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Keywords:

  • environmental heterogeneity;
  • genotype–environment interaction;
  • maintenance of variation

Abstract

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References
  9. Supporting Information

Theory predicts that genetic variation in phenotypic plasticity (genotype × environment interaction or G × E) should be eroded by selection acting across environments. However, it appears that G × E is often maintained under selection, although not universally. This variation in the presence and strength of G × E requires explanation. Here I ask whether the explanation may lie in the grain of the environment at which G × E is expressed. The grain (or grain size) of the environment refers to the scale of environmental heterogeneity relative to generation time – that is, relative to the window of operation of selection – with higher rates of heterogeneity occurring in finer-grained environments. The hypothesis that the grain of the environment explains variation in the expression of G × E encapsulates variation in the power of selection to shape reaction norms: selection should be able to erode G × E in fine-grained environments but lose its power as the grain becomes coarser. I survey studies of G × E in sexual traits and demonstrate that the strength of G × E varies with the grain of the environment across which it is expressed, with G × E being stronger in coarser-grained environments. This result elucidates when G × E is most likely to be sustained in the reaction norms of fitness-related traits and when its evolutionary consequences will be most pronounced.


Introduction

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References
  9. Supporting Information

Genotype × environment interaction (G × E) is genetic variation in phenotypic plasticity. With plasticity described in terms of reaction norms – which plot the phenotypes that different genotypes express across environments – G × E is variation in reaction norms (Fig. 1). G × E has a prominent role in evolutionary thought for various reasons. It offers, for example, a mechanism that can help maintain genetic variation under selection: when G × E is strong and reaction norms cross (Fig. 1), the fitness ranking of genotypes may change among environments so that selection favours different genotypes in different environments; consequently, with gene flow among environments, genetic variation within environments may be sustained under selection (Lynch & Walsh, 1998; Radwan, 2008). Although G × E offers a mechanism for the maintenance of variation, theory also predicts that G × E should itself be eroded by selection acting across environments; that is, it should be eroded by selection on reaction norms (Via & Lande, 1985; Via & Conner, 1987, 1995; Gomulkiewicz & Kirkpatrick, 1992; Gavrilets & Scheiner, 1993; Roff, 2002). This diversity of theoretical expectations appears to be matched in nature by a diversity of outcomes, with G × E in fitness-related traits such as sexual ornaments being present often but not always (Greenfield & Rodríguez, 2004; Miller & Brooks, 2005; Kemp & Rutowski, 2007; Bussière et al., 2008; Ingleby et al., 2010). Variation in the expression of G × E in nature requires explanation as well as exploration of its consequences for the course of evolution (Rodríguez et al., 2008; Rodríguez & Al–Wathiqui, 2011).

image

Figure 1. Potential patterns of phenotypic variation attributed to differences in genotype and to environmental effects. Lines (reaction norms) plot the range of phenotypes expressed by different genotypes across two environments. In each panel, the x-axis shows two developmental environments, and the y-axis the corresponding expressed phenotypes or trait values. The panels in the top row (panels a, b, c, and d) show a mean effect of the developmental environment, which is absent from the panels in the bottom row (panels e, f, g, and h). Genetic and environmental components of variation interact to generate different patterns, as follows. There may be genetic variation and phenotypic plasticity but no G×E (panel a); plasticity but no genetic variation (panel d); genetic variation but no plasticity (panel e); neither genetic variation nor plasticity (panel h); finally, there may be genetic variation in plasticity (G×E), corresponding to nonparallel reaction norms, with the level of nonparallelism indicating the strength of G×E (panels b, c, f, and g). Reaction norms may differ so much that they cross (panels c and g).

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Here I test the grain-size model (Levins, 1968) as an explanation for variation in the expression (i.e. in the presence and strength) of G × E. The grain size of the environment describes the scale at which environmental heterogeneity occurs in relation to generation time: in a fine-grained environment, individuals from any one generation may encounter various environment types, whilst in a coarse-grained environment, individuals from any one generation encounter a single environment type (Gillespie, 1974). The grain-size model states that adaptive plasticity is more likely to evolve in fine-grained environments (Levins, 1968). The reason is that, in fine-grained environments, environmental heterogeneity occurs within the window of operation of selection; that is, heterogeneity is experienced by every generation. By contrast, as grains become coarser heterogeneity is experienced less and less frequently relative to generation time, with the consequence that selection loses the ability to shape reaction norms expressed across those grains, and populations adapt instead to prevailing conditions. This hypothesis has considerable empirical and theoretical support (Sultan & Spencer, 2002; Lind & Johansson, 2007; Hollander, 2008; Baythavong, 2011; Lind et al., 2011).

Applied to the problem of variation in the presence and strength of G × E, the grain-size model states that variation in the ability of selection to shape reaction norms will be reflected in its ability to erode G×E, because G × E is genetic variation in reaction norms (Fig. 1). Thus, variation in the expression of G × E may be explained by the grain at which G × E is expressed. This hypothesis predicts that the strength of G × E should increase with grain size, that is, with the coarseness of the environment. I tested this prediction with a survey of studies of G × E in sexual traits. I focused on G × E in sexual traits because of their relevance to the ‘lek paradox’ – that is, the special problem of the maintenance of genetic variation under (very strong) sexual selection (Greenfield & Rodríguez, 2004). I assessed the relationship between the grain size at which G × E was assessed in each study and the strength of G × E that was detected. Because there are still relatively few studies of G × E in sexual traits, my goal here is to present a preliminary test of the hypothesis and to identify variables that studies of G × E should quantify to facilitate more complete tests in the future.

Materials and methods

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References
  9. Supporting Information

This survey includes to my knowledge all studies of G × E in sexual traits from which it is currently possible to extract the information necessary to test the grain-size hypothesis. I located the studies through a search on Web of Knowledge and by consulting reviews (Greenfield & Rodríguez, 2004; Bussière et al., 2008; Ingleby et al., 2010) and my reference collection. I used two criteria for inclusion of studies in the analysis: (i) G × E was detected in the trait regardless of heritability, or G × E was not detected but heritability was detected – that is, I excluded a trait/study if neither G × E nor heritability were detected, because in such cases lack of G × E may be due to lack of genetic variation, and thus be uninformative about the effect of the grain size of the environment; (ii) it was possible to estimate the effect size of G × E from the P-value of the corresponding term in the statistical analysis. These criteria resulted in the inclusion of 17 studies on 12 species ranging from insects and snails to fish and mammals, each study involving 1–17 traits (Appendix S1). The above criteria excluded eight studies (Aspi & Hoikkala, 1993; Olvido & Mousseau, 1995; Jia & Greenfield, 1997; Qvarnström, 1999; Doty & Welch, 2001; Sheldon et al., 2003; Welch, 2003; Kemp & Rutowski, 2007). It is unlikely that the current literature overestimates the occurrence of G × E, because any study testing for genetic parameters in sexual traits is likely to be deemed worthy of publication regardless of the findings. Instead, because most experiments have used few environmental conditions, the prevalence of G × E may currently be underestimated (Bussière et al., 2008). At this stage in the study of G × E, a meta-analysis is not possible, because no single study has tested for the effect of the grain size of the environment on the expression of G × E. Instead, each study in the survey contributed 1–2 values for grain size and as many data points for the strength of G × E as sexual traits it included.

I described the strength of G × E with an effect size approach (Nakagawa & Cuthill, 2007). I estimated the effect size (0 < < 1) of G × E from the P-value of the G × E term in the statistical analysis in each study (Rosenthal, 1991; Hunt et al., 2004); thus, r = Z/√n where Z is the standard normal deviate equivalent of the P-value and n is the sample size of genotypes (e.g. the number of full–sibling families).

I categorized the grain size across which G × E was evaluated in each study in four levels (Fig. 2): fine (scale of environmental heterogeneity equivalent to generation time or less); medium (scale of heterogeneity corresponding to a few generations); coarse (scale of heterogeneity corresponding to many generations); and very coarse (scale of heterogeneity corresponding to hundreds or thousands of generations, as in the colonization of novel environments). Although these categories span several orders of magnitude of variation in environmental heterogeneity, it is possible to specify thresholds that should mark crucial changes in the strength of the expression of G × E. The predicted increase in the effect size of G × E (r) should largely occur between fine and medium grains, which is the transition predicted to mark the most pronounced difference in the ability of selection to shape reaction norms. However, there are also documented instances of the evolution of adaptive plasticity expressed in medium-grained environments (e.g. Moran, 1992). Consequently, an additional increase in r from medium to coarse grains would also support the hypothesis.

image

Figure 2. Variation in the effect size (r) of G × E in sexual traits according to the grain size of the environment across which G × E was expressed. (a) Raw data from 17 studies surveyed. Each column (x-axis tick marks) corresponds to a study, and each data point corresponds to an estimate for r for a trait. Arrows indicate studies with very small n's (2–3 genotypes). The r values above the dotted line are overestimated. (b) Least square mean r (±1 SE) from the following models: grain size, n, species (black symbols); grain size, species (grey symbols).

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To test the relationship between the four grain-size categories and r, I used a linear mixed model implemented with the REML method (fitting no intercept) in JMP (v. 7.0.1; SAS Institute, Cary, NC, USA). The REML method provides significance for fixed terms and variance component estimates with 95% confidence intervals for random terms. The dependent variable was r for each trait in each study. The explanatory variables were grain size as an ordinal variable, the sample size of genotypes (n) and species identity as a random term to account for nonindependence of traits within species and for species used in more than one study. This model thus tests the effect of grain size on r whilst accounting for overestimation of r because of small n's. I also tested other models that included or excluded n, and that included or excluded study as a random term nested within species, which doubly accounts for variation in n.

Results

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References
  9. Supporting Information

There was a considerable variation within and between studies in the effect size (r) of G × E (Fig. 2). Some of this variation arises from the overestimation of r in studies with very small n's (indicated by arrows in Fig. 2a). Nevertheless, there was a robust pattern for r to be smaller in fine-grained environments, intermediate in medium-grained environments and larger in coarser-grained environments (Fig. 2). The effect of grain size was significant (F3,10.86 = 5.49, P = 0.015; Fig. 2b, black symbols). By contrast, the effect of n was not significant (F1,26.21 = 0.76, P = 0.39). Excluding n retained significance for grain size (F3,9.336 = 8.53, P = 0.0049) in a nearly identical pattern, except that r for fine-grains had a least square mean = 0 (Fig. 2b, grey symbols). Models including study (nested within species) as well as species yielded the same pattern: the effect of grain size was significant whether n was included (F3,9.204 = 5.78, P = 0.017) or excluded (F3,8.647 = 9.14, P = 0.0047). The 95% confidence intervals for the species and study terms always overlapped zero.

Discussion

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References
  9. Supporting Information

A survey of the current literature on G × E in sexual traits provides robust support for the grain-size model as an explanation for variation in the expression of G × E: G × E was stronger at coarser grains. This finding supports the notion that selection can erode G × E in fine-grained environments, but that it loses the ability to do so as grain size exceeds generation time. At coarse grains, G × E is expressed at scales that are beyond the window of operation of selection.

These results are necessarily tentative, because to date there have been relatively few studies of G × E in sexual traits. As the literature accumulates, it will be desirable to expand the tests of the grain-size model as an explanation for variation in the expression of G×E. One potential concern for this study and for future assessments is how the grain size of the environment is quantified. Here I used four categories, each spanning a broad range of heterogeneity. Detecting variation in the strength of G × E across these categories suggests that there is a general and robust pattern associated with grain size. Going forward, such tests would be strengthened if individual studies provided their own estimation of the grain of the environments involved in their assessment of G × E. Rather than sticking too tightly to the categories used here, it would perhaps be fruitful to focus on what the natural history and generation time of each species say about when selection should be effective in shaping reaction norms. What might be most useful is studies using experimental treatments representing different grain sizes and testing for an effect on the strength of G × E detected. A sample of such studies would facilitate a meta-analytical test. Another refinement might be to consider explicitly the relative rate of encounter of each of the environments used in assessments of G × E (Kingsolver et al., 2007).

Besides an increase in the strength of G × E from fine to coarse grains, there was considerable variation in the expression of G × E within grain-size categories and between traits within the same study (Fig. 2a). This suggests that additional factors may influence the expression of G×E. For example, there may be variation in the strength of selection to which different traits are subject (Hoekstra et al., 2001; Kingsolver et al., 2001). Another potential factor is the variation in the level of canalization or condition dependence of different traits – there is evidence that traits likely to be less canalized and more strongly condition-dependent tend to express stronger G × E (Rodríguez & Al–Wathiqui, 2011). Note, however, that such variables should contribute to variation within (rather than between) grain sizes, because whether selection is at all able to shape reaction norms should have a predominant effect. The test of the grain-size hypothesis presented here is thus likely to be noisy but conservative.

The ability to predict the strength of the expression of G × E on the basis of the grain of the environment will help understand the evolutionary consequences of G×E. First, G × E in fine-grained environments was weak but present to some extent. The standard error for the least square mean of the effect size of G × E in fine-grained environments overlapped zero (Fig. 2b), but at least in some cases, weak G × E was present. This suggests that G × E can contribute to the maintenance of variation even when selection across environments most effectively erodes it. In coarser grains, G × E is stronger and its effect may be more dramatic. Here, the consequences will mainly bear on the process of divergence, because with strong G × E phenotypes with different genetic backgrounds may be favoured in different environments, and with coarse grains there is low gene flow between environments. These conditions should promote differences in the response to selection across environments (even if selection is the same), leading to phenotypic and evolutionary divergence through genetic accommodation (Rodríguez et al., 2008; cf. West–Eberhard, 2003, 2005; Suzuki & Nijhout, 2006, 2008; Shaw et al., 2007). These consequences will be the strongest in the coarsest grains. For example, the divergence-promoting consequences of G × E may be most pronounced in events such as the colonization of novel environments (Cocroft et al., 2008; Rodríguez et al., 2008) – events that are rare (hence coarse grained) but hugely important in the process of divergence.

Acknowledgments

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References
  9. Supporting Information

I thank Troy Day, Gerlinde Höbel, Locke Rowe and two anonymous reviewers for comments on the earlier drafts of the manuscript. This work was supported by NSF grants IOS–1120790 and IOS–0919962.

References

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References
  9. Supporting Information

Data deposited at Dryad: doi: 10.5061/dryad.hq54s

Supporting Information

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References
  9. Supporting Information

As a service to our authors and readers, this journal provides supporting information supplied by the authors. Such materials are peer-reviewed and may be re-organized for online delivery, but are not copy-edited or typeset. Technical support issues arising from supporting information (other than missing files) should be addressed to the authors.

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jeb2565-sup-0001-AppendixS1.docWord document162KAppendix S1 Studies of G × E in sexual traits included in the survey, associated references, and corresponding data used in the analysis.

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