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Heritability is not Evolvability

Abstract

Short-term evolutionary potential depends on the additive genetic variance in the population. The additive variance is often measured as heritability, the fraction of the total phenotypic variance that is additive. Heritability is thus a common measure of evolutionary potential. An alternative is to measure evolutionary potential as expected proportional change under a unit strength of selection. This yields the mean-scaled additive variance as a measure of evolvability. Houle in Genetics 130:195–204, (1992) showed that these two ways of scaling additive variance are often inconsistent and can lead to different conclusions as to what traits are more evolvable. Here, we explore this relation in more detail through a literature review, and through theoretical arguments. We show that the correlation between heritability and evolvability is essentially zero, and we argue that this is likely due to inherent positive correlations between the additive variance and other components of phenotypic variance. This means that heritabilities are unsuitable as measures of evolutionary potential in natural populations. More generally we argue that scaling always involves non-trivial assumptions, and that a lack of awareness of these assumptions constitutes a systemic error in the field of evolutionary biology.

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Acknowledgments

We thank the many participants in the measurement-theory discussion group at the University of Oslo during 2008 and 2009 for discussions of the topic of this paper. DH was supported in this research by a visiting professorship at CEES and TFH by grant #177857 from the Norwegian Research Council.

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Correspondence to Thomas F. Hansen.

Electronic supplementary material

Below is the link to the electronic supplementary material.

11692_2011_9127_MOESM1_ESM.xls

Supplementary File S1: Excel sheet with data used in this study: The data are organized by study and species. We give a short description of the trait, which should allow identification in the original study. We give classification of the trait and its scale type as described in the main text. We classify the organisms involved into some very general categories. The column “measure” indicates the type of estimate of additive genetic variance that was used. Finally, we indicate if any traits from the study were not used with the same coded reason as explained in the supplementary file S2. We report estimates with three decimal digits and at least two significant digits, but this should not be taken as an indication of the true number of significant digits, which was often impossible to discern. The column "Ie" gives the mean-scaled residual variance computed as explained in the main text, and should not be mistaken for residual or environmental variance reported in the original study. (XLS 345 kb)

11692_2011_9127_MOESM2_ESM.doc

Supplementary file S2: List of studies of quantitative genetic variation published in Evolution and Journal of Evolutionary Biology from 1992-2009 that are not included in our database (S1). For each paper we indicate the reason we could not include it. This is divided into five categories: 1. MBS: Missing basic statistics. This means that we could not find sufficient basic statistics necessary to compute evolvabilities or heritabilities, or that some necessary numbers were given with only a single significant digit (but we did include variance and heritability estimates given as “0”). 2. IS: Incompatible scales: Information to compute heritability and evolvability were given, but not on the same scale (e.g. heritabilities were reported for log-transformed traits). 3. NST: Not suitable scale type: Traits were on a scale type that did not allow mean or variance standardization (e.g. interval scales on which means are not meaningful). 4. IIM: Incomplete or inconsistent methods: This includes cases where we could not find sufficient information to be sure what the reported numbers represented (e.g. the scale of reported numbers was unclear), or cases where there were inconsistencies in the reported method or results (e.g. alternative ways of computing the same statistics gave different results and we could not locate the error). 5. DG: Different groups: The necessary statistics were not given for the same groups of individuals (e.g. we did not compute evolvabilities based on trait means calculated for a different population than the one in which the additive variance was estimated).

The papers we considered were found based on reading titles and abstracts of every original research paper published in the two journals in the given period, and then further checking those that gave some indication of being a quantitative genetics study. Due to the large number of papers we needed to check, we could not spend a long time to resolve apparent problems and inconsistencies. We excluded many studies and traits were we had doubts as to exactly what had been done or reported, and have excluded some data that might have been included after more careful considerations or consultation with authors. We apologize for such omissions. Also, the exclusion of data does not imply that there was anything wrong with the study, as the studies we consulted often had different goals that did not necessitate the types of statistics and information that we required. We hope that this list can be of use for other surveys of quantitative genetic information. (DOC 66 kb)

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Supplementary Figure 1: Plot of heritability against evolvability for narrow-sense estimates only (excluding negative estimates). The correlation is 0.09 ± 0.02 for positive values. (PDF 350 kb)

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Supplementary Figure 2: Plot of heritability against “evolvability” for full-sib estimates only (excluding negative estimates). The correlation is 0.23 ± 0.05 for positive values. (PDF 175 kb)

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Supplementary Figure 3: Plot of heritability against “evolvability” for broad-sense estimates only (excluding negative estimates). The correlation is 0.14 ± 0.07 for positive values. (PDF 206 kb)

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Supplementary Figure 4: Plot of narrow-sense heritability against evolvability for linear size traits (excluding negative estimates). The correlation is 0.01 ± 0.05 for positive values. (PDF 230 kb)

Appendix

Appendix

List of papers used in the literature review: Agrawal et al. (2002), Arnold and Phillips (1999), Ashman (2003), Asteles et al. (2006), Bacigalupe et al. (2004), Beraldi et al. (2007), Berwaerts et al. (2008), Birkhead et al. (2006), Boake and Konigsberg (1998), Brandt and Greenfield (2004), Brodie (1993), Bryant and Meffert (1995), Cadee (2000), Campbell (1996, 1997), Caruso (2004), Caruso et al. (2005), Charmantier et al. (2004a, b), Cheetham et al. (1993, 1994), Cheverud (1996), Coltman et al. (2001, 2005), Conner and Via (1993), Conner et al. (2003, Cotter et al. 2004), Czesak and Fox (2003a, b), De Winter (1992), Evanno et al. (2006), Evans and Marshall (1996), Evans et al. (2006), Fenster and Carr (1997), Fernandez et al. (2003), Fox (1993), Fox et al. (1999), Friberg et al. (2005), Garant et al. (2004), Garcia-Gonzales and Simmons (2005), Gardner and Latta (2008), Gomez et al. (2009), Gomez-Mestre et al. (2008), Gray and Cade (1999), Groeters and Dingle (1996), Han and Lincoln (1994), Hansen et al. (2003b), Hawthorne (1997), Hegyi et al. (2002), Hendrickx et al. (2008), Hoffman et al. (2006), Hoffmann and Schiffer (1998), Horne and Ylönen (1998), House and Simmons (2005), House et al. (2008), Hughes (1995), Ivy (2007), Jensen et al. (2003, 2008), Jia et al. (2000), Johnson et al. (2009), Juenger and Bergelson (2000), Kaczorowski et al. (2008), Karoly and Conner (2000), Kause et al. (1999, 2001), Kellermann et al. (2006), Ketola and Kotiaho (2009), Kilpimaa et al. (2005), Kobayashi et al. (2003), Koelwijn and Hunscheid (2000), Kontiainen et al. (2008), Kruuk et al. (2002, 2003), Larsson (1993), Lauteri et al. (2004), Le Galliard et al. (2006), Leamy (1999), Lew et al. (2006), Linder and Rice (2005), Long et al. (2009), Lynch et al. (1999), MacColl and Hatchwell (2003), Magalhaes et al. (2007), Manier et al. (2007), Mappes and Koskela (2004), Mazer et al. (1999), McAdam and Boutin (2003), Merilä (1997), Merilä and Gustafsson (1993), Merilä et al. (1998), Messina and Fry (2003), Miller and Sinervo (2007), Milner et al. (2000), Morrow et al. (2008), Nespolo et al. (2003, 2005), Nilsson et al. (2009), Noach et al. (1996), ONeil (1997), Ostrowski et al. (2002), Parker and Garant (2004), Pélabon et al. (2004), Pelletier et al. (2007), Perez and Garcia (2002), Perry et al. (2004), Pettay et al. (2008), Platenkamp and Shaw (1992), Platenkamp and Shaw (1993), Podolsky et al. (1997), Polak and Starmer (2001), Radwan (1998), Rauter and Moore (2002), Reale and Festa-Bianchet (2000), Reale et al. (2003), Ritland and Ritland (1996), Rodriguez and Greenfield (2003), Roff (1995), Rolff et al. (2005), Rønning et al. (2007), Routley and Husband (2005), Ryder and Siva-Jothy (2001), Sakai et al. (2008), Santos (1996, 2001, 2002), Santos et al. (1992), Sarkissian and Harder (2001), Sgro and Hoffmann (1998), Shaw and Platenkamp (1993), Shaw et al. (1995), Sherrard et al. (2009), Simmons (2003), Simmons and Garcia-Gonzalez (2007), Simmons and Kotiaho (2002), Simons and Johnston (2006), Simons and Roff (1994), Simons et al. (1998), Steigenga et al. (2005), Teplitsky et al. (2009), Theriault et al. (2007), Thessing and Ekman (1994), Thiede (1998), Thomas and Simmons (2008), Tonsor and Goodnight (1997), Tucic and Stojkovic (2001), Van Kleunen and Ritland (2004), Verhoeven et al. (2004), Watkins (2001), Wayne et al. (1997), Weber and Scheiner (1992), Weller et al. (2006), Wilson et al. (2003), Wilson et al. (2005), Windig (1994), Winn (2004), Woods et al. (1998), Worley and Barrett (2000).

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Hansen, T.F., Pélabon, C. & Houle, D. Heritability is not Evolvability. Evol Biol 38, 258 (2011). https://doi.org/10.1007/s11692-011-9127-6

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Keywords

  • Evolvability
  • Heritability
  • Genetic variance
  • Quantitative genetics
  • Measurement theory
  • Scaling