Genetic control of interactions among individuals: contrasting outcomes of indirect genetic effects arising from neighbour disease infection and competition in a forest tree


Author for correspondence:

João Costa e Silva

Tel: +351 213653130



  • Indirect genetic effects (IGEs) are heritable effects of individuals on trait values of their conspecifics. IGEs may substantially affect response to selection, but empirical studies on IGEs are sparse and their magnitude and correlation with direct genetic effects are largely unknown in plants.
  • Here we used linear mixed models to estimate genetic (co)variances attributable to direct and indirect effects for growth and foliar disease damage in a large pedigreed population of Eucalyptus globulus.
  • We found significant IGEs for growth and disease damage, which increased with age for growth. The correlation between direct and indirect genetic effects was highly negative for growth, but highly positive for disease damage, consistent with neighbour competition and infection, respectively. IGEs increased heritable variation by 71% for disease damage, but reduced heritable variation by 85% for growth, leaving nonsignificant heritable variation for later age growth. Thus, IGEs are likely to prevent response to selection in growth, despite a considerable ordinary heritability.
  • IGEs change our perspective on the genetic architecture and potential response to selection. Depending on the correlation between direct and indirect genetic effects, IGEs may enhance or diminish the response to natural or artificial selection compared with that predicted from ordinary heritability.


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.

Materials and Methods

Study species

Eucalyptus globulus Labill. is a foundation species of lowland forests of south-eastern Australia, and is widely planted for pulpwood production in temperate regions of the world. Numerous studies have shown that substantial genetic variation in many adaptive traits occurs across its native range (e.g. Dutkowski & Potts, 2012). Genetic variation in susceptibility to many pests and diseases has been reported (Milgate et al., 2005; Barbour et al., 2009), which can contribute to genetic variation in later age growth (Milgate et al., 2005). Mycosphaerella leaf disease (MLD) is one of the major foliar diseases of E. globulus (Mohammed et al., 2003; Freeman et al., 2008; Hunter et al., 2009). The most obvious symptoms of MLD are necrotic leaf spots or lesions that grow in size and can coalesce to form large blotches (Hunter et al., 2009). MLD is caused by fungi of the genus Teratosphaeria (previously Mycosphaerella; Crous et al., 2007), which infect eucalypts growing in native forests as well as plantations around the world (Mohammed et al., 2003; Hunter et al., 2009). Teratosphaeria nubillosa and Teratosphaeria cryptic are the main species usually reported as causing MLD in E. globulus (Mohammed et al., 2003; Hunter et al., 2009).

Plant material and crossing design

Forty-four first-generation E. globulus trees, selected on an index combining growth and wood density from base population progeny trials in Australia, were crossed using a diallel mating design. The base population parents of the selected first-generation trees belonged to three races (Furneaux, Otways and Strzelecki ranges). Self crosses in the diallel were not undertaken. The diallel scheme was unbalanced, with successful crosses comprising a total of 28 female parents, 44 male parents and 363 full-sib families. Reciprocal matings in the diallel involved 117 of these full-sib families. Additional crosses, performed using a sparse factorial mating design, were included in the trial to create pedigree links with previous breeding and research trials. There were 67 female parents and 71 male parents represented in this factorial, contributing 207 full-sib families. In most cases, the parents used in the crossing were also selected from first-generation breeding trials, and the respective base population parents belonged to six races (Furneaux, King Island, Otways, Strzelecki, Northeast and Southeast Tasmania). There were 30 individuals that were used as parents in both mating designs, although there were no full-sib families in common. All base population parents were assumed to be unrelated and non-inbred as a result of widely spaced sampling.

Field experiment and trait measurements

Progenies were planted in a field trial at Manjimup (Western Australia) (latitude 34°13′34″S, longitude 116°8′37″E). The trial was on ex-agricultural land, with trees planted in a rectangular array with a spacing of 2.125 m within rows and 5.0 m across rows.

The trial was designed as a resolvable row-column design (John et al., 1997) with 15 replicates of 35 rows and 18 columns each. Full-sib families were randomized within each replicate, and one seedling per full-sib family was generally planted as a single-tree plot within each replicate. There were 9450 individuals originally planted. In terms of the number of full-sib families and individuals, this field trial is among the largest eucalypt trials subjected to quantitative genetic analysis to date and, according to results obtained by Bijma (2010b), our power for detecting indirect genetic effects was expected to be high.

The trial was infected by an outbreak of MLD in the second year of growth while most trees were still in the juvenile leaf stage. Lesion morphology and DNA (ITS 1 and 2) sequence suggested that the main species causing damage to the juvenile leaves was Teratosphaeria nubilosa (K. Taylor, pers. comm.). This species mainly infects juvenile foliage (Carnegie & Ades, 2002; Hunter et al., 2009) and, as the trees assessed were at the threshold of transition to adult foliage, the risk of infection by this species is expected to diminish rapidly with age. However, while the direct genetic correlation between growth and MLD damage in the present trial was insignificant at an early age (data not shown), significant negative direct genetic correlation have been reported between MLD damage and post-infection growth traits in a trial where the MLD infection was more severe (Milgate et al., 2005).

Each tree in the trial was assessed in December 2009 for the percentage of the juvenile foliage affected by MLD following the approach of Milgate et al. (2005). To quantify growth rate, over-bark diameter at breast height (DBH) was measured. Measurement ages from planting were 2 yr for MLD, and 2 and 4 yr for DBH (Table 1).

Table 1. Means of the Mycosphaerella leaf disease (MLD) and diameter at breast height (DBH) traits, overall percentage of survival, and averages for numbers of first-order neighbours of a focal tree, intensity of interaction factors and additive genetic relatedness within a neighbourhood, at ages 2 and 4 yr from planting in a Eucalyptus globulus field trial
 Age 2 yrAge 4 yr
  1. a

    MLD was not measured at age 4 yr.

  2. b

    The mean additive genetic relatedness among the various trees within a neighbourhood was similar, confirming randomization of families within replicates.

MLD (%)22.5 a
DBH (mm)98.4135.1
Survival (%)96.494.3
Total number of neighbours of a focal tree7.727.56
Number of same-row neighbours of a focal tree1.931.89
Number of same-column neighbours of a focal tree1.931.89
Number of diagonal neighbours of a focal tree3.863.78
Intensity of interaction factor for same-row neighbours0.5930.601
Intensity of interaction factor for same-column neighbours0.2520.256
Intensity of interaction factor for diagonal neighbours0.2320.235
Additive relationship among all trees in a neighbourhood b0.02330.0232
Additive relationship between a focal tree and its neighbours b0.02350.0234
Additive relationship between the neighbours of a focal tree b0.02320.0231

Data analysis

To quantify the contributions of direct and indirect genetic effects to trait variation, data were analysed using the following full linear mixed model:

display math(Eqn 1)

where y is a vector of individual tree observations for a given trait; b is a vector of fixed effects; ua is a vector of random additive genetic effects; us is a vector of random full-sib family effects; um is a vector of random maternal effects in the diallel cross; ur is a vector of random reciprocal effects in the diallel cross; uo is a vector of additional random effects; e is a vector of random residuals; X, Za , Zs , Zm , Zr and Zo are incidence matrices relating the observations to the fixed and random effects.

The vector of additive genetic effects ua contains two subvectors such that math formula with the incidence matrix being defined as math formula, where math formula and math formula are vectors for direct and indirect additive genetic effects, respectively, math formula relates the record of the focal individual to its own direct additive genetic effect, and math formula relates the record of a focal individual to the indirect additive genetic effects of its nearest neighbours. In math formula, the row for the observed record of a focal individual contains intensity of interaction factors in the columns that match the indirect effects in math formula belonging to its neighbours, and zero values otherwise. Intensity of interaction factors were used to account for the differential intensity of indirect effects that neighbours may exert on the phenotype of a focal tree as a result of differences in inter-tree distance and in the number of neighbours (Cappa & Cantet, 2008; for further details, see Supporting Information Methods S1). The general formulae derived by Costa e Silva & Kerr (2012) were used to compute intensity of interaction factors for row, column and diagonal neighbours.

For vector y, an arcsine transformation was used for MLD (i.e. sin−1(math formula)) to improve normality in the data, as the original distribution was slightly skewed. To avoid convergence problems which may occur when trait variances are very small, the transformed MLD data were then rescaled by multiplying the observations by 100.

Fixed effects in b comprised the overall mean, linear covariates in the row and/or column directions of the trial to accommodate global environmental trend (see next paragraph), and two conditional factors which accounted for additive differences among race effects within each of the two cross types. The vectors us , um and ur pertained also to conditional terms: us contained two subvectors corresponding to separate full-sib family effects for each cross type, and the effects in um and ur were allowed to be fitted for the diallel only. The design matrices X, Zs , Zm and Zr were specified in order to accommodate the conditioning required for the effects fitted. The family effects in us are expected to capture the specific combining ability (SCA; at both the intra- and inter-race levels) of the crosses, although us may confound both SCA and reciprocal effects in the factorial. As the female genotypes within the diallel were unrelated and unreplicated, it was not possible to separate the maternal term into genetic and environmental components. Thus, effects in um may be interpreted as maternal effects confounding genetic and environmental sources of variation.

When appropriate to account for global environmental trend (see Methods S3), we used the mixed model formulation proposed by Verbyla et al. (1999) to fit a smoothing spline in the row and/or column directions of the trial: this needed the inclusion of a slope (i.e. a linear covariate) in b and an associated subvector of random effects in uo. In addition, the vector uo included subvectors pertaining to the different terms associated with the experimental design of the trial, such as effects attributable to replicates, and rows and columns within replicates.

Under the mixed model defined in Eqn 1, the joint distribution of the random terms was assumed to be multivariate normal, with mean vector zero and a variance matrix defined as a direct sum of variance-covariance submatrices related to ua , us , um , ur , uo and e (for further details, see Methods S2). In particular, the variance-covariance submatrix for the random terms in ua was defined as:

display math(Eqn 2)

where math formula and math formula are direct and indirect additive genetic variances, respectively; math formula is the genetic covariance between direct and indirect additive effects; ⊗ denotes the Kronecker product operation; and A denotes the matrix of additive genetic relationship coefficients among all individuals (i.e. base population parents, first-generation parents and their progeny), allowing direct and indirect additive effects to be linked through individual genetic relationships within and across neighbourhoods. The math formula are the main parameters of interest in this study, as they quantify the magnitude of direct and indirect genetic effects on trait values, and the relationship between these effects.

The vector of random residuals e was partitioned into a subvector ξ, whose elements follow a spatially correlated process, and a subvector η, whose elements are pair-wise uncorrelated and distributed independently of ξ. The general form of the variance-covariance matrix for the effects in e was then defined as:

display math(Eqn 3)

where Σ is the correlation matrix for the spatially dependent process (conditional on the parameters in vector α) with the associated variance math formula; and math formula is the variance of the independent residuals. For Σ, separable spatially dependent processes were assumed in the row and column directions of the planting grid, and thus Σ was defined as (for data ordered as columns within rows):

display math(Eqn 4)

where αrow and αcol are vectors for row and column autocorrelation parameters, respectively. Modelling the residual covariance structure followed a sequential procedure using autoregressive models in Σ, as suggested by Gilmour et al. (1997), Stringer (2006) and Stringer et al. (2011) (for further details, see Methods S3).

In addition to the full model already described, the following three reduced models were also fitted.

  • Model 1, which does not account for interaction effects among neighbouring trees at the genetic level, nor does it consider a correlation structure for the residuals. Thus, the classical additive genetic effect was fitted, and the residual effects were assumed to be independently distributed.
  • Model 2, which accounts for interaction effects at the genetic level, but does not consider a correlation structure for the residuals. Thus, genetic effects were modelled as in the full model, but residuals as in Model 1.
  • Model 3, which fits a correlation structure for the residuals, but ignores interaction effects at the genetic level. Thus, genetic effects were modelled as in Model 1, but residuals as in the full model.

We undertook a sequential modelling approach, starting with the reduced models (following the order given above; see also Methods S3) and finalizing with the full model, which attempts to be the most complete in terms of incorporating sources of variation at the genetic and residual levels. All models were fitted with the ASReml software (Gilmour et al., 2009), using restricted maximum likelihood (REML) for the estimation of (co)variance parameters and their standard errors. Likelihood-ratio (LR) tests were performed for testing the significance of (co)variance parameter estimates and for comparing nested models. Reduced Models 2 and 3 are non-nested, and thus LR tests could not be used to compare these models. For comparing all models, the Akaike information criterion (AIC; Akaike, 1974) was computed for each model. Smaller values of AIC reflect a better model fit.

Heritable variation and response to individual mass selection

In the framework of IGEs, Bijma et al. (2007a) and Bijma (2011) demonstrated the distinction between the additive genetic component of phenotypic variance and the heritable variance that determines the potential of a population to respond to selection. The former relates to an individual's trait value, which depends on the genetic effects of multiple individuals (including the focal individual itself). The latter represents the total impact of an individual's genes on trait values in a population, which is known as the total breeding value (TBV), and is a genetic property of the focal individual.

The phenotypic variance (denoted by math formula) and the additive genetic component of the phenotypic variance (denoted by math formula) for the full model were derived as described in Methods S4. The total heritable effect of the jth individual's genes on trait values in a population equals (see also Costa e Silva & Kerr, 2012):

display math(Eqn 5)

where math formula, math formula and math formula denote the average number of row, column and diagonal neighbours of a focal individual, respectively; and math formula, math formula and math formula are the corresponding average intensity of interaction factors (Table 1, Methods S1). As the per generation genetic change in mean trait value equals the per generation change in mean TBV, it is the variance associated with TBV (denoted by Var(TBV )) rather than math formula that determines the potential of a population to respond to selection (Bijma, 2011). Thus, the heritable variance for response to selection is given by:

display math(Eqn 6)

For traits affected by IGEs, math formula does not impose an upper bound for Var(TBV ) (unlike math formula, which is limited by math formula; Bijma et al., 2007a; Bijma, 2011).

A comparison of math formula and Var(TBV ) shows that the impact of IGEs differs between the phenotypic variance and the heritable variance for response to selection. First, Var(TBV ) depends on the direct–indirect genetic covariance, whereas math formula does not with unrelated neighbours (Bijma, 2011). For example, a direct–indirect genetic correlation of –1 can reduce Var(TBV ) to zero, despite nonzero direct and indirect genetic variances. Secondly, compared with math formula, the contribution of IGEs to Var(TBV ) is increased by a factor math formula ≈ 2.52 = 6.25 (cf. Table 1), indicating that IGEs contribute much more to heritable variance for response than to phenotypic variance. To facilitate the interpretation of results, ratios of estimates of math formula or Var(TBV ) relative to the estimated math formula will be presented below.

The consequences of IGEs for response to selection can be illustrated for individual mass selection, where individuals with the highest trait values are selected as parents of the next generation. The derivations of equations for the expected response to individual mass selection when neighbours are unrelated are provided in Methods S5.


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 (< 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 blogLNo. of random parameters cLikelihood-ratio tests dΔAIC e
Tested againstTest statistic (P value; df)
  1. a

    Restricted maximum likelihood (REML) log-likelihood at model convergence (logL), number of random parameters, results from likelihood-ratio tests and Akaike information criterion (i.e. ΔAIC; see e below) for the different models fitted to the Mycosphaerella leaf disease (MLD) and diameter at breast height (DBH) traits, measured at ages 2 and 4 yr from planting in a Eucalyptus globulus field trial.

  2. b

    Models 1 to 3 are reduced models, and Model 4 is the full model (for details of the terms fitted in these models, see the Materials and Methods section, and Supporting Information Methods S2, S3).

  3. c

    The random parameters also included a cubic spline term in each of the row and column directions for MLD, and a cubic spline term in the column direction for DBH.

  4. d

    Rather than determining the correct theoretical asymptotic distribution of the likelihood-ratio test statistic for each model comparison, two-tailed likelihood-ratio tests were always used with the stated degrees of freedom (df). Thus, for all the examined model comparisons, the degrees of freedom were not adjusted to account for the fact that the hypothesis test involves also testing a variance component (besides correlation components), which is restricted to be greater than or equal to zero (Stram & Lee, 1994). Hence all the performed tests are conservative.

  5. e

    The Akaike information criterion (AIC) was computed for each model as −2logL + 2t, where logL is defined as above and t is the number of random terms (Akaike, 1974). Then, the AIC values were scaled to a minimum value of zero, which refers to the best fitting model for a given trait. Therefore, ΔAIC = AICM – AICbest, where AICM is the AIC for model M and AICbest is the lowest AIC value of all models fitted for a trait.

  6. f

    For MLD, a first-order autoregressive (AR1) model with separable AR1 processes in the row and column directions (AR1 x AR1) was used to fit the residual covariance structure in Model 3 (and kept in Model 4), as the equal-roots third-order autoregressive (EAR3) model was not found to be significantly ( 0.05) better than the AR1 in either of the two directions.

  7. g

    For DBH, the EAR3 was found to be significantly ( 0.05) better than the AR1 in the column direction, and thus the residual covariance structure in Model 3 (and kept in Model 4) was fitted according to a (separable) AR1 x EAR3 process (i.e. AR1 in the row direction and EAR3 in the column direction).

MLD (age 2 yr)
Model 1−27753.3411  156.96
Model 2−27715.0213Model 176.64 (< 0.001; 2 df)84.32
Model 3 f−27682.0414Model 1142.60 (< 0.001; 3 df)20.36
Model 4−27669.8616Model 324.36 (< 0.001; 2 df)0
DBH (age 2 yr)
Model 1−29058.7010  250.22
Model 2−29039.7112Model 137.98 (< 0.001; 2 df)216.24
Model 3 g−28947.0214Model 1223.36 (< 0.001; 4 df)34.86
Model 4−28927.5916Model 338.86 (< 0.001; 2 df)0
DBH (age 4 yr)
Model 1−31994.3810  501.48
Model 2−31914.7212Model 1159.32 (< 0.001; 2 df)346.16
Model 3 g−31781.4514Model 1425.86 (< 0.001; 4 df)83.62
Model 4−31737.6416Model 387.62 (< 0.001; 2 df)0

Under the full model, LR tests showed that both direct (math formula) and indirect (math formula) variances were significant at the 5% level (Table 3). While math formula was marginally significant (i.e. = 0.05) for MLD and DBH at age 2 yr, highly significant ( 0.001) estimates were detected in math formula for all traits and ages, and in math formula 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 math formula. 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 (math formula) was always highly significant (< 0.001; Table 3). Absolute values of math formula were high, and positive for MLD (math formula) but negative for DBH (math formula ≈ −0.9). Thus, for MLD, the positive math formula indicates that trees that are genetically more prone to be infected are also more liable to infect other trees. For DBH, however, the negative math formula 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 math formula) coupled with a high negative math formula 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).

Table 3. Estimates of (co)variance components and their standard errors obtained under the full model for the Mycosphaerella leaf disease (MLD) and diameter at breast height (DBH) traits, measured at ages 2 and 4 yr from planting in a Eucalyptus globulus field trial
Trait (age) math formula a math formula a math formula a math formula math formula math formula b math formula b math formula math formula math formula math formula math formula
  1. For the additive genetic components, results (ie. P-values) from likelihood-ratio (LR) tests are presented for variance math formula and correlation math formula parameters, respectively. math formula, direct additive genetic variance; math formula, indirect additive genetic variance; math formula, genetic correlation between direct and indirect additive effects; math formula, full-sib family variance in the diallel crosses; math formula, full-sib family variance in the factorial crosses; math formula, variance associated with maternal effects; math formula, variance associated with reciprocal effects; math formula, variance of the independent residuals; math formula, correlated residual variance associated with a spatially dependent process; math formula and math formula, autocorrelation parameters in the row and column directions.

  2. a

    One-tailed LR tests were applied for variance estimates (Stram & Lee, 1994), and two-tailed LR tests were applied for correlation estimates.

  3. b

    The variance estimates are based on the diallel crosses only.

  4. c

    The estimates refer to the (arcsine) transformed and rescaled observations for MLD.

  5. d

    For MLD, math formula pertain to a first-order autoregressive (AR1) model with separable AR1 processes in the row and column directions, as the equal-roots third-order autoregressive (EAR3) model was not previously (ie. under the reduced Model 3; see Table 2) found to be significantly better (at the 5% level) than the AR1 in either of the two directions.

  6. e

    For DBH, the math formula pertains to an AR1 process in the row direction, and math formula and math formula pertain to an EAR3 process in the column direction, as the EAR3 was found previously (ie. under the reduced Model 3; see Table 2) to be significantly better (at the 5% level) than the AR1 in the column direction.

MLD (2 yr)c73.34 (± 13.17) < 0.0011.51 (± 0.64) = 0.0500.80 (± 0.14) < 0.0011.60 (± 1.51)6.26 (± 2.17)0.33 (± 0.67)4.51 (± 1.79)104.08 (± 6.79)33.38 (± 5.25)0.49 (± 0.07)0.98 (± 0.004) d
DBH (2 yr)78.67 (± 15.01) < 0.0015.05 (± 1.45) = 0.050−0.91 (± 0.07) < 0.00116.76 (± 2.83)16.47 (± 4.0)2.42 (± 1.37)1.04 (± 2.12)138.15 (± 8.50)26.52 (± 3.47)0.74 (± 0.04)0.93 (± 0.01)−0.20 (± 0.13)e
DBH (4 yr)190.89 (± 28.36) < 0.00128.22 (± 5.33) = 0.001−0.93 (± 0.04) < 0.00120.60 (± 5.66)25.46 (± 7.15)1.24 (± 1.75)6.51 (± 5.17)275.37 (± 16.62)91.04 (± 9.37)0.76 (± 0.03)0.91 (± 0.01)−0.20 (± 0.08)e

While small compared with direct genetic effects, IGEs had a substantial impact on the heritable variation determining potential response to selection (Var(TBV )). IGEs contributed substantially more to math formula(TBV ) than to math formula, with the contributions to math formula(TBV ) for DBH being greater than those for MLD (Table 4). For MLD, IGEs increased heritable variance by 71% compared with the ordinary (direct) additive genetic variance (125.6 vs 73.3; Table 4). By contrast, IGEs decreased heritable variance for DBH. At age 2 yr, IGEs decreased heritable variance in DBH by 75% (19.5 vs 78.7; Table 4), but by age 4 yr, IGEs decreased heritable variance by as much as 85% (27.7 vs 190.9; Table 4) to a level at which math formula(TBV ) did not differ significantly from zero, as suggested by its estimated standard error.

Table 4. Estimates of biological parameters and their standard errors for the Mycosphaerella leaf disease (MLD) and diameter at breast height (DBH) traits, measured at ages 2 and 4 yr from planting in a Eucalyptus globulus field trial
Estimated parametersMLD (age 2 yr)aDBH (age 2 yr)DBH (age 4 yr)
TotalRelative to math formula bTotalRelative to math formula bTotalRelative to math formula b
  1. a

    The estimates refer to the (arcsine) transformed and rescaled observations for MLD.

  2. b

    Taylor series expansion was used to obtain approximate standard errors for estimated variance ratios (Lynch & Walsh, 1998).

  3. c

    See Methods S4 for details of the calculation of the phenotypic variance (Eqn S4_2).

  4. d

    See Methods S4 for the definition of the terms contributing to the heritable component of phenotypic variance (Eqns S4_3 to S4_6); in particular, math formula.

  5. e

    For details of the definition of the terms contributing to the heritable variance, see the subsection ‘Heritable variation and response to individual mass selection’ of the Materials and Methods section (Eqn 6).

Phenotypic variance (math formula)c186.61 (± 7.32)239.96 (± 8.06)517.68 (± 16.05)
Heritable component of math formula76.01 (± 13.34)0.407 (± 0.057)82.24 (± 15.07)0.343 (± 0.053)214.79 (± 28.77)0.415 (± 0.045)
Contributions to math formula due to all the additive genetic effectsd
math formula 73.34 (± 13.17)0.393 (± 0.057)78.67 (± 15.01)0.328 (± 0.053)190.89 (± 28.37)0.369 (± 0.046)
2math formula0.98 (± 0.22)0.005 (± 0.001)−2.10 (± 0.39)−0.009 (± 0.001)−7.73 (± 0.97)−0.015 (± 0.002)
math formula 1.69 (± 0.71)0.009 (± 0.004)5.67 (± 1.63)0.024 (± 0.007)31.63 (± 5.98)0.061 (± 0.011)
Heritable variance (math formula(TBV))125.58 (± 21.55)0.672 (± 0.094)19.52 (± 8.97)0.081 (± 0.036)27.74 (± 16.50)0.054 (± 0.031)
Contributions to math formula(TBV) due to indirect genetic effectse
2(math formula42.63 (± 9.69)0.228 (± 0.047)−91.36 (± 16.79)−0.381 (± 0.063)−340.65 (± 42.60)−0.658 (± 0.070)
math formula 9.61 (± 4.05)0.051 (± 0.021)32.21 (± 9.23)0.134 (± 0.038)177.50 (± 33.53)0.343 (± 0.062)

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 math formula(TBV )/math formula 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 math formula(TBV )/math formula 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 math formula(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: math formula. 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: math formula. 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.


This work demonstrates that interactions among E. globulus trees have a substantial impact on individual trait values, and have both a genetic and a nongenetic component. This means that neighbour genes are part of the environment in E. globulus, and that this environment can evolve through selection (Wolf et al., 1998).

The magnitude of IGEs

IGEs change our perspective on the genetic architecture and heritable variance available for selection (Bijma, 2011). Because estimates of the indirect genetic variance are often considerably smaller than those of the direct genetic variance, the impact of IGEs on the total heritable variance available for selection (Var(TBV )) is often overlooked. Our results, however, demonstrate that tree interactions may substantially alter a population's ability to respond to selection, even when impacts on phenotypic variance are small. While our indirect genetic variances were only 2–15% of the corresponding direct genetic variances, the impact of IGEs on heritable variance was up to 85% compared with the direct genetic variance (Table 4), most of which was attributable to the direct–indirect covariance. This illustrates that Var(TBV ) may differ markedly from the heritable component of phenotypic variance. This occurs because an individual's IGE is spread to all its neighbours, so that its full IGE does not appear in a single phenotype, whereas it does appear in the TBV (Bijma, 2011). Indeed, the impact of IGEs on all neighbours is reflected by the factor math formula in Eqn 5, which represents an individual's total IGE on its neighbours. Hence, the interpretation of the magnitude of the IGEs will depend upon whether they are scaled by the intensity of interaction factors or not, which is important when comparing studies (e.g. compare Eqn 5 above to Eqn 6 in Bijma et al., 2007a.)

The benefit of kin selection

Relatedness among interacting individuals is a key factor in response to selection in traits affected by IGEs. With IGEs, relatedness together with group size, total heritable variance and strength of selection determine the response (Agrawal et al., 2001; Donohue, 2003; Bijma et al., 2007a; Ellen et al., 2007; Bijma & Wade, 2008; McGlothlin et al., 2010; this statement ignores a potential dependence of IGEs on relatedness among neighbours, as discussed in the next paragraph). Relatedness among interacting individuals increases the utilization of heritable variation (Bijma, 2011; Costa e Silva & Kerr, 2012). This suggests that relatedness can be used to increase response to artificial selection for growth, and that kin selection may increase responses in natural populations of E. globulus. Theoretical and empirical studies have shown that, for example, relatedness can prevent the negative response to positive selection, which would have occurred with traditional selection under competition (Griffing, 1977; Muir, 1996, 2005; Bijma & Wade, 2008). This suggests that artificial kin selection could be used in forest tree breeding to prevent increased competition and accelerate response to selection.

The above paragraph has assumed that IGEs do not depend on relatedness among neighbours. Relatedness among neighbours, however, may affect IGEs through two processes (File et al., 2012). The kin recognition and selection hypothesis predicts that related individuals cooperate and, therefore, outperform groups of strangers (Hamilton, 1964). The niche partitioning hypothesis, by contrast, predicts that groups of strangers outperform kin groups because of differential resource use by neighbours (Young, 1981). Nevertheless, both hypotheses predict that interactions differ among relatives vs strangers, and there is increasing evidence of neighbour recognition in plants (Biedrzycki et al., 2010; Bhatt et al., 2011). Our estimates reflect an average indirect effect across all population members, without a priori classification into relatives or strangers. When IGEs differ between relatives and strangers, the total breeding values for both situations will show incomplete correlation, which reduces the benefits of artificial kin selection, because kin-selected benefits will emerge only partially in interactions among strangers. Thus, the benefits of artificial kin selection discussed above, and values for response presented in the next paragraph, may be interpreted as an upper bound.

Our estimates showed that total heritable variation for DBH at age 4 yr is very small. Thus, though kin selection may increase the utilization of heritable variation, the limited heritable variation causes the response to be small, irrespective of relatedness among neighbours or the selection criterion. The use of related neighbours, therefore, does not enable substantial improvement of DBH. For example, with unrelated neighbours, response to mass selection equals math formula (see Results; this assumes no difference between IGEs on kin vs strangers). With fully related neighbours (i.e. clones), and parameters taken from Table 4, response to selection equals math formula = 0.054S (Bijma et al., 2007a; Bijma & Wade, 2008), which is still only 5.4% of the selection differential. Thus, the small heritable variation in DBH presents a biological limitation to the response to selection regardless of selection strategy.

Mechanisms of interaction among individuals

Our estimated correlations between direct and indirect effects are among the highest in the literature, and suggest a functional link between the two effects. The high negative direct–indirect additive genetic correlation for growth is likely to be typical of adverse interactions involving resource competition in trees (Resende et al., 2005; Cappa & Cantet, 2008). In our population, genotypes with high DBH depressed the growth of neighbours as early as 2 yr of age. This adverse interaction persisted (i.e. math formula ≈ −0.9) and accentuated the importance of IGEs for DBH by age 4 yr, which is near the age of canopy closure. The study site is among the more productive E. globulus sites, and canopy closure and competition are likely to occur earlier than on less productive sites (Costa e Silva et al., 2011, 2012; Forrester et al., 2011). Increasing neighbour competition is expected with age (Binkley et al., 2002; Costa e Silva et al., 2011; Forrester et al., 2011), which may explain the increased impact of adverse IGEs with age. However, the age trends in growth are probably complex, and influenced by the dynamic interplay between size-dependent mortality and suppression of survivors that can occur during stand development (Chambers et al., 1996; Stackpole et al., 2010; Costa e Silva et al., 2011). For example, fast-growing genotypes may exploit water reserves more rapidly and initially suppress neighbours, but may more easily succumb to drought (Dutkowski & Potts, 2012).

The low heritable variation in DBH indicates that variation in direct and indirect genetic effects originates mainly from variation in adverse competitive interactions with neighbours, rather than from heritable variation in the efficiency of resource utilization (e.g. root proliferation vs rooting depth; fig. 1 in File et al., 2012). Heritable variation in the efficiency of resource utilization or in the ability to acquire additional resources without compromising neighbours (i.e. niche partitioning) would not contribute to the negative direct–indirect genetic correlation (de Jong & van Noordwijk, 1992), and thus generate heritable variation. The nonsignificant heritable variation for DBH at age 4 yr, however, indicates that heritable variation in those mechanisms is small.

The increasing competitiveness of neighbouring genotypes with directional selection for DBH will result in ‘evolutionary environmental deterioration’, which masks the phenotypic and evolutionary changes in the underlying direct and indirect effects (Hadfield et al., 2011). With a fixed resource, the population average of the trait reflecting resource availability may remain constant, despite underlying evolutionary changes in other traits. Such resource limitations and underlying evolutionary dynamics are pertinent to eucalypts, as nutrients and particularly water are key factors limiting net primary productivity (e.g. across Australia - Eamus, 2003).

Interactions between host individuals contribute to disease transmission in many host–pathogen systems (Detilleux, 2005; Lively, 2010; Lipschutz-Powell et al., 2012). Teratosphaeria nubilosa is mainly spread by wind-dispersed ascospores (Park, 1988). The positive correlation between the direct and indirect genetic effects observed in the case of MLD (i.e. math formula = 0.8) means that genetically susceptible trees increase MLD damage on neighbouring trees, consistent with increased disease transmission. Thus, in contrast to resource-limited traits, the rapid evolution of host defence traits may be favoured by the positive covariance between direct and indirect genetic effects on disease damage. With IGEs for disease transmission, the relative importance of local to global host dispersal and disease transmission can significantly alter the evolution of host defences (Agrawal et al., 2001; Detilleux, 2005; Debarre et al., 2012). In the presence of IGEs and spatial genetic structure resulting from genetically related neighbours, such evolution can involve traits that not only reduce disease susceptibility of the focal individual (Roy & Kirchner, 2000; Medzhitov et al., 2012) but also reduce transmission to related neighbours (Detilleux, 2005). Indeed, it is only in the presence of local spatial structure that kin selection can act, and that traits are expected to evolve which reduce transmission, including the altruistic strategy of suicide upon infection (Hamilton, 1964; Debarre et al., 2012).

Evolutionary causes of the genetic parameters

While we have studied IGEs in an artificial population, the mechanisms and genes underlying those IGEs will have evolved in wild populations of E. globulus, given its short period of domestication. In wild populations, local dispersal creates spatial genetic structure and genetic relationships among neighbours. This is certainly the case with E. globulus, where limited seed dispersal results in forests comprising a mosaic of related individuals, causing individuals within 25 m (i.e. one to two tree heights) to have an average relationship nearly as high as cousin (i.e. 0.125; Jones et al., 2007), if not higher (i.e. 0.25; Hardner et al., 1998; Skabo et al., 1998). With spatial genetic structure, interactions among neighbours give rise to kin selection, which not only affects the evolution of trait values but also shapes the genetic variances and covariances underlying those trait values.

The contrasting results observed for MLD vs DBH may be explained by the scale of the interactions. For DBH, interactions are largely local as a result of competition for resources with the nearest neighbours. As neighbours are related in wild populations of E. globulus, local interactions enhance the utilization of heritable variation for DBH (Bijma, 2011; Costa e Silva & Kerr, 2012), and consequently lead to the gradual exhaustion of heritable variation and the build-up of negative covariances between the direct and indirect components of the total breeding value (Denison et al., 2003). For MLD, by contrast, which is mainly spread by wind-dispersed ascospores (Park, 1988), interactions will reach much further than the nearest neighbours. Consequently, a substantial proportion of the interactions for MLD will involve unrelated individuals, leaving less opportunity for kin selection. As natural selection does not target IGEs in the absence of kin selection or multilevel selection (Griffing, 1977; Bijma & Wade, 2008), it will not exhaust heritable variation for MLD, nor create negative covariances between components of the total breeding value for MLD (Denison et al., 2003). Thus, the contrasting relationships between direct and indirect genetic effects found for DBH vs MLD may result from the difference in the scale of interactions for both traits in wild populations, which are expected to lead to kin selection for DBH but not for MLD.

The above argument has ignored a potential difference between IGEs on relatives and IGEs on strangers (Biedrzycki et al., 2010; File et al., 2012). When IGEs differ systematically between relatives and strangers, evolution by kin selection should not fully deplete heritable variation which could be expressed under interactions among strangers. Hence, a change in the ecology, from kin groups before domestication to planted forests with unrelated neighbours after domestication, should release utilizable heritable variation (Denison et al., 2003). With niche partitioning (Young, 1981), for example, one would expect heritable variation in the ability to utilize niches not occupied by unrelated neighbours to emerge after domestication. Our results, however, demonstrate very little heritable variation in DBH in a population of mainly unrelated neighbours. This would seem to suggest a general mechanism of competition among neighbours for DBH in E. globulus, which occurs among both kin and strangers. Boyden et al. (2008), however, found that genetic variation greatly reduced competition in a eucalypt trial, which suggests niche partitioning. Thus, there is clearly scope for further genetic studies that distinguish between IGEs on kin and strangers.


Our results challenge the traditional perspective on the genetic architecture of growth and disease traits in E. globulus. Both direct and indirect additive genetic effects may be important when individuals grow in close spatial proximity. The IGEs appear to be driven by neighbour competition and infection, respectively. These processes have contrasting effects on the total heritable variance available for selection. If variances in IGEs and their covariance with direct genetic effects persist in natural populations, then neighbour competition is likely to constrain evolutionary progress in resource-limited traits, whereas neighbour infection is likely to amplify the evolutionary response over that predicted from considering direct genetic effects alone.


The financial support given to João Costa e Silva by Fundação para a Ciência e Tecnologia (Portugal) through the Ciência 2007 initiative, and by the University of Tasmania for a visiting scholarship, is gratefully acknowledged. The contribution of Piter Bijma was supported by the Dutch Science Council (NWO-STW). The trial site was provided by WAPRES and data collection was supported by an Australian Research Council Grant (LP0884001), seedEnergy Pty Ltd, Southern Tree Breeding Association Inc. and CRC for Forestry.