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- Materials and Methods
- Supporting Information
Heritable variation is essential for adaptive evolution in nature and for the genetic improvement of breeding populations (Falconer & Mackay, 1996). Although classical quantitative genetic models have made a major contribution to our understanding of inheritance and response to selection, they have neglected the fact that individuals may interact. Such social interactions among individuals are a fundamental property of life, occurring in virtually all taxa (Frank, 2007). With social interactions, the influence of an individual's genes may extend beyond the individual itself to affect other individuals with which it interacts. These effects are known as indirect genetic effects (IGEs), and occur when the genotype of an individual influences the phenotype of another (Griffing, 1977; Moore et al., 1997; Wolf et al., 1998; Muir, 2005; Bijma, 2011). Maternal genetic effects are a special case of IGEs occurring across generations, where the genotype of the mother affects the trait values of her offspring (e.g. Galloway et al., 2009).
IGEs change conceptually the inheritance of trait values and response to selection (Griffing, 1977; Moore et al., 1997; Bijma, 2011). IGEs can, for example, reverse the direction of response to selection, increase heritable variation to levels exceeding the phenotypic variance among individuals, and fully remove heritable variance despite a considerable ordinary (i.e. direct) heritability (Griffing, 1977; Bijma, 2011). Therefore, models incorporating IGEs are essential to study the genetic basis of traits affected by interactions among individuals (Muir, 2005; Costa e Silva & Kerr, 2012), to understand the theory of kin and multilevel selection (Bijma & Wade, 2008), to address the evolution of fitness (Bijma, 2010a; Wolf & Moore, 2010) and, when involving different species, are fundamental to the field of community genetics (Whitham et al., 2006).
Interactions among individuals can generally be defined as being either cooperative or competitive. Depending on the target trait, IGEs arising from interactions among conspecifics may lead to positive (heritable cooperation) or negative (heritable competition) covariances between the direct and indirect effects of an individual's genes. This covariance is a key determinant of the impact of IGEs on heritable variation and the potential response to selection. A positive covariance increases heritable variation and potential response to selection, whereas a negative correlation decreases both (Bijma, 2011).
Although little is known about the direct–indirect genetic covariance, ecological considerations suggest that the sign of the covariance may differ among traits. In plants, root growth and structure may affect the resource pool shared by neighbouring plants (Casper & Jackson, 1997), so that competition for resource utilization may lead to a negative covariance between direct and indirect genetic effects (Griffing, 1989; Mutic & Wolf, 2007). Moreover, plant size itself can also have a direct influence on competitive ability (Schwinning & Weiner, 1998), which may impact negatively on traits of neighbouring plants. Yet, there are several biotic and abiotic factors that can change competitive relationships in plants and may lead to positive neighbour effects (Callaway & Walker, 1997). In this sense, cooperative interactions occurring through microbial colonization (Wilson et al., 2006) or competition for light (Botto & Smith, 2002) are examples of how positive covariances between direct and indirect genetic effects may arise in plants (Mutic & Wolf, 2007; Wolf et al., 2011). However, a positive covariance may also occur with adverse interactions. In the case of pathogens (or pests), prevalence in a population depends upon the disease susceptibility of a host individual as well as host infectivity, which reflects the propensity for disease transmission between interacting individuals (Lipschutz-Powell et al., 2012). A positive covariance between direct and indirect effects may thus result in genetically susceptible hosts having an adverse effect through increasing the infection risk for neighbouring individuals.
In animals, there is growing evidence that a wide range of species exhibit significant IGEs, as a result of cooperative or competitive interactions among conspecifics (e.g. Muir, 2005; Bijma et al., 2007a,b; Bergsma et al., 2008; Wilson et al., 2009, 2011; Ellen et al., 2010). Empirical studies have also shown a genetic basis for traits involved in interactions among plants (Griffing, 1989; Astles et al., 2005; Mutic & Wolf, 2007; Wolf et al., 2011; File et al., 2012). In particular, recent work with Arabidopsis thaliana has demonstrated a complex genetic basis for intraspecific interactions based on size-, developmental- and fitness-related traits, with the relationship between direct and indirect genetic effects involving a combination of positive and negative effects through the different traits (Mutic & Wolf, 2007; Wolf et al., 2011). There is also evidence of kin recognition in plants, which may alter competitive interactions and trait expression among neighbours (Biedrzycki et al., 2010; Bhatt et al., 2011).
Theoretical work has shown that, when the covariance between direct and indirect genetic effects is negative, IGEs may cause a negative response to positive individual selection among unrelated individuals, which could limit the efficacy of individual selection for yield in agriculture (Griffing, 1977; Muir, 2005). Nevertheless, for traits affected by IGEs, selection among groups prevents the negative response to selection that can arise with individual selection (Griffing, 1977; Bijma & Wade, 2008). Simulated data under mating designs and plot configurations commonly used in forest genetic trials indicated that a negative selection response can indeed result if competition at the genetic level is present but selection is based on direct genetic effects only (Costa e Silva & Kerr, 2012). This suggests that classical breeding programmes ignoring IGEs, as currently used in forest tree breeding, may lead to little or even negative response to selection, because selection may result in increased competition among trees.
However, there are few empirical studies quantifying IGEs in tree species. Although estimates of genetic (co)variance components attributable to competitive additive effects have been reported for growth traits (Resende et al., 2005; Cappa & Cantet, 2008), empirical evidence of IGEs is lacking for other traits such as infectious diseases. Moreover, to our knowledge, there are no experimental studies in tree species quantifying the impact of IGEs on the total heritable variance that determines the potential for a population to respond to selection (Bijma, 2011). As argued above, the magnitude of IGEs and the correlation between direct and indirect genetic effects may depend on the trait of interest. For classical heritabilities there is a clear relationship with the trait, where morphological traits usually show rather high values, while traits related to fitness show low values (Falconer & Mackay, 1996). It is unclear at present whether similar patterns exist for IGEs. This information will be needed to optimize artificial selection schemes for genetic improvement of tree species, as well as to better understand the evolution of trees in natural populations.
Here we quantify the direct and indirect additive genetic effects on growth and disease susceptibility traits in a planted forest of Eucalyptus globulus. In particular, we test the hypotheses that fast-growing genotypes will have a significant indirect genetic effect in suppressing the growth of their neighbours, and that disease-susceptible genotypes will increase the disease infection of their neighbours. We then assess the extent to which interactions among neighbours affect the potential of growth and disease susceptibility traits to respond to selection.
- Top of page
- Materials and Methods
- Supporting Information
Model comparison clearly demonstrated significant IGEs for both traits (Table 2). As indicated by the AIC, including both indirect genetic and residual autocorrelation effects as in the full model (Model 4) fitted the data better than models with either of these effects alone. In addition, for both traits, the full model resulted in a highly significant (P < 0.001) improvement in log-likelihood over the reduced Model 3 (i.e. the second best model based on ΔAIC; Table 2), supporting the presence of significant indirect genetic (co)variances, and their higher relative importance for DBH at age 4 yr.
Table 2. Model comparisona
|Model b||logL||No. of random parameters c||Likelihood-ratio tests d||ΔAIC e|
|Tested against||Test statistic (P value; df)|
|MLD (age 2 yr)|
|Model 1||−27753.34||11|| || ||156.96|
|Model 2||−27715.02||13||Model 1||76.64 (P < 0.001; 2 df)||84.32|
|Model 3 f||−27682.04||14||Model 1||142.60 (P < 0.001; 3 df)||20.36|
|Model 4||−27669.86||16||Model 3||24.36 (P < 0.001; 2 df)||0|
|DBH (age 2 yr)|
|Model 1||−29058.70||10|| || ||250.22|
|Model 2||−29039.71||12||Model 1||37.98 (P < 0.001; 2 df)||216.24|
|Model 3 g||−28947.02||14||Model 1||223.36 (P < 0.001; 4 df)||34.86|
|Model 4||−28927.59||16||Model 3||38.86 (P < 0.001; 2 df)||0|
|DBH (age 4 yr)|
|Model 1||−31994.38||10|| || ||501.48|
|Model 2||−31914.72||12||Model 1||159.32 (P < 0.001; 2 df)||346.16|
|Model 3 g||−31781.45||14||Model 1||425.86 (P < 0.001; 4 df)||83.62|
|Model 4||−31737.64||16||Model 3||87.62 (P < 0.001; 2 df)||0|
Under the full model, LR tests showed that both direct () and indirect () variances were significant at the 5% level (Table 3). While was marginally significant (i.e. P = 0.05) for MLD and DBH at age 2 yr, highly significant (P ≤ 0.001) estimates were detected in for all traits and ages, and in for DBH at age 4 yr (Table 3). With respect to phenotypic variance, the relative contribution of IGEs vs direct genetic effects is reflected by the ratio . This ratio was 2% and 6% for MLD and DBH at age 2 yr, respectively, but increased to 15% for DBH at age 4 yr, suggesting increasing interactions among individuals over time for DBH. The estimated genetic correlation between direct and indirect additive effects () was always highly significant (P < 0.001; Table 3). Absolute values of were high, and positive for MLD () but negative for DBH ( ≈ −0.9). Thus, for MLD, the positive indicates that trees that are genetically more prone to be infected are also more liable to infect other trees. For DBH, however, the negative indicates competition, where an individual with a positive heritable effect on its own growth has, on average, a negative heritable effect on the growth of its neighbours. In particular, for DBH at age 4 yr, moderate differences among individuals in IGEs (as indicated by the magnitude of ) coupled with a high negative value indicate strong heritable competition. Further results concerning estimates of other variance components and autocorrelation parameters are described in Notes S1 and S2, respectively. Of particular relevance was also the detection of competition effects at the nongenetic (i.e. residual) level for DBH (see Notes S2).
The contrasting effects of IGEs on heritable variance in MLD vs DBH originated from opposing genetic correlations between direct and indirect genetic effects. For MLD, the direct–indirect genetic correlation was strongly positive. Consequently, the ratio (TBV )/ was 0.67, which is substantially greater than ordinary (direct) heritability (0.39; Table 4). For DBH, the direct–indirect genetic correlation was strongly negative. Consequently, the ratio (TBV )/ was only 0.08 at age 2 yr and 0.05 at age 4 yr, while ordinary heritability varied from 0.33 to 0.37 (Table 4). Thus, for a trait expressing strong heritable competition, such as DBH, interactions among individuals may decrease the total heritable variation almost to zero, leaving little potential for response to selection. The direct–indirect genetic covariance contributed more to (TBV ) in both traits than the indirect genetic variance, a result that mirrors the strong direct–indirect genetic correlation estimates in Table 3. For DBH, the contribution of the direct–indirect genetic covariance even exceeded (in absolute value) the contribution of direct genetic effects to heritable variance.
Substitution of the estimated (co)variances in the expressions for expected responses to mass selection (see Methods S5) yielded the following results for MLD: . Thus, for MLD, 50% of the selection differential (S) is translated into response, response is positive for both direct and indirect effects, and direct effects contributed 78% of the total response. For DBH at age 4 yr, expected responses were: . Consequently, for DBH, only 4% of the selection differential is translated into response, response is positive for direct effects, but negative for indirect effects, and response in indirect effects equals −89% of the response in direct effects. Therefore, individual mass selection for DBH at age 4 yr will increase competition among trees, which annuls 89% of the direct response, leaving very little net response.