THE EVOLUTION OF SOCIAL INTERACTIONS CHANGES PREDICTIONS ABOUT INTERACTING PHENOTYPES

Authors

  • Erem Kazancıoğlu,

    1. Animal Ecology, Evolutionary Biology Centre, Uppsala University, Uppsala 752 36, Sweden
    2. E-mail: erem.kazancioglu@ebc.uu.se
    3. Department of Ecology and Evolutionary Biology, Yale University, New Haven, Connecticut 06520-8106
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  • Hope Klug,

    1. Department of Biological and Environmental Sciences, University of Tennessee-Chattanooga, Chattanooga, Tennessee 37403
    2. Department of Ecology and Evolutionary Biology, Yale University, New Haven, Connecticut 06520-8106
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  • Suzanne H. Alonzo

    1. Department of Ecology and Evolutionary Biology, Yale University, New Haven, Connecticut 06520-8106
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Abstract

In many traits involved in social interactions, such as courtship and aggression, the phenotype is an outcome of interactions between individuals. Such traits whose expression in an individual is partly determined by the phenotype of its social partner are called “interacting phenotypes.” Quantitative genetic models suggested that interacting phenotypes can evolve much faster than nonsocial traits. Current models, however, consider the interaction between phenotypes of social partners as a fixed phenotypic response rule, represented by an interaction coefficient (ψ). Here, we extend existing theoretical models and incorporate the interaction coefficient as a trait that can evolve. We find that the evolution of the interaction coefficient can change qualitatively the predictions about the rate and direction of evolution of interacting phenotypes. We argue that it is crucial to determine whether and how the phenotypic response of an individual to its social partner can evolve to make accurate predictions about the evolution of traits involved in social interactions.

Social interactions among individuals are a common property of many biological systems. Consequently, the evolution of social behavior and traits that facilitate social interactions are of considerable interest to evolutionary studies (e.g. Hamilton 1964; Trivers 1985; Frank 1998; West et al. 2006). Many traits that are involved in social interactions are unique in the sense that their expression does not depend only on genetic properties of an individual, but also on the phenotype of other individuals in the population. For example, in many species that exhibit parental care, the amount of care provided by a parent to its offspring is found to depend on the amount of care provided by the other parent (Johnstone and Hinde 2006; Harrison et al. 2009). Similarly, parental investment is often determined by traits of the offspring, such as begging displays or chemical cues (Kölliker 2005; Kölliker et al. 2006; Mas et al. 2009). Furthermore, traits such as aggression and dominance are typically defined in a social context such that the behavior of an individual depends on the behavior of individuals with which it interacts (Moore et al. 1997; Wilson et al. 2009; McGlothlin et al. 2010; Wilson et al. 2011). As most phenotypes have a genetic component, an interaction between traits expressed in different individuals implies that genes in an individual affect the phenotype of its social partner, resulting in indirect genetic effects (IGEs; Moore et al. 1997; Wolf et al. 1998). IGEs connect the phenotype of an individual with the genes in its social environment, and broaden the scope in which genetic variation affects trait expression beyond classic quantitative genetics. The role of IGEs in trait expression raises the question of whether evolutionary dynamics of traits involved in social interactions are expected to be different than other traits.

Evolutionary dynamics of traits involved in social interactions have often been examined with a theoretical framework that extends classic quantitative genetic models by including IGEs (Moore et al. 1997). In this framework, where social traits are referred to as “interacting phenotypes,” the phenotype of an individual (“interacting individual”) constitutes a part of the environmental effect on the phenotype of another individual (“focal individual”). Accordingly, the environmental component of the phenotype of an individual is partitioned between a general environmental effect and the environment contributed by the phenotype of the interacting individual. As a result, the total environmental effect on a phenotype also has a genetic component, and therefore can evolve. The extent to which the phenotype of the interacting individual contributes to the phenotype of the focal individual is determined by the interaction coefficient ψ (Fig. 1). An analysis of the interacting phenotypes framework showed that traits that are involved in social interactions can evolve much more rapidly than other traits (Moore et al. 1997).

Figure 1.

In the interacting phenotypes framework, expression of a trait is partly determined by the phenotype of the social partner. The interaction between traits are mediated through the interaction coefficient ψ. For example: (A) a nonreciprocal interaction, where the expression of a trait (z1) is influenced by the value of another trait in the social partner (inline image); (B) a reciprocal interaction, where the expression of a trait (z1 or z2) is partly determined by the other trait in the social partner (inline image or inline image, respectively); (C) a reciprocal interaction, where a trait is influenced by the value of the same trait in the social partner.

The interacting phenotypes approach provides an intuitive theoretical framework that builds on classic quantitative genetics and allows us to examine the effect of social interactions among individuals on evolutionary dynamics. The original framework, however, treats the interaction between phenotypes as a response rule which is determined by the coefficient ψ and assumed to be fixed on both ecological and evolutionary time scales (Moore et al. 1997). The response of an individual’s phenotype to its social partner, however, is likely to be a trait that has underlying genetic variation, is potentially under strong selection, and, therefore, can evolve (Moore et al. 1997; McGlothlin and Brodie 2009; Chenoweth et al. 2010). For example, theoretical models on parental care showed that the response of a parent’s effort to the amount of care provided by the other parent is likely to be adaptive, and therefore, to be under selection (Johnstone and Hinde 2006). Furthermore, a recent study found empirical evidence for the evolution of the interaction coefficient ψ in the fruit fly Drosophila serrata, where it mediates the response of cuticular hydrocarbon (CHC) profiles of males to changes in the social environment (Chenoweth et al. 2010).

Despite the evidence suggesting that the degree of interactions between phenotypes is not evolutionarily static, but likely to evolve, it has not been investigated whether considering this additional complexity affects qualitatively the evolutionary dynamics of traits involved in social interactions. Here, we address this question by expanding the interacting phenotypes framework developed by Moore et al. (1997) and incorporating the interaction coefficient ψ not as a fixed population parameter, but as a trait that can evolve. We use this revised framework first to investigate the evolutionary dynamics of traits in a scenario where interacting phenotypes are under directional selection, but the interaction coefficient is evolutionarily static. We then allow the interaction coefficient to evolve and ask whether the rate and direction of evolutionary change are significantly altered. We show that the evolution of the interaction coefficient results in qualitatively different predictions about the evolutionary dynamics of traits, compared to the classic model. Our analyses suggest that detecting genetic variation and assessing the nature of selection on the interaction between phenotypes is an essential task to understand the evolution of traits involved in social interactions among individuals. We discuss this finding in relation to biological scenarios to which the interacting phenotypes framework is applicable.

The Model

In our model, we determine the trait value of an individual using two components. The first component is associated with the direct additive genetic value for the trait, which we term as “the baseline value.” The second component involves the IGEs through the interaction with the trait value of the social partner, mediated through the interaction coefficient, ψ. We call this second component “the indirect value.” Furthermore, although recent theoretical studies have investigated the coevolutionary dynamics of phenotypes that are involved in social interactions between related individuals (Kölliker et al. 2010; McGlothlin et al. 2010), we follow the original framework of Moore et al. (1997) and focus our analyses on the case where social partners are not related to one another.

We use our theoretical framework to focus on three biological scenarios that involve interacting phenotypes, following Moore et al. (1997).

CASE 1—INTERACTIONS WITH NONRECIPROCAL EFFECTS BETWEEN TWO TRAITS

First, we consider the interaction between two different traits in two individuals, where one trait is partly determined by the value of the other trait (Fig. 1A). For example, in many species, a female’s investment into the offspring, such as the allocation of resources into eggs or the amount of parental care, depends on the quality or attractiveness of the male the female has mated with (e.g., Burley 1986; De Lope and Møller 1993; Kolm 2001). The male trait, here the quality or attractiveness, however, is not influenced by the female investment into the offspring. Consequently, there is a nonreciprocal interaction between the female trait and the male trait.

We model this biological scenario by considering two traits with values z1 and z2, where z1 is partly determined by z2 through the interaction coefficient ψ12. Accordingly, ψ12 is a trait of the focal individual that determines its phenotypic response to the trait of its social partner. In all equations, we use a prime () to denote the trait expressed in a social partner. We write the trait value z1 as:

image(1)

In equation (1), we separate the value of trait z1 into two components. The first component, which we call the “baseline value”z1b, gives the part of the trait value that is independent of the phenotype of the social partner. Accordingly, the baseline value corresponds to the trait value of the focal individual in the absence of any information about the trait value of its social partner. The second component (i.e., inline image), which we call the “indirect value”, gives the part of the trait value that is determined by the phenotype of the social partner (inline image). We further assume that these two components of the phenotype are under separate selection gradients, inline image and inline image, respectively. Considering two separate selection gradients allows us to examine biological cases where the two components of the phenotype are under differential, and potentially opposing, forces of selection. For example, in species where individuals adjust their parental effort according to the effort of their social partners (Burley 1986; Gowaty 2008), changes in biological conditions such as the degree of information about the offspring condition (Johnstone and Hinde 2006; also see “Discussion”) or relative costs and benefits of phenotypic plasticity (e.g., DeWitt et al. 1998) could favor a shift in the degree or direction of an individual’s plastic response to its social partner, but not in its baseline effort.

The baseline value for trait 1 (z1b) is composed of an additive genetic value, a1b, and a general environmental effect, e1b:

image(2)

Because we are interested in modeling the interaction coefficient ψ12 as an evolving trait, we decompose the value of ψ12 into its additive genetic and environmental components:

image(3)

On the other hand, in this first case, the value for trait 2 is not influenced by the value of trait 1 (i.e., ψ21= 0), and is only determined by its baseline value, z2b, which is composed of the additive genetic value, a2b, and the environmental effect, e2b:

image(4)

Using equations (2 through 4), mean values for z1b, z2, and ψ12 are found as:

image(5)
image(6)
image(7)

where environmental effects are assumed to be random with a mean of zero (Moore et al. 1997). Using equation (1), the mean of z1 is found as:

image(8)

where we assume that social partners are not related and therefore inline image.

Following Moore et al. (1997) and making standard quantitative genetic assumptions (Falconer and Mackay 1996), the breeding values for the baseline value of trait 1, z1b, the interaction coeefficient, ψ12, and value of trait 2, z2, are:

image(9)
image(10)
image(11)

According to Price’s theorem, the change in mean value of a trait z is equal to the covariance between the breeding value and the fitness:

image(12)

Following Wolf et al. (1999), we give the relative fitness, w, as a regression equation of the phenotype of an individual:

image(13)

where α is the intercept, ε is the error term, and β1b, inline image, and β2 are the selection gradients for z1b, ψ12, and z2, respectively.

Using equations (12) and (13), the change in the mean baseline value of trait 1, inline image, per generation is:

image(14)

where G11, G12, and G are respective genetic variances and covariances.

Similarly, the change in the mean values of traits z2 and ψ12 is found as:

image(15)
image(16)

where G22, G12, G, G, and Gψψ are respective genetic variances and covariances.

Using equation (8), the mean phenotypic value of z1 in the next generation, denoted as inline image, can be written as:

image(17)

It is important to note that equation (17) has two new terms (i.e., inline image and inline image) in addition to the corresponding equation in Moore et al. (1997), which reflect the effect of the evolution of the interaction coefficient ψ on evolutionary dynamics. Subtracting (8) from (17), we find the per-generation change in the mean phenotypic value of the trait z1, inline image,

image(18)

which can be written in terms of variances, covariances, and selection gradients using equations (14) through (16).

Finally, because the value of trait 2, z2, does not depend on the phenotype of the social partner, the per-generation change in its mean value is given simply by inline image.

CASE 2—INTERACTIONS BETWEEN TWO DIFFERENT TRAITS WITH RECIPROCAL EFFECTS

Second, we consider the case with two different traits in two interacting individuals, where the value of a trait of an individual is affected by the value of the other trait in its social partner (Fig. 1B). For example, in some species with male parental care, such as sand gobies, females prefer to mate with males who exhibit greater care for previous clutches of eggs (Lindström et al. 2006). In such a system, the initial investment in eggs might depend on whether a female mates with a more or less-preferred male (e.g., Burley 1986; De Lope and Møller 1993; Kolm 2001), in this case with a male that provides more or less care. In turn, males might adjust the amount of care that they provide depending on the level of female investment, using cues such as clutch size (e.g., Sargent 1988; Ridgway 1989; Lindström 1998; Karino and Arai 2006) or egg size (e.g., Nussbaum and Schultz 1989). Consequently, there would be a reciprocal interaction between the amount of care provided by males and the amount of resources invested into eggs by females.

Adapting our theoretical framework to this biological scenario, the value of the first trait, z1, is given as:

image(19)

Similarly, the value of the second trait, z2, is:

image(20)

Incorporating (20) into (19), the value for the first trait is found as:

image(21)

Similarly, the value of the second trait is found as:

image(22)

Because we consider the interaction coefficients ψ12 and ψ21 as evolvable traits, it is mathematically complex to derive an analytical solution for the means of z1 and z2. Therefore, we approximate the values of inline image and inline image by simulating a population with a large number of individuals, calculating the trait values for each individual, and finding the mean values of z1 and z2 in this population. In these analyses, we use given values of inline image, inline image, inline image, inline image, and respective standard deviations to simulate values of z1b, z2b, ψ12, and ψ21 for each individual.

Similarly, we calculate the mean trait values in the next generation, inline image and inline image, by simulating a large population of individuals, but using new values for z1b, z2b, ψ12, and ψ21, such that:

image(23)
image(24)
image(25)
image(26)

where inline image, inline image, inline image, inline image are found as in equations (1416).

CASE 3—INTERACTIONS WITH RECIPROCAL EFFECTS ON A SINGLE TRAIT

Here, we consider a single trait whose value is partly determined by the value of the same trait in the social partner (Fig. 1C). For example, in many species that exhibit biparental care, the amount of care provided by each parent is affected by the the amount of care provided by the other parent (reviewed in Johnstone and Hinde 2006), resulting in a reciprocal interaction between the values of the same trait (i.e., parental care) in two social partners.

Under this biological scenario, the value of the trait, z1, in the focal individual is written as:

image(27)

Using the procedure we described above in Case 2, we approximate inline image numerically.

ANALYSES OF THE MODEL

In all analyses, we assumed that baseline trait values are under positive directional selection (i.e., inline image and inline image) and that starting values for interaction coefficients are positive (i.e., inline image, inline image, inline image), such that trait values are expected to increase when interaction coefficients are evolutionarily fixed. We implemented these conditions into our model by setting parameter values inline image and inline image. Assigning different positive starting values for interaction coefficients or changing the strength of the positive directional selection on baseline values did not alter the main conclusions that arise from our model. We used this modeling framework to investigate whether the evolution of ψ influences predictions about the rate and direction of evolutionary change in traits. To this end, we first analyzed the models under the assumption that interaction coefficients do not evolve. Accordingly, we set corresponding parameters for the per-generation change in mean interaction coefficients to 0 (i.e., inline image), and analyzed the coevolutionary dynamics of mean values of traits, inline image and inline image. We then considered interaction coefficients as evolving traits. Here, we assumed that the interaction coefficient is under directional selection to increase (inline image, inline image, inline image) or to decrease (inline image, inline image, inline image). We further assumed that the strength of selection on baseline trait values and interaction coefficients does not change over time (but see “Discussion” for cases where this is likely not to be the case). To implement these conditions, we set corresponding parameters for the per-generation change in mean interaction coefficients inline image or inline image, inline image or inline image, and inline image or inline image. Even though the magnitude of values of these parameters relative to the per-generation change in baseline trait values affected the degree of change in the coevolutionary dynamics, main conclusions from our analyses were not affected. Finally, in Cases 2 and 3, we estimated mean trait values by simulating 10,000 individuals, calculating trait values, and repeating this procedure 10,000 times. In all simulations, we used mean baseline values for traits (i.e., inline image and inline image), mean interaction coefficients (i.e., inline image, inline image and inline image) and corresponding standard deviations of 1.0 and 0.05 for baseline values and interaction coefficients, respectively. Simulating more individuals, performing a greater number of iterations, or using a different standard deviation for mean baseline values and interaction coefficients did not affect significantly the results of our analyses.

Results

CASE 1—INTERACTIONS WITH NONRECIPROCAL EFFECTS BETWEEN TWO TRAITS

Our analyses of the version of the model with two traits that interact nonreciprocally showed that the evolution of the interaction coefficient, here ψ12, affects the rate as well as the direction of predicted evolutionary change in traits. When ψ12 is evolutionarily fixed and has a positive value, our model predicts an increase in both trait values (Fig. 2, dashed lines). Similarly, both trait values are predicted to increase when there is selection to increase the value of ψ12 (Fig. 2, gray lines). Furthermore, we find that the rate of increase in the value of the trait that is affected by the interaction (i.e., trait 1) is enhanced by the increase in the value of the interaction coefficient (Fig. 2; dashed lines compared to corresponding gray lines). In contrast, however, we find that selection to decrease the value of the interaction coefficient can reverse this prediction, and result in a decrease in the value of the trait affected by the interaction (i.e., trait 1; Fig. 2, black lines).

Figure 2.

The evolution of the interaction coefficient, ψ12, changes qualitatively the predictions about the coevolutionary dynamics of two traits with nonreciprocal interaction (Case 1). In the figure legend, symbols +, , and 0 denote that the mean interaction coefficient is selected to increase (inline image), is selected to decrease (inline image), or does not evolve (inline image), respectively. Mean values of both traits are predicted to increase when the interaction coefficient does not evolve (dashed black line) or is selected to increase (gray line). When the interaction coefficient is selected to decrease, however, the mean value of one of the traits is predicted to decrease (solid black line). Graphs A through D illustrate the predictions of the model using various starting mean values for the two traits, through parameter values (A) inline image, inline image; (B) inline image; (C) inline image; (D) inline image, inline image. In all analyses, the starting mean value for the interaction coefficient is set inline image. Remaining parameter values are: inline image, inline image.

CASE 2—INTERACTIONS BETWEEN TWO DIFFERENT TRAITS WITH RECIPROCAL EFFECTS

Similar to the previous case, we found that the evolution of interaction coefficients, here ψ12 and ψ21, changes the rate and direction of evolutionary change in the values of two traits with reciprocal interactions. When interaction coefficients are evolutionarily fixed and have a positive value, our model predicts that both trait values would increase (Fig. 3, dashed lines). Similarly, we predict that both trait values would increase when there is selection to increase the values of both interaction coefficients (Fig. 3, light gray lines). As in the previous case, we also find that the evolution of interaction coefficients further enhances the predicted rate of increase in trait values (Fig. 3, dashed lines compared to corresponding light gray lines). In contrast, however, we find that selection to decrease one or both interaction coefficients can change qualitatively the predicted coevolutionary dynamics, and result in a decrease in the value of one or both traits, depending on parameter values (Fig. 3, gray, dark gray, and black lines).

Figure 3.

The evolution of interaction coefficients, ψ12 and ψ21, changes qualitatively the predictions about the coevolutionary dynamics of two traits with reciprocal interaction (Case 2). In the figure legend, symbols +, , and 0 denote that the corresponding mean interaction coefficient is selected to increase (inline image, inline image), is selected to decrease (inline image, inline image), or does not evolve (inline image, inline image), respectively. Mean values of both traits are predicted to increase when the interaction coefficients do not evolve (dashed black line) or both are selected to increase (light gray line). Otherwise, the model predicts a decrease in the mean value of one or both traits, depending on parameter values (gray, dark gray, and black lines). Graphs A through D illustrate the predictions of the model using various starting mean values for the two traits, through parameter values (A) inline image; (B) inline image, inline image; (C) inline image, inline image; (D) inline image. In all analyses, the starting mean value for the interaction coefficient is set inline image. Remaining parameter values are: inline image, inline image.

CASE 3—INTERACTIONS WITH RECIPROCAL EFFECTS ON A SINGLE TRAIT

Again, our analyses showed that the evolution of the interaction coefficient, here ψ11, changes qualitatively the predictions about the coevolutionary dynamics of the same trait in two individuals with reciprocal effects. When the interaction coefficient is evolutionarily fixed and has a positive value, we predict that the value of the trait would increase (Fig. 4, dashed line). Similarly, we predict an increase in the trait value when the value of the interaction coefficient is selected to increase (Fig. 4, gray line). Again, selection to increase the interaction coefficient further enhances the rate of increase in the trait value (Fig. 4, dashed lines compared to corresponding gray lines). Finally, in contrast to these predictions, selection to decrease the interaction coefficient can reverse the evolutionary dynamics and result in a decrease in trait value (Fig. 4, black lines).

Figure 4.

The evolution of the interaction coefficient, ψ11, changes qualitatively the predictions about the evolutionary dynamics of a trait expressed in two social partners with reciprocal interaction (Case 3). In the figure legend, symbols +, , and 0 denote that the interaction coefficient is selected to increase (inline image), is selected to decrease (inline image), or does not evolve (inline image), respectively. The mean value of the trait is predicted to increase when the interaction coefficient does not evolve (dashed black line) or is selected to increase (light gray line). When the interaction coefficient is selected to decrease, however, the mean value of the trait is predicted to decrease (solid black line). Graphs A and B illustrate the predictions of the model using different starting mean value for the traits, through parameter values (A) inline image; (B) inline image. In all analyses, the starting mean value for the interaction coefficient is set inline image. Remaining parameter values are: inline image.

Discussion

The expression of many traits that are involved in social interactions are determined not only by genetic properties of an individual, but also by the phenotype of other individuals in its social environment. These so-called “interacting phenotypes” are predicted to evolve much faster than traits whose expression are not influenced by social interactions (Moore et al. 1997). In theoretical models of interacting phenotypes, the degree to which the expression of a trait in an individual depends on the phenotype of its social partner is implemented through the interaction coefficient ψ. Here, we show that predictions about evolutionary dynamics of interacting phenotypes change qualitatively, if ψ is not a fixed population parameter but an evolving trait. For example, in all versions of our model (Cases 1 through 3), if an increase in trait values is predicted when the the interaction coefficient is evolutionarily static, this prediction can be reversed by allowing the interaction coefficient to evolve (Figs. 2 through 4). We also found that how the interaction coefficient ψ evolves determines whether there is a qualitative change in predictions about the evolutionary dynamics of interacting phenotypes. For example, in versions of our model where the interaction coefficient evolves and is selected to increase, we found that predicted evolutionary dynamics are quantitatively different from, but qualitatively similar to patterns observed when the interaction coefficient does not evolve (Figs. 2 through 4). In contrast, however, we found that, all else being equal, selection to decrease the interaction coefficient reverses this prediction, leading to qualitatively different patterns of trait evolution (Figs. 2 through 4). In sum, our results demonstrate that, to make accurate predictions about the evolution of traits involved in social interactions, it is essential to know not only whether interactions between phenotypes evolve, but also how they evolve.

Predictions that arise from our model call for further research focused on measuring the interaction coefficient ψ and investigating biological conditions that facilitate its evolution. The interaction coefficient ψ is similar to reaction norms in the sense that it mediates a plastic response to the social environment. Therefore, some biological factors that underlie the evolution of reaction norms, and phenotypic plasticity in general (Scheiner 1993; Pigliucci 2005), might also shape the evolution of ψ. For example, physiological costs that have been suggested to limit the degree of phenotypic plasticity might, under some circumstances, also select for a decrease in the interaction coefficient ψ. Unfortunately, our current empirical understanding of ψ and biological factors that underlie its evolution is vastly incomplete. Apart from a few studies that measured ψ in biological systems (Kent et al. 2008; Bleakley and Brodie 2009), so far there is only one study that demonstrated that ψ is not evolutionarily static, but is under selection and can evolve (Chenoweth et al. 2010). Using an experimental evolution approach, Chenoweth et al. (2010) raised populations of the fruit fly D. serrata for multiple generations under a treatment with different strengths of natural and sexual selection. Through assays of CHC phenotypes of males in two different contexts (solitary vs. social), Chenoweth et al. (2010) concluded that the interaction coefficient ψ, which mediates the response of CHC profiles to changes in the social environment, had evolved in response to the experimental treatment. Even though their analyses did not reveal the direction and strength of selection on ψ, the fact that only part of the experimental treatment led to the evolution of ψ suggests that biological conditions underlying natural and sexual selection determine the degree of selection on ψ. We predict that experimental evolution studies, such as the work of Chenoweth et al. (2010), will be crucial to reveal the nature of selection on the interaction coefficient ψ.

In addition to the empirical evidence, recent theoretical studies have highlighted several biological conditions that could result in the evolution of the interaction coefficient ψ. For example, in species exhibiting biparental care, a key evolutionary problem is how parents should respond to each other’s effort. In some species, parents are found to compensate for the reduction in the other parent’s level of care (analogous to ψ < 0), whereas in other species, parents exhibit a matching response to changes in their partner’s effort (analogous to ψ > 0). Using a game-theoretical model, Johnstone and Hinde (2006) suggested that these seemingly conflicting patterns of parental care can be reconciled by considering the relative effects of the marginal benefit of care and the amount of information parents have about the condition of the offspring and its need for care. Accordingly, if parents have only partial information about the condition of the offspring, one parent’s effort would indicate the offspring’s need for care and a matching response (ψ > 0) would be selected for. On the other hand, a more complete information about the offspring would favor a compensatory response (ψ < 0) in the level of parental care. Consequently, a change in the degree of information parents have about the condition of their offspring would favor a change in their parental effort and underlie the evolution of the interaction coefficient ψ.

A similar problem concerns how females should allocate their reproductive effort depending on male quality. It has been suggested that females should invest more resources to their offspring when they are mated with a high-quality male (“differential allocation hypothesis”, Burley 1986; analogous to ψ > 0). In contrast, others have argued that females that are mated with low-quality males should increase their parental effort to compensate for the negative effect of the quality of their partner (“reproductive compensation hypothesis”, Gowaty 2008; analogous to ψ < 0). Harris and Uller (2009) used a state-dependent model to demonstrate that the energetic state of females, likelihood and quality of future mating opportunities, and baseline offspring survivorship play a crucial role in determining the observed pattern of resource allocation. Therefore, changes in these biological conditions would favor a shift in the resource allocation strategy of females, mediated through the evolution of the interaction coefficient ψ.

In our analyses, we have modeled the evolution of the interaction coefficient ψ through a fixed selection coefficient. Although our model clearly demonstrates that the evolution of ψ can significantly affect evolutionary dynamics, it is important to note that selection on ψ is likely to be dynamic and to change over ecological and evolutionary time. For example, if biological conditions that underlie the selection on ψ (e.g., offspring survivorship) are partially determined by traits that constitute the social environment (e.g., level of parental effort), we would expect the selection on ψ to change as traits and, consequently, the social environment evolve. We argue that identifying and incorporating explicitly the biological conditions that underlie the evolution of ψ would greatly enhance our ability to predict long-term coevolutionary dynamics of interacting phenotypes. Furthermore, while we focused on phenotypes of social partners that are not related to one another, many traits are involved in social interactions between related individuals, such as parents and their offspring (reviewed in Kölliker 2005). Extended analyses of our theoretical framework would help elucidate if the evolution of the interaction coefficient ψ would also be expected to strongly affect the evolution of interacting phenotypes of related individuals.

The expression of many traits is partially determined by the phenotype of social partners. Quantitative genetic models predict that these “interacting phenotypes” would be expected to evolve much faster than nonsocial traits (Moore et al. 1997). Here, we showed that considering the evolution of the effect of an individual’s phenotype on its social partner (implemented through the interaction coefficient ψ) qualitatively changes predictions about the evolution of social traits. In addition to the existing body of theoretical research on the evolution of interacting phenotypes, further empirical studies will be critical to identify biological processes that underlie the evolution of ψ, which, our model shows, has important consequences for the evolutionary dynamics of traits that are involved in, and are influenced by, social interactions.

Associate Editor: S. West

ACKNOWLEDGMENTS

We thank the Associate Editor, J. W. McGlothlin, and M. Kölliker for their constructive and helpful suggestions. This research was supported by NSF grants EF-0827504 and IOS-0950472 to S. H. A.

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