika 58: 545. [Google Scholar]
37. Ridley, M., 1995.The Red Queen: Sex and the Evolution of Human Nature. Penguin Books, New York.
38. Roff, D. A., 1997.Evolutionary Quantitative Genetics. Chapman & Hall, New York.
39. Teichertcoddington, D. R., and R. O. Smitherman, 1988. Lack of response by Tilapia-Nilotica to mass selection for rapid early growth. Trans. Am. Fish. Soc. 117: 297–300. [Google Scholar]
40. Vangen, O., 1993. Results from 40 generations of divergent selection for litter size in mice. Livest. Prod. Sci. 37: 197–211. [Google Scholar]
41. Wade, M. J., 1979. The evolution of social interactions by family selection. Am. Nat. 113: 399–417. [Google Scholar]
42. Wald, A., 1943. Test of statistical hypothesis concerning several parameters when the number of observations is large. Trans. Am. Math. Soc. 54: 426–482. [Google Scholar]
43. West, S. A., I. Pen and A. S. Griffin, 2002. Conflict and cooperation—cooperation and competition between relatives. Science 296: 72–75. [DOI] [PubMed] [Google Scholar]
44. Williams, G. C., 1966.Adaptations and Natural Selection. Princeton University Press, Princeton, NJ.
45. Williams, G. C., and D. C. Williams, 1957. Natural selection of individually harmful social adaptations among sibs with special reference to social insects. Evolution 11: 32–39. [Google Scholar]
46. Wilson, D. S., and E. Sober, 1989. Reviving the superorganism. J. Theor. Biol. 136: 337–356. [DOI] [PubMed] [Google Scholar]
47. Wolf, J. B., 2003. Genetic architecture and evolutionary constraint when the environment contains genes. Proc. Natl. Acad. Sci. USA 100: 4655–4660. [DOI] [PMC free article] [PubMed] [Google Scholar]
48. Wolf, J. B., E. D. Brodie, J. M. Cheverud, A. J. Moore and M. J. Wade, 1998. Evolutionary consequences of indirect genetic effects. Trends Ecol. Evol. 13: 64–69. [DOI] [PubMed] [Google Scholar]
49. Wright, S., 1968.Evolution and Genetics of Populations. Chicago University Press, Chicago.
50. Wright, S., 1977.Evolution and Genetics of Populations, Vol. 1. Chicago University Press, Chicago.