EVOLUTION OF HELPING AND HARMING IN HETEROGENEOUS GROUPS

Authors


Abstract

Social groups are often composed of individuals who differ in many respects. Theoretical studies on the evolution of helping and harming behaviors have largely focused upon genetic differences between individuals. However, nongenetic variation between group members is widespread in natural populations, and may mediate differences in individuals’ social behavior. Here, we develop a framework to study how variation in individual quality mediates the evolution of unconditional and conditional social traits. We investigate the scope for the evolution of social traits that are conditional on the quality of the actor and/or recipients. We find that asymmetries in individual quality can lead to the evolution of plastic traits with different individuals expressing helping and harming traits within the same group. In this context, population viscosity can mediate the evolution of social traits, and local competition can promote both helping and harming behaviors. Furthermore, asymmetries in individual quality can lead to the evolution of competition-like traits between clonal individuals. Overall, we highlight the importance of asymmetries in individual quality, including differences in reproductive value and the ability to engage in successful social interactions, in mediating the evolution of helping and harming behaviors.

The worst pathologies of the kin-selection criterion arise when genes for social behavior are unconditionally expressed—i.e. expressed by every individual of a given genotype … there are numerous asymmetries that make conditional expression the natural course … Conditionality, although mentioned, was insufficiently emphasized in my previous work.

Hamilton (1987, p. 433)

Understanding cooperation is a major challenge for evolutionary biology (Hamilton 1996; Sachs et al. 2004; West et al. 2007; Bourke 2011). Hamilton's (1963, 1964, 1970, 1972, 1975) theory of inclusive fitness provides a general explanation for the adaptive evolution of cooperation. The idea is that individuals can increase their genetic representation in future populations not only by improving their own reproductive success, but also by improving the reproductive success of their genetic relatives. The key result of inclusive fitness theory is Hamilton's rule, which states that natural selection will favor an increase in any trait if −c + rb > 0, where c is the direct fitness cost to the actor, b is the benefit enjoyed by the recipient, and r is the genetic relatedness between actor and recipient (Hamilton 1963, 1964, 1970; Charnov 1977). Relatedness has often taken central stage in the literature on inclusive fitness (Lehmann and Keller 2006; Bourke 2011), and is understood to be an important driver of a diversity of evolutionary phenomena, including eusociality (Boomsma 2007, 2009; Hughes et al. 2008), cooperative breeding (Cornwallis et al. 2010), multicellularity (Dawkins 1982; Maynard Smith 1988; Maynard Smith and Szathmáry 1995; Grosberg and Strathmann 1998, 2007), sex allocation (Hamilton 1967; Charnov 1982; West 2009), virulence (Frank 1996b), parent–offspring conflict (Trivers 1974), and genomic imprinting (Haig 2002).

One mechanism that can give rise to relatedness between social partners is population viscosity, whereby individuals do not move far from their place of origin during their lives (Hamilton 1964, 1971). In such scenarios, even indiscriminate cooperation toward one's neighbors is likely to involve significant genetic relatedness between interactants. However, limited dispersal may also increase resource competition among social partners, and this tends to inhibit the evolution of cooperation (Hamilton 1971; Taylor 1992a; Queller 1992; Frank 1998; West et al. 2002). In the simplest models of population viscosity these two effects exactly cancel, giving no net effect of dispersal on the evolution of cooperation (Taylor 1992a, b; Kümmerli et al. 2009). This result has motivated a large body of theoretical (and, increasingly, empirical) research on factors that may decouple relatedness and competition to allow viscosity to promote the evolution of helping and harming behaviors (reviewed by West et al. 2002; Lehmann and Rousset 2010).

Most of this literature has assumed that populations are homogeneous in individual quality, other than differences relating to sex (but see Frank 1996a, 2003, 2010; Johnstone 2008; Rodrigues and Gardner 2012, 2013). However, within-group heterogeneities are likely to be important for the evolution of social behavior, especially in determining which individuals enact which behaviors (Hamilton 1964; Alexander 1974; Michener and Brothers 1974; West-Eberhard 1975; Milinski 1978; Rubenstein 1982; Craig 1983; Alexander et al. 1991; Pamilo 1991; Crozier and Pamilo 1996; West-Eberhard 2003; Bourke 2007; West et al. 2007). In social amoebae, larger cells tend to develop as reproductive spores rather than altruistic stalk (Leach et al. 1973). In brewer's yeast, damaged cells appear more predisposed to self-sacrifice (Fabrizio et al. 2004; Herker et al. 2004). In primitively eusocial insects, individuals of better nutritional state are more likely to develop as reproductives (Gadagkar et al. 1988), and workers kill their queen if her fecundity drops below a threshold (Bourke 1994). Thus, a better understanding of how within-group variation in individual quality mediates the evolution of helping and harming is desired.

Here, we investigate how within-group variation in quality influences the evolution of helping and harming behaviors. We consider both unconditional social behavior and also social behavior that is conditionally adjusted according to the quality of the actor and/or her social partners. We first perform a general analysis that treats genetic relatedness and local competition as separate parameters that can be varied independently of each other (e.g., Frank 1998). We then consider an explicit viscous population model, in which relatedness and local competition emerge from explicit demographic assumptions (e.g., Taylor 1992a). We use our analyses as a foundation upon which to discuss the role of individual quality in mediating the evolution of social behaviors.

General Model

BASIC MODEL

We assume a population of haploid, asexually reproducing individuals of which a fraction uH is high quality and a fraction uL is low quality. Low-quality individuals have a fecundity that is a fraction 1 − s of that of high-quality individuals. Offspring quality is assigned at random, the individual being high quality with probability p and low quality with probability 1 − p, independently of parent quality.

Juveniles engage in social interactions that mediate survival to adulthood. Specifically, high-quality juveniles survive with probability SH(xH,yH,yL), where xH is the focal juvenile's phenotype, yH is the average phenotype among high-quality juveniles in the local neighborhood, and yL is the average phenotype among low-quality juveniles in the local neighborhood; and low-quality juveniles survive with probability SL(xL,yH,yL), where xL is the focal juvenile's phenotype. We classify social behavior according to two factors: first, whether it is conditioned on the actor's quality and second, whether it is conditioned on the recipient's quality.

The marginal survival cost of social behavior is ∂SH(xH,yH,yL)/∂xH = −C and ∂SL(xL,yH,yL)/∂xL = −C for high-quality and low-quality juveniles, respectively. The marginal survival benefit depends on the type of social interaction. For example, if there is no discrimination of recipients’ quality and focusing on a focal high-quality individual, the marginal survival benefit is ∂SH(xH,yH,yL)/∂yH = uHB and ∂SH(xH,yH,yL)/∂yL = uLB; whereas, if there is discrimination of recipients’ quality, and high-quality individuals are the sole recipients of the social behaviors, the marginal survival benefit is ∂SH(xH,yH,yL)/∂yH = B and ∂SH(xH,yH,yL)/∂yL = (uL/uH)B. Similar functions can be derived for all other types of behavior as well as for low-quality individuals. We assume that the costs and benefits of social actions are small, that is C, B << 1, and we scale survival probability such that the baseline is one (see Appendix S1 for details).

After social interactions, juveniles compete for scarce resources, where a fraction a of the competition is among juveniles in the local neighborhood, and a fraction 1 − a of the competition occurs globally (Frank 1998). Thus, fitness is

display math(1)

and

display math(2)

for high-quality and low-quality juveniles, respectively (see Appendix S2 for details). The denominator represents the amount of competition for a focal individual, where zH and zL are the population average phenotypes of high-quality and low-quality juveniles, respectively. Note that, owing to the assumption of small marginal effects and identical baseline survival between the two classes, the expectation of fitness over all high-quality individuals, and the expectation of fitness over all low-quality individuals, is unity. Natural selection favors those heritable traits that are, on average, associated with higher fitness. The appropriate average of fitness is given by W = cHWH + cLWL, where cH and cL are the class-reproductive values for high-quality and low-quality individuals, respectively (Fisher 1930; Price and Smith 1972; Taylor 1990; Taylor and Frank 1996; Frank 1998; Grafen 2006; see Appendix S3 for details). Model notation is summarized in Table 1.

Table 1. A summary of model notation
SymbolMeaning
HHigh-quality individual
LLow-quality individual
BBoth high- and low-quality individuals
FCorresponding to Frank's (1998) analysis
TCorresponding to Taylor's (1992a) analysis
AActor
PPrimary recipient
SSecondary recipient
aScale of competition
AZPotential for helping corresponding to reference model Z
AX|Y,ZPotential for helping where actor is in condition X, and primary recipients are in condition Y, for reference model Z
pProbability that an offspring becomes a high-quality juvenile
cXClass reproductive value in condition X (cX = uXvX)
FXFecundity of a breeding female in condition X (FL = (1 − s)FH)
hXProbability of co-philopatry in condition X
mMigration rate
nGroup-size
neEffective group-size
ρXLife-for-life relatedness (or value) of an individual in condition X (ρX = υXrX)
rX“Others-only” relatedness of an individual in condition X
sReproductive asymmetry
uXFrequency of individuals in condition X
vXReproductive value of an individual in condition X
υXRelative reproductive value of an individual in condition X (υX = vX/vA)
xAverage social behavior of focal actor
yAverage social behavior of juveniles in focal patch
zAverage social behavior of juveniles in population
z*Convergence stable strategy for the social behavior

EVOLUTION OF HELPING AND HARMING

We classify social behaviors according to their impact upon the survival of group mates (Lehmann et al. 2006; West and Gardner 2010). Specifically, helping behaviors are those where B > 0, and harming behaviors as those where B < 0. We use the neighbor-modulated fitness approach to kin-selection analysis (Taylor and Frank 1996; Frank 1997, 1998; Rousset 2004; Taylor et al. 2007) to determine the direction of selection acting upon social traits (see Appendices S2–S4 for details). This yields a form of Hamilton's (1963, 1964, 1970, 1972) rule:

display math(3)

This Hamilton's rule comprises three additive terms, each of which can be associated with an individual or set of individuals affected by the behavior of the actor. The first term concerns effects of the behavior on the actor; the second term concerns the immediate effects of the behavior on social partners, that is, primary recipients; and the third term concerns the kin competition effects of the behavior on social partners, that is, secondary recipients.

Thus, inequality (3) can be read as follows: vA is the actor's reproductive value (Fisher 1930; Taylor 1990, 1996; Grafen 2006); vP is the reproductive value of the primary recipients; vS is the reproductive value of the secondary recipients; rP = r is the relatedness between actor and primary recipients (Hamilton 1964, 1970; Grafen 1985); rS = ar is the relatedness between actor and secondary recipients (Hamilton 1964, 1970; Grafen 1985), where a is the scale of competition (Frank 1998), that is the proportion of secondary recipients who are also primary recipients. Note that if the scale of competition is one (a = 1), then relatedness of secondary recipients is equal to that of primary recipients (rS = rP = r), and that if the scale of competition is zero (a = 0), then the relatedness of secondary recipients is zero (rS = 0). Also, because juvenile quality is assigned at random, relatedness is independent of actor and recipient class.

Consequently, an actor's social behavior has a three-fold impact upon her own inclusive fitness. First, the actor pays a survival cost C, and this is weighted by actor's reproductive value vA. Second, primary recipients receive a survival benefit B, and this is weighted by primary recipient relatedness rP and reproductive value vP. Third, owing to the impact of the social behavior upon local competition, secondary recipients suffer a cost BC, and this is weighted by secondary recipient relatedness rS and reproductive value vS,

Inequality (3) can be normalized with respect to the actor's reproductive value, to derive what we call relative reproductive values (υ). Note that in this case actor's relative reproductive value is one. Thus, the weights of the marginal survival effects on primary and secondary recipients are now the product of relative reproductive value and relatedness, that is “life-for-life relatedness” (ρ; Hamilton 1972; Bulmer 1994). Specifically, the life-for-life relatedness of primary recipients is ρP = υPr, and the life-for-life relatedness of secondary recipients is ρS = υSar, where υP = vP/vA and υS = vS/vA are the relative reproductive values of primary and secondary recipients, respectively. Life-for-life relatedness describes how much an actor values the recipients of her actions, taking into account not only the extent to which they share genes in common (r), but also their relative capacity to transmit genes to future generations (υ; see Appendix S3 for details).

Setting the left-hand side (LHS) of inequality (3) equal to 0, we find the condition where the actor is indifferent with regards to helping/harming slightly more versus slightly less. This condition can be re-arranged into the form C/B = A, where A defines the potential for helping (Rodrigues and Gardner 2012; cf. Gardner 2010) and −A defines the potential for harming (Rodrigues and Gardner 2012). Assuming that the life-for-life relatedness of a secondary recipient is less than that of the actor (ρS < 1), then A = (ρP − ρS)/(1 − ρS). Consequently: if the life-for-life relatedness of a primary recipient exceeds that of a secondary recipient (ρP > ρS), there is potential for helping (A > 0); whereas, if the life-for-life relatedness of a secondary recipient exceeds that of a primary recipients (ρP < ρS), there is potential for harming. In contrast, if the life-for-life relatedness of a secondary recipient is greater than that of the actor (ρS ≥ 1), actors are favored to invest all of their resources into helping or harming, because any cost incurred by an actor is fully compensated by benefits to secondary recipients. This may be better understood if one rewrites Hamilton's rule (inequality 3) in the form −(1 − ρS)C + (ρP − ρS)B > 0: if ρS ≥ 1 then −(1 − ρS)C > 0, which means that the actor's inclusive fitness increases with increasing personal survival cost, even in the absence of any survival benefit to primary recipients. Whether the actor is selected to invest into helping or harming depends upon the value of primary versus secondary recipients (ρP > ρS vs. ρP < ρS). We establish a convention of setting A = ∞ if ρP > ρS, and A = −∞ if ρP < ρS. Thus, we have

display math(4)

where the last two lines define the region of parameter space where actors are selected to invest all of their resources into social interactions. This effect was foreshadowed by Dawkins (1976, p. 130): “As soon as a runt becomes so small and weak that his expectation of life is reduced to the point where benefit to him due to parental investment is less than half the benefit that the same investment could potentially confer on the other babies, the runt should die gracefully and willingly … he should give up and preferably let himself be eaten by his litter-mates or his parents.” We term the portion of parameter space in which the potential for helping has infinite magnitude the “Dawkins’ Runt” region. The potential for helping for the different types of behavior is given in Table 2.

Table 2. The potential for helping (A) in the general model is shown for different combinations of the actor's quality and the primary recipients’ quality
 Recipients
ActorsBothHighLow
Both math image math image math image
High math image math image math image
Low math image math image math image

Island Model

MODEL

Here we elaborate upon the model presented in the previous section, making the demography of the population more explicit. We assume that the population is subdivided into an infinite number of social groups with n adults each, that is Wright's (1931) island model. Groups are composed of nH high-quality adults and nL low-quality adults, where nH and nL are random variables that satisfy the constraint n = nH + nL. Both high- and low-quality individuals produce a large number of offspring, denoted FH and FL = (1 − s)FH, respectively. After reproduction, all adults die, and juveniles engage in social interactions that mediate their survival to adulthood. After social interactions, each juvenile disperses with probability m to a random group or else, with probability 1 − m, remains in the natal group.

EVOLUTION OF HELPING AND HARMING

As in the previous section, we perform a neighbor-modulated fitness analysis (Taylor and Frank 1996; Frank 1997, 1998; Rousset 2004; Taylor et al. 2007; see Appendices S2–S4 for details) to determine the direction of selection acting on the social trait. This yields a Hamilton's rule that takes the same form as given for the previous model (Inequality 3). However, we find that the scale of competition a is now given by the probability of co-philopatry h, that is the probability that two individuals sampled at random are philopatric to the group. Hence, a = h = (1 − m)2. Moreover, relatedness is given by

display math(5)

where ne is effective group-size (see Appendix S5 for details). Reproductive asymmetry decreases effective group-size: ne < n for s > 0. As a result, relatedness is always greater than that of Taylor's (1992a) model (r > rT; Fig. 1). We find that relatedness is highest when reproductive asymmetry is high (high s) and migration rate is low (low m), and attains a maximum at an intermediate value p* of the frequency of high-quality individuals, where p* ≤ ½. Furthermore, we find that p* decreases with increasing reproductive asymmetry. The relatedness of primary recipients is given by rP = r whereas that of secondary recipients is given by rS = (1 − m)2r. Consequently, the relatedness of primary recipients is always greater than or equal to that of secondary recipients (rPrS), and the difference between the two is greatest when p = p*. As before, we set the LHS of Hamilton's rule to 0 and rearrange to derive the potential for helping A. These results are given in Table 3.

Table 3. The potential for helping (A) in the island model is shown for different combinations of the actor's quality and the primary recipients’ quality
 Recipients
ActorsBothHighLow
Both math image math image math image
High math image math image math image
Low math image math image math image
Figure 1.

Relatedness as a function of the frequency of high-quality individuals (p) and reproductive asymmetry (s). Darker shades represent higher relatedness. Parameter values: m = 0.25 and n = 10.

Analysis and Results

For each of our two models, we define a “reference model.” In the general-model analysis, the reference model corresponds to a homogeneous population, where each individual's fecundity is identical, that is s = 0. This recovers the model of Frank (1998, pp. 114–115), where the potential for helping is AF = (r − ar)/(1 − ar). Note that under the assumptions of Frank's model, the potential for helping is always nonnegative (AF ≥ 0), and is greatest when relatedness is high (high r) and when local competition is low (low a). In the island-model analysis, the reference model also corresponds to a homogeneous population, where each individual's fecundity is identical, that is s = 0. This recovers Taylor's (1992a) asexual model. In this case, the potential for helping is given by AT = (rThTrT)/(1 − hTrT), where hT = (1 − m)2 is the probability of co-philopatry. As relatedness is given by rT = 1/(n − (n − 1)hT), the potential for helping is given by AT = 1/n. Consequently, the potential for helping is independent of the migration rate (m) and decreases with increasing group size (n). We use these reference models as a benchmark upon which to compare our results for heterogeneous groups (s > 0).

We divide our analysis into three sections. In the first section, we consider that actors cannot discriminate recipients’ quality. In the second section, we consider that actors can discriminate recipients’ quality, and that they direct the social behavior to high-quality recipients only. In the third section, we consider that actors direct the social behavior to low-quality recipients only. In each of the three sections, we consider social behavior that is either unconditional or conditional upon actor's quality.

INDISCRIMINATE SOCIAL BEHAVIOR

Individuals often express different phenotypes independently of their genotype and in ways that correlate with their quality. For example, in yeast, programmed cell death (PCD) is mostly expressed by senescent cells (Fabrizio et al. 2004; Herker et al. 2004). In this section, we assume that actors cannot discriminate the quality of recipients, hence all individuals in the group are equally likely to be recipients of the social actions, and therefore we focus on unconditional and conditional behavior on actor's quality.

We find that the potential for unconditional helping is always nonnegative (AB|B,F ≥ 0 and AB|B,T ≥ 0). Furthermore, although in the general model reproductive asymmetry has no impact upon the potential for helping (which is equal to that of Frank's model: AB|B,F = AF; Fig. 2A, Table 2), in the island model reproductive asymmetry does have an impact upon the potential for helping (which is greater than that of Taylor's model: AB|B,T > AT; Fig. 3A, Table 3). In both models, reproductive asymmetry (s > 0) does not lead to differences in the reproductive value of actors, primary recipients and secondary recipients (vA = vP = vS). However, in the island model, reproductive asymmetry inflates relatedness (dr/ds > 0), which, in turn, increases the potential for helping (dA/ds > 0). Importantly, if the reproductive values of actor, primary recipients, and secondary recipients are equal, the potential for helping is unaffected by the dispersal rate (dAB|B,T /dm = 0). This recovers and explains Taylor's (1992a) result. If the reproductive values of actor and recipients are not equal, then the potential for helping may be mediated by dispersal rate (dA/dm ≠ 0).

Figure 2.

The potential for helping (A) is shown for different combinations of unconditional and conditional social traits. The potential for helping is given as a function of the frequency of high-quality juveniles (p) and the reproductive asymmetry (s). The potential for helping of Frank's (1998) reference model corresponds to s = 0. (A) Unconditional social behavior: the potential for helping is equal to that of the reference model (AB|B,F = AF). As a result, the potential for helping is always nonnegative (AB|B,F ≥ 0). (B) Behavior that is unconditional on actor's quality and is directed to high-quality group mates: the potential for helping is always nonnegative (AB|H,F ≥ 0), and it is always greater than that of the reference model (AB|H,F > AF). (C) Behavior that is unconditional on actor's quality and is directed to low-quality group mates: the potential for helping is always less than that of the reference model (AB|L,F < AF); high reproductive asymmetry and high local competition promote harming behavior (AB|L,F < 0). (D) Behavior expressed by high-quality juveniles and directed to all group mates: the potential for helping is always nonnegative (AH|B,F ≥ 0), and it is always less than that of the reference model (AH|B,F < AF). (E) Behavior expressed by high-quality juveniles and directed to high-quality group mates: the potential for helping is always nonnegative (AH|H,F ≥ 0), and it is always greater than that of the references model (AH|H,F > AF). (F) Behavior expressed by high-quality juveniles directed to low-quality group mates: the potential for helping is always less than that of the reference model (AH|L,F < AF); high reproductive asymmetry and high local competition promote harming behavior (AH|L,F < 0). (G) Behavior expressed by low-quality juveniles and directed to all group mates: the potential for helping is always nonnegative (AL|B,F ≥ 0), and it is always greater than that of the reference model (AL|B,F > AF). (H) Behavior expressed by low-quality juveniles and directed to high-quality group mates: the potential for helping is always nonnegative (AL|H,F ≥ 0), and it is always greater than that of the reference model (AL|H,F > AF). (I) Behavior expressed by low-quality juveniles and directed to low-quality group mates: there is potential for helping and potential for harming (AL|L,F > 0 and AL|L,F < 0). The potential for helping is always less than that of the reference model (AL|L,F < AF). (G–I) When secondary recipients’ value is greater than or equal to actor's value (ρS ≥ 1), there is infinite potential for helping (AL|B,F = ∞ and AL|H,F = ∞, Dawkins’ Runt region, panels G and H) and infinite potential for harming (AL|L,F = −∞, Dawkins’ Runt region, panel I). In all cases, relatedness is set to r = 0.5 and local competition is set to a = 0.5.

Figure 3.

The potential for helping (A) is shown for different combinations of unconditional and conditional social traits. The potential for helping is given as a function of the frequency of high-quality individuals (p) and reproductive asymmetry (s). The potential for helping of Taylor's (1992a) reference model corresponds to s = 0. Darker shades represent higher potential for helping or harming. (A) Unconditional social behavior: the potential for helping is greater than that of the reference model (AB|B,T > AT). (B) Behavior that is unconditional on actor's quality and directed to high-quality group mates: the potential for helping is always nonnegative (AB|H,T ≥ 0), and it is always greater than that of the reference model (AB|H,T > AT). (C) Behavior that is unconditional on actor's quality and directed to low-quality group mates: the potential for helping is always less than that of the reference model (AB|L,T < AT). High reproductive asymmetry and high local competition promote harming behavior (AB|L,T < 0). (D) Behavior expressed by high-quality juveniles and directed to all group mates: the potential for helping is always nonnegative (AH|B,T ≥ 0), and it is always less than that of the reference model (AH|B,T < AT). (E) Behavior expressed by high-quality juveniles and direct to high-quality group mates: the potential for helping is always nonnegative (AH|H,T ≥ 0), and it is always greater than that of the reference model (AH|H,T > AT). (F) Behavior expressed by high-quality juveniles and directed to low-quality group mates: the potential for helping is always less than that of the reference model (AH|L,T < AT). High reproductive asymmetry and high local competition promote harming behavior (AH|L,T < 0). (G) Behavior expressed by low-quality juveniles and directed to all group mates: the potential for helping is always nonnegative (AL|B,T ≥ 0), and it is always greater than that of the reference model (AL|B,T > AT). (H) Behavior expressed by low-quality juveniles and directed to high-quality group mates: the potential for helping is always nonnegative (AL|H,T ≥ 0), and it is always greater than that of the reference model (AL|H,TAT). (I) Behavior expressed by low-quality juveniles and directed to low-quality group mates: there is potential for helping and potential for harming (AL|L,T > 0 and AL|L,T < 0). For a wide range of parameter values, the potential for helping is less than that of the reference model (AL|L,T < AT). However, if reproductive asymmetry is high and frequency of high-quality juveniles is low, the potential for helping may be greater than that of the reference model (AL|L,T > AT). (G-I) When secondary recipients’ value is greater than or equal to actor's value (ρS ≥ 1) there is an infinite potential for helping (AL|B,T = ∞ and AL|H,T = ∞, Dawkins’ Runt region, panels G and H) and infinite potential for harming (AL|L,T = −∞, Dawkins’ Runt region, panel I). In all cases, group size is set to n = 10 and migration rate is set to m = 0.25.

We now assume that actors can conditionally adjust their behavior according to their own quality. We start by considering conditionally adjusted behavior enacted by high-quality juveniles. We find that the potential for helping is always nonnegative (AH|B,F ≥ 0 and AH|B,T ≥ 0). Moreover, reproductive asymmetry reduces the potential for helping in the general model, and, for a wide range of parameters, in the island model (AH|B,F < AF, and often AH|B,T < AT; Figs. 2D, 3D, Tables 2 and 3). We find that the reproductive value of primary recipients is equal to that of secondary recipients (vP = vS). The reproductive value of the actor is always greater than that of the primary and secondary recipients (vA > vP = vS). This decreases the potential for helping relative to that of the reference models for two reasons: first, it decreases the difference in life-for-life relatedness between primary and secondary recipients (lower ρPρS); second, it increases the difference in life-for-life relatedness between actor and secondary recipients (higher 1 − ρS). Turning our attention to the island model, we find that for extreme values of reproductive asymmetry (high s), sufficiently high migration rate (high m) and intermediate frequency of high-quality juveniles (medium p), there may be a positive effect on the potential for helping, which can be greater than that of the reference model (AH|B,T > AT). This is because, under these circumstances, the actor is more closely related to primary recipients than to secondary recipients.

We now turn our attention to conditional behavior of low-quality juveniles. We find that the potential for helping is always nonnegative (AL|B,F ≥ 0 and AL|B,T ≥ 0). Moreover, we find that reproductive asymmetry (s > 0) increases the potential for helping (AL|B,F > AF and AL|B,T > AT; Figs. 2G, 3G, Tables 2, 3). We find that although the reproductive value of primary recipients is equal to that of secondary recipients (vP = vS), the reproductive value of the actor is always less than that of primary and secondary recipients (vA < vP = vS). Consequently, actors put more value on their social partners, and this yields a potential for helping that is greater than that of the reference model. Extreme values of reproductive asymmetry (high s), together with high local competition (low m or high a) and sufficiently high frequency of high-quality juveniles (high p), can lead to the life-for-life relatedness of secondary recipients being greater than or equal to that of the actor (ρS ≥ 1), which favors actors to invest all of their resources into social behavior (AL|B,F = ∞ and AL|B,T = ∞; Dawkins’ Runt region in Figs. 2G, 3G).

QUALITY DISCRIMINATION

Individuals often condition their behavior not only on their own quality, but also on the quality of their social partners. For example, paper-wasp workers appear to directly assess their queen's quality by monitoring her egg production, and behave more selfishly if her fecundity declines (Liebig et al. 2005). In the following two subsections, we consider that actors can discriminate the quality of recipients and can direct their behavior accordingly.

High-quality recipients

Here, we assume that actors direct their actions toward high-quality group mates, who are the sole primary recipients of their social actions. We begin by considering behavior that is expressed independently of the actor's quality. We find that the potential for helping is always nonnegative (AB|H,F ≥ 0 and AB|H,T ≥ 0). Furthermore, we find that reproductive asymmetry (s > 0) has a positive impact upon the potential for helping (AB|H,T > AT and AB|H,F > AF; Figs. 2B, 3B, Tables 2, 3). This is because, although the reproductive value of the actor is equal to that of secondary recipients (vA = vS), the reproductive value of primary recipients is greater than that of secondary recipients (vP > vS).

We now turn our attention to social behavior that is conditional on the actor's quality. Let us begin by considering that only high-quality juveniles express the behavior. We find that the potential for helping is always nonnegative (AH|H,T ≥ 0 and AH|H,F ≥ 0). In addition, reproductive asymmetry (s > 0) increases the potential for helping (AH|H,F > AF and AH|H,T > AT; Figs. 2E, 3E, Tables 2, 3). The reproductive value of primary recipients is greater than that of secondary recipients (vP > vS) whereas that of the actor is equal to that of primary recipients (vA = vP). Thus, although there is a positive impact upon the potential for helping in relation to that of the reference model, the potential for conditional helping by high-quality juveniles is less than the potential for helping that is unconditional on the actor's quality (AH|H,F < AB|H,F and AH|H,T < AB|H,T).

We now consider that only low-quality juveniles express the behavior. We find that the potential for helping is always nonnegative (AL|H,F ≥ 0 and AL|H,T ≥ 0). In addition, reproductive asymmetry (s > 0) increases the potential for helping (AL|H,F > AF and AL|H,T > AT; Figs. 2H, 3H, Tables 2, 3). The reproductive value of primary recipients is greater than that of secondary recipients (vP > vS). Moreover, the reproductive value of secondary recipients is always greater than that of the actor (vS > vA). This drives the increase in potential for helping by low-quality juveniles. The life-for-life relatedness of secondary recipients is greater than that of the actor (ρS ≥ 1) when local competition is high (low m or high a), reproductive asymmetry is high (high s), and frequency of high-quality juveniles is high (high p). This promotes the evolution of unconstrained helping, whereby actors are favored to invest all of their resources into helping (AL|H,F = ∞ and AL|H,T = ∞; Dawkins’ Runt region in Figures 2H, 2H).

Low-quality recipients

Here, we consider that individuals can discriminate the quality of recipients, and that low-quality individuals are the sole primary recipients of their social actions. We begin by considering behavior expressed independently of actor's quality. We find that there is both potential for helping and harming (AB|L,F > 0 or AB|L,F < 0 and AB|L,T > 0 or AB|L,T < 0). In addition, we also find that, for a wide range of model parameters, reproductive asymmetry (s > 0) decreases the potential for helping (AB|L,F < AF and generally AB|L,T < AT; Figs. 2C, 3C, Tables 2, 3). This occurs because the reproductive value of primary recipients is less than that of secondary recipients (vP < vS), and the reproductive value of the actor is equal to that of secondary recipients (vA = vS). However, in the island model, if high-quality juveniles are rare (low p) and migration rate is high (high m), reproductive asymmetry may increase the potential for helping (AB|L,T > AT). This occurs because relatedness of actors to primary recipients is high whereas relatedness to secondary recipients is low. This asymmetry in relatedness offsets the asymmetry in reproductive value.

We now turn our attention to social behavior that is conditional on actor quality. We first consider behavior that is expressed by high-quality juveniles only. We find that there is both potential for helping and harming (AH|L,F > 0 or AH|L,F < 0 and AH|L,T > 0 or AH|L,T < 0). In addition, reproductive asymmetry (s > 0) decreases the potential for helping (AH|L,F < AF and AH|L,T < AT; Figs. 2F, 3F, Tables 2, 3). We find that the reproductive value of primary recipients is less than that of secondary recipients (vP < vS) and that of secondary recipients is always less than that of the actor (vS < vA). This drives a potential for helping that is always less than that for helping behavior expressed independently of the actor's quality (AH|L,F < AB|L,F and AH|L,T < AB|L,T; if AH|L,F > 0 and AH|L,T > 0), and a potential for harming that is always less than that for harming behavior expressed independently of the actor's quality (AH|L,F > AB|L,F and AH|L,T > AB|L,T; if AH|L,F < 0 and AH|L,T < 0). Harming is most favored when local competition is high (high a or low m), reproductive asymmetry is high (high s), and frequency of high-quality juveniles is high (high p).

We now consider behavior that is expressed by low-quality juveniles only. We find that there is both potential for helping and harming (AL|L,F > 0 or AL|L,F < 0 and AL|L,T > 0 or AL|L,T < 0). We find that reproductive asymmetry (s > 0) typically decreases the potential for helping (AL|L,F < AF and in general AL|L,T < AT; Figs. 2I, 3I, Tables 2, 3). We find that the reproductive value of primary recipients is always less than that of secondary recipients (vP < vS). Low frequency of high-quality individuals (low p), high reproductive asymmetry (high s), and low local competition (low a or high m) favor high potential for helping. By contrast, high frequency of high-quality individuals (high p), and high local competition (high a or low m), favor high potential for harming. The life-for-life relatedness of secondary recipients is greater than or equal to that of the actor (ρS ≥ 1) for higher local competition (higher a or lower m), higher reproductive asymmetries (higher s), and higher frequency of high-quality individuals (higher p). This promotes the evolution of unconstrained helping, whereby actors are favored to invest all of their resources into harming behaviors (AL|H,F = −∞ and AL|H,T = −∞; Dawkins’ Runt region in Figs. 2I, 3I).

Discussion

HELPING AND HARMING

We have considered how the impact of within-group variation in individual quality drives the evolution of helping and harming behaviors in structured populations. We have found that the exact cancellation of relatedness and kin competition effects of dispersal, observed in the simplest models of population viscosity (Taylor 1992a, b), need no longer obtain. Specifically, the cancellation result requires that the actor, primary recipients, and secondary recipients all have the same (expected) reproductive value and, although this is true for unconditional behavior, it need not be true for behavior that is conditioned on actor and/or recipient quality. Moreover, we have also shown that low-quality individuals may even be favored to invest all of their resources into suicidal helping or harming behaviors. This clarifies that heterogeneity in individual quality may be an important factor in social evolution.

CONDITIONAL PHENOTYPES

We find that selection operating on social traits that are expressed irrespective of the actor's quality can greatly differ from selection operating on social traits that are conditional on the actor's quality. In particular, the potential for helping or harming unconditional on the actor's quality is always intermediate between the potentials for helping or harming conditional on the actor's quality. Moreover, although the potential for helping of high-quality individuals is always less than the potential for helping that is unconditional on the actor's quality, the potential for helping of low-quality individuals is always greater than the potential for helping that is unconditional on the actor's quality. This is because, all else being equal, a high-quality individual has more to lose in terms of direct genetic contribution to future generations (i.e., reproductive value; Fisher 1930), such that any investment in costly behavior has a larger negative impact on its fitness than the same costly investment by a low-quality individual. We suggest that these different selection pressures may provide the basis for the evolution of phenotypic divergence between high- and low-quality individuals, leading these to exhibit very different adaptive phenotypes.

A large number of social species exhibit conditional phenotypes within groups, whereby individuals exhibit differences in morphology and/or behavior independently of their genotypes (Pardi 1948; Wilson 1971; Ross and Matthews 1991; Bourke and Franks 1995; Crozier and Pamilo 1996; Gross 1996; Brockmann 2001; Gadagkar 2001). In agreement with our predictions, there is evidence for helping being associated with low quality (i.e., poor prospects of direct fitness), and selfishness being associated with high quality (i.e., good prospects of direct fitness). For example, in hanuman langurs, older females exhibit traits associated with helping (e.g., group defense) whereas younger females exhibit traits associated with selfishness (e.g., harassment of older females). Hrdy and Hrdy (1976) suggest that this owes to differences in relative reproductive value: as older females have lower reproductive value than younger females, they stand to gain more, relative to younger females, from helping younger females than from investing in their own reproduction.

Another example is provided by several species of primitively eusocial wasps, where individuals in better nutritional status are more likely to adopt reproductive roles (Gadagkar et al. 1988, 1991; O'Donnell 1998; Keeping 2002; Hunt et al. 2007, 2010). The idea that individual condition influences social behavior is also present in the “subfertility hypothesis” (West 1967; West-Eberhard 1969, 1975; Craig 1983), which suggests that individuals with lower reproductive potential should have a higher tendency to become helpers. In our analysis, we have not specified the causes underlying differences in reproductive value. Depending on the specific biological system, these causes could involve multiple factors, such as differences in ovary development (Pardi 1948), infection status (Shykoff and Schmid-Hempel 1991; O'Donnell 1997), or timing of birth (Queller 1989, 1994).

QUALITY DISCRIMINATION

We find that selection operating on social traits that are unconditional on the primary recipients’ quality can greatly differ from selection operating in traits that are conditional on the primary recipients’ quality. In particular, we find that the potential for helping of traits that are not conditional on recipients’ quality is always intermediate between the potentials for helping of traits that are conditional on the recipients’ quality. Thus, if actors direct their actions toward high-quality recipients, the potential for helping is always greater than the potential for helping when actors do not discriminate recipients’ quality. By contrast, if actors direct their actions toward low-quality recipients, the potential for helping is always lower than the corresponding potential for helping when actors do not discriminate recipients’ quality. Furthermore, if the social behavior is directed toward low-quality recipients, harming behavior can be favored. These results suggest that natural selection may favor quality discrimination, as this may have important inclusive-fitness consequences to those involved in social interactions.

Previous work has already highlighted the significance of quality discrimination for the evolution of social traits (West-Eberhard 2003, ch. 25; Keller and Nonacs 1993). Several empirical studies have proposed a number of quality discrimination mechanisms. For example, female paper wasps can discriminate each others’ quality by assessing the number of laid eggs (Liebig et al. 2005) or by use of facial marks or patterns (Tibbetts and Dale 2004; Tibbetts 2006; Tibbetts and Curtis 2007; Cervo et al. 2008), and ponerine ants do so by assessing correlates of quality such as cuticular hydrocarbons (Liebig et al. 2000; D'Ettorre et al. 2004). In the context of social insects, workers monitor their queen's quality, and when the queen's quality starts to decline, workers may shift their behavior from helping to aggression, which can culminate in worker matricide (Forsyth 1980; Bourke 1994).

DAWKINS’ RUNT

If the differences in the reproductive value of high- and low-quality juveniles are sufficiently large, local competition may drive low-quality juveniles to invest all of their resources into helping. We term an individual that expresses such extreme altruistic behavior a “Dawkins’ Runt” (after Dawkins 1976, p. 130). This phenomenon has received some theoretical treatment (e.g., O'Connor 1978; Godfray and Harper 1990), but convincing empirical evidence is lacking. One of the factors that may explain its rarity among traditional organisms is that relatedness is often less than one, which may constrain the evolution of such extreme altruistic behavior. Moreover, a weak offspring may still be able to recover and derive high reproductive success as an adult. More generally, reproductive value should be an important factor mediating the evolution of family interactions.

Altruistic suicide seems to be more common in unicellular organisms, where recent studies have identified a number of mechanisms that are likely to be suicide programmes. Several authors have suggested that mechanisms of cell death have evolved as social traits (Lewis 2000; Longo et al. 2005; Buttner et al. 2006; Nedelcu et al. 2010; Reece et al. 2011). For example, in yeast, PCD is mostly expressed by senescent cells (Fabrizio et al. 2004; Herker et al. 2004). PCD, in these cases, may be favored not only because it alleviates local competition, but also because it enriches the environment with additional resources. In the protozoan parasites Leishmania, Trypanosoma cruzi, and Trypanosoma brucei, PCD has been suggested as a mechanism whereby the best cells are chosen to be transmitted to the next host (Debrabant and Nakhasi 2003; Seed and Wenk 2003). Our analysis suggests that local competition for resources may be key to generating the selection pressure for the suicide of low-quality cells.

More generally, we highlight that cooperation can be favored not only owing to an increase in group productivity, but also owing to an increase in average group quality, that is to say groups that produce fewer but higher-quality individuals may be at an evolutionary advantage in relation to those groups that produce more but lower-quality individuals. Moreover, our framework also predicts that any asymmetry in quality can be reinforced by the action of natural selection. Worse-off cells are selected to give up some of their survival, thereby becoming even more worse-off. This leads to a causal association between helping and survival or, in other words, between kin-selected traits and senescence (e.g., Bourke 2007; Ronce and Promislow 2010).

Ronce and Promislow (2010) used a kin selection model of limited dispersal to study the evolution of senescence. They showed that a mother of age x is selected to give up some of her survival if her expected reproductive value vx+1 is less than the probability of offspring's co-philopatry h(x) times their reproductive value v1 (vx+1 < h(x)v1; the condition (3.6) of Ronce and Promislow (2010)). If we consider our model for conditional social behavior, and if we assume that patch size is one (n = 1), and that the benefits are zero (B = 0), then we find that the selection gradient, as given by Hamilton's rule in inequality (3), is vA < hvS, which is true when the actor is a low-quality individual: vL < hvS; and which is equivalent to Ronce and Promislow's (2010) condition (3.6). Note also that this condition says implicitly that the life-for-life relatedness to secondary recipients must be larger than one (hvS/vL = ρS > 1), which is similar to our definition of the Dawkin's Runt region (ρS ≥ 1). Interestingly, empirical studies have suggested that PCD may be associated with benefits provided by the dying cells (i.e., B > 0; Herker et al. 2004; Durand et al. 2011). Overall, these findings and studies provide further evidence for an interaction between helping/harming behavior, kin competition and senescence that represents an interesting avenue for future research.

INDIVIDUAL QUALITY

Here we have focused on one component of individual quality that we defined as an individual's reproductive value (Fisher 1930; Grafen 2006), and which emerges as a weighting factor in Hamilton's rule (Hamilton 1972; Taylor 1990; Taylor and Frank 1996; Frank 1998). In our model, differences in reproductive value emerge because of differences in fecundity between high- and low-quality individuals. These differences in fecundity can result in turn from a number of underlying factors. For example, it has been suggested that ovarian development in paper wasps is positively correlated with fecundity (Pardi 1948). The reproductive value that derives from these traits, which can be said to be intrinsic to the individual, has been called “basal” or “solitary” reproductive value (West-Eberhard 2003, p. 451), or “inherent reproductive potential” (Röseler 1991, p. 334).

However, differences in reproductive value can arise for other reasons. For example, an individual can gain a reproductive advantage over group mates by suppressing the group mates’ reproduction (Vehrencamp 1983a, b). In these cases, differences in reproductive value emerge due to asymmetries in control over social interactions, and this has been called “social reproductive value” (West-Eberhard 2003, p. 451). Frank (1990, 1998) has analyzed natural selection of social traits in terms of three measures of value: marginal value, relatedness, and reproductive value. The marginal value criterion states that candidate evolutionary end points are reached when the genetic benefits of extra investment in a fitness component are exactly cancelled by associated genetic costs in a different fitness component (Frank 1990). These marginal values are mediated by relatedness and reproductive value, and implicitly by costs and benefits.

In the context of our model, differences in social skills, which we call “social value,” are better captured by asymmetries in costs and benefits affecting either survival or fecundity (i.e., B's and C's; see Appendix S6). In the main text, we have assumed that social value is equal among all juveniles (i.e., CH = CL and BHH = BHL = BLL = BLH), thus juveniles with high reproductive value are selected to invest less in helping than juveniles with low reproductive value. However, this prediction may be reversed if we also allow differences in social value. For example, juveniles with higher reproductive value may be selected to invest more into helping if they also have higher social value (e.g., suffer a lower cost from expressing helping behaviors, CH < CL; see Appendix S6). In summary, our conceptual framework divides individual quality into reproductive value and social value, both of which interact to mediate selection acting on social traits. Under this conceptual framework, asymmetries in social value may offset asymmetries in reproductive value such that individual quality may be more-or-less uniform among group members, and therefore marked differences among individuals need not lead to differences in social behavior (see Appendix S6).

SOCIAL AMOEBAE

The cellular slime mould Dictyostelium discoideum has a peculiar life cycle: when feeding and dividing it lives a relatively solitary life; however, when local resources are depleted, they may initiate aggregation to form a multicellular fruiting body (reviewed by Bonner 2009; Queller et al. 2003). After aggregation, cells either differentiate into stalk cells, dying in the process, or spore cells, which will ultimately disperse to more favorable environments. Thus, stalk-forming cells have been viewed as altruists that benefit the spore-forming cells in the fruiting body (Strassmann et al. 2000).

Most of the research on this topic has been centered on how relatedness mediates the evolution of the altruistic trait (Strassmann et al. 2000; Kuzdzal-Fick et al. 2011). However, several studies have found that stalk-cell differentiation correlates with other factors, such as nutritional status (Leach et al. 1973; Castillo et al. 2011), cell size, or cell-cycle stage (Weijer et al. 1984; McDonald and Durston 1984). These factors do not appear to directly correlate with any characteristic that make cells more efficient stalk cells, and so it is unlikely that a tendency to differentiate as stalk is driven by asymmetries in social value. Rather, these factors may well be correlated with intrinsic differences in their reproductive value. That is, smaller or food-deprived cells may have lower reproductive value, and hence have less to lose by altruistically developing as stalk.

During development, cells produce a differentiation-inducing factor (DIF) that reinforces the predisposition of cells to differentiate into stalk cells (Shaulsky and Loomis 1996). Evidence suggests that the main producers of DIF are cells who already show some predisposition to become spore cells (Kay and Thompson 2001) as well as lower sensitivity to DIF (Thompson and Kay 2000). This has led several authors to interpreted DIF as a competitive trait, whereby fitter cells force weaker cells to differentiate into stalk cells (Atzmony et al. 1997). If this trait has evolved in the context of clonal groups, then standard social evolution theory struggles to explain this “competitive-like” trait. Our results suggest that, owing to reproductive value asymmetries, there is in fact potential for the evolution of competition-like traits, which can function as a mechanism for increasing average group quality. Low-quality cells should voluntarily give up their survival, thus sparing high-quality cells from paying the additional costs of inducing others to cooperate. However, constraints at different levels (e.g., lack of information about relative cell-quality or cells inability to act) may indeed favor the evolution of competition-like traits among genetically identical individuals. This principle may in fact be a general design mechanism of organisms as a way of increasing group average quality in different taxa. This idea is supported by evidence from different species, both unicellular (Khare and Shaulsky 2006) and multicellular (Khare and Shaulsky 2006; Sadras and Denison 2009; see also Livnat and Pippenger 2006).

SOCIAL WASPS

Our results predict that, all else being equal, individuals with lower prospects of direct fitness (i.e., lower reproductive value) should invest more in helping behavior, whereas individuals with higher prospects of direct fitness (i.e., higher reproductive value) should invest less in helping and behave more selfishly. Several species of social wasps are characterized by reproductive and social dominance hierarchies, where top-ranked females with queen-like physiology and/or behavior tend to monopolize reproduction, and where low-ranked females with worker-like physiology and/or behavior tend to have low fecundity (Pardi 1948; West 1967; West-Eberhard 1969; Röseler 1991). Group social dynamics seem to follow the dominance hierarchy, such that if the top-ranked female dies or is lost from the nest it is usually the female just below in rank that assumes the dominant role (Pardi 1948; West-Eberhard 1981; Jeanne 1991). Furthermore, females at the bottom of the hierarchy usually exhibit traits that involve high-risk tasks, whereas high-ranked females are more likely to adopt idle, low-risk behaviors (Gadagkar and Joshi 1983; West-Eberhard 1986; Gadagkar 2001).

Several authors have used verbal arguments based on asymmetries in reproductive value to explain the social structure of these social wasps (West-Eberhard 1981; Jeanne 1991; cf. Field et al. 2006). The basic ideas are: those individuals with lower reproductive value should try to derive indirect fitness benefits and therefore adopt riskier cooperative behaviors; those with higher reproductive value should invest less in riskier cooperative behaviors, and invest more in behavioral or physiological traits associated with their own reproduction; those with the best prospects of future direct fitness should invest their resources in reproductive traits and in other traits that allow them to keep their reproductive dominant role. Although our model does not incorporate all aspects of these groups’ biology (e.g., overlapping generations), it yields predictions about how individuals should behave according to their own reproductive value as well as that of their social partners.

ACKNOWLEDGMENTS

The authors thank J. Biernaskie, S. Estrela, S. Frank, A. Grafen, A. Kacelnik, O. Ronce, S. West, and an anonymous referee for helpful discussion and/or comments on previous versions of this article. AMMR is supported by PDBC-IGC and funded by FCT (SFRH/BD/33851/2009), and AG is supported by research fellowships from Balliol College and the Royal Society.

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