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Defining behavioural syndromes and the role of ‘syndrome deviation’ in understanding their evolution

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This commentary highlights multivariate tools that have been used by evolutionary biologists in the study of syndromes and their evolution and discusses the insights that these methods provide into evolutionary processes relative to the metric ‘syndrome deviation’ that has recently been proposed by Herczeg and Garamszegi (Behav Ecol Sociobiol 66:161–169, 2012). We clarify that non-zero phenotypic correlations arise from the joint influences of within- and between-individual correlations, whereas only non-zero between-individual correlations represent behavioural syndromes, and discuss how acknowledgement of this subtle difference between phenotypic and between-individual correlations affects the applicability of syndrome deviation for the study of behavioural syndromes.

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NJD was supported by the Max Planck Society, and SN, by the Humboldt Fellowship and Marsden Fund. We acknowledge the input of two anonymous referees who both shared a number of ideas for the analyses of syndrome structure that have been gratefully included in a revised version of this paper.

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Correspondence to Niels J. Dingemanse.

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Communicated by J. Lindström

Appendix: The relationships among phenotypic, between-individual and within-individual correlations

Appendix: The relationships among phenotypic, between-individual and within-individual correlations

Using the symbols introduced in Eq. 1, the between-individual, within-individual and phenotypic correlations at the observation level are, respectively, defined as (Snijders and Bosker 1999; p. 204):

$$ \matrix{ {{r_{{{\mathrm{in}}{{\mathrm{d}}_{{0y}}},{\mathrm{in}}{{\mathrm{d}}_{{0z}}}}}} = \frac{{{{\mathrm{cov}}_{{{\mathrm{in}}{{\mathrm{d}}_{{0y}}},{\mathrm{in}}{{\mathrm{d}}_{{0z}}}}}}}}{{\sqrt {{{v_{{{\mathrm{in}}{{\mathrm{d}}_{{0y}}}}}}{v_{{{\mathrm{in}}{{\mathrm{d}}_{{0z}}}}}}}} }},} \hfill \\ {{r_{{{e_{{0y}}},{e_{{0z}}}}}} = \frac{{{{\mathrm{cov}}_{{{e_{{0y}}},{e_{{0z}}}}}}}}{{\sqrt {{{v_{{{e_{{0y}}}}}}{v_{{{e_{{0z}}}}}}}} }},} \hfill \\ {{r_{{{P_y},{P_z}}}} = \frac{{{{\mathrm{cov}}_{{{\mathrm{in}}{{\mathrm{d}}_{{0y}}},{\mathrm{in}}{{\mathrm{d}}_{{0z}}}}}} + {{\mathrm{cov}}_{{{e_{{0y}}},{e_{{0z}}}}}}}}{{\sqrt {{({v_{{{\mathrm{in}}{{\mathrm{d}}_{{0y}}}}}} + {v_{{{e_{{0y}}}}}})({v_{{{\mathrm{in}}{{\mathrm{d}}_{{0z}}}}}} + {v_{{{e_{{0z}}}}}})}} }},} \hfill \\ }<!end array> $$

where \( {\mathrm{cov}_{{{\mathrm{in}}{{\mathrm{d}}_{{0y}}},{\mathrm{in}}{{\mathrm{d}}_{{0z}}}}}} \) and \( {\mathrm{cov}_{{{e_{{0y}}},{e_{{0z}}}}}} \) are the co-variances between the phenotypic attributes at the individual level (i.e. between individuals) and the observation level (i.e. within individuals), respectively. Therefore,

$$ \matrix{ {{r_{{{P_y},{P_z}}}} = \frac{{{r_{{{\mathrm{in}}{{\mathrm{d}}_{{0y}}},{\mathrm{in}}{{\mathrm{d}}_{{0z}}}}}}\sqrt {{{v_{{{\mathrm{in}}{{\mathrm{d}}_{{0y}}}}}}{v_{{{\mathrm{in}}{{\mathrm{d}}_{{0z}}}}}}}} + {r_{{{e_{{0y}}},{e_{{0z}}}}}}\sqrt {{{v_{{{e_{{0y}}}}}}{v_{{{e_{{0z}}}}}}}} }}{{\sqrt {{({v_{{{\mathrm{in}}{{\mathrm{d}}_{{0y}}}}}} + {v_{{{e_{{0y}}}}}})({v_{{{\mathrm{in}}{{\mathrm{d}}_{{0z}}}}}} + {v_{{{e_{{0z}}}}}})}} }},} \hfill \\ {{r_{{{P_y},{P_z}}}} = {r_{{{\mathrm{in}}{{\mathrm{d}}_{{0y}}},{\mathrm{in}}{{\mathrm{d}}_{{0z}}}}}}\frac{{\sqrt {{{v_{{{\mathrm{in}}{{\mathrm{d}}_{{0y}}}}}}{v_{{{\mathrm{in}}{{\mathrm{d}}_{{0z}}}}}}}} }}{{\sqrt {{({v_{{{\mathrm{in}}{{\mathrm{d}}_{{0y}}}}}} + {v_{{{e_{{0y}}}}}})({v_{{{\mathrm{in}}{{\mathrm{d}}_{{0z}}}}}} + {v_{{{e_{{0z}}}}}})}} }} + {r_{{{e_{{0y}}},{e_{{0z}}}}}}\frac{{\sqrt {{{v_{{{e_{{0y}}}}}}{v_{{{e_{{0z}}}}}}}} }}{{\sqrt {{({v_{{{\mathrm{in}}{{\mathrm{d}}_{{0y}}}}}} + {v_{{{e_{{0y}}}}}})({v_{{{\mathrm{in}}{{\mathrm{d}}_{{0z}}}}}} + {v_{{{e_{{0z}}}}}})}} }},} \hfill \\ {{r_{{{P_y},{P_z}}}} = {r_{{{\mathrm{in}}{{\mathrm{d}}_{{0y}}},{\mathrm{in}}{{\mathrm{d}}_{{0z}}}}}}\sqrt {{\left( {\frac{{{v_{{{\mathrm{in}}{{\mathrm{d}}_{{0y}}}}}}}}{{{v_{{{\mathrm{in}}{{\mathrm{d}}_{{0y}}}}}} + {v_{{{e_{{0y}}}}}}}}} \right)\left( {\frac{{{v_{{{\mathrm{in}}{{\mathrm{d}}_{{0z}}}}}}}}{{{v_{{{\mathrm{in}}{{\mathrm{d}}_{{0z}}}}}} + {v_{{{e_{{0z}}}}}}}}} \right)}} + {r_{{{e_{{0y}}},{e_{{0z}}}}}}\sqrt {{\left( {\frac{{{v_{{{e_{{0y}}}}}}}}{{{v_{{{\mathrm{in}}{{\mathrm{d}}_{{0y}}}}}} + {v_{{{e_{{0y}}}}}}}}} \right)\left( {\frac{{{v_{{{e_{{0z}}}}}}}}{{{v_{{{\mathrm{in}}{{\mathrm{d}}_{{0z}}}}}} + {v_{{{e_{{0z}}}}}}}}} \right)}} } \hfill \\ }<!end array> $$

where the latter equation corresponds to Eq. 1.

The phenotypic correlation of individual means, which is also often used in behavioural syndrome research, can be approximated by the following (Snijders and Bosker 1999):

$$ \matrix{ {{{\overline r}_{{{P_y},{P_z}}}} = \frac{{{{\mathrm{cov}}_{{{\mathrm{in}}{{\mathrm{d}}_{{0y}}}{\mathrm{in}}{{\mathrm{d}}_{{0z}}}}}} + {{\mathrm{cov}}_{{{e_{{0y}}}{e_{{0z}}}}}}/n}}{{\sqrt {{\left( {{v_{{{\mathrm{in}}{{\mathrm{d}}_{{0y}}}}}} + \frac{{{v_{{{e_{{0y}}}}}}}}{n}} \right)\left( {{v_{{{\mathrm{in}}{{\mathrm{d}}_{{0z}}}}}} + \frac{{{v_{{{e_{{0z}}}}}}}}{n}} \right)}} }},} \hfill \\ {{{\overline r}_{{{P_y},{P_z}}}} = \frac{{{r_{{{\mathrm{in}}{{\mathrm{d}}_{{0y}}},{\mathrm{in}}{{\mathrm{d}}_{{0z}}}}}}\sqrt {{{v_{{{\mathrm{in}}{{\mathrm{d}}_{{0y}}}}}}{v_{{{\mathrm{in}}{{\mathrm{d}}_{{0z}}}}}}}} + {r_{{{e_{{0y}}},{e_{{0z}}}}}}\sqrt {{{v_{{{e_{{0y}}}}}}{v_{{{e_{{0z}}}}}}}} /n}}{{\sqrt {{\left( {{v_{{{\mathrm{in}}{{\mathrm{d}}_{{0y}}}}}} + \frac{{{v_{{{e_{{0y}}}}}}}}{n}} \right)\left( {{v_{{{\mathrm{in}}{{\mathrm{d}}_{{0z}}}}}} + \frac{{{v_{{{e_{{0z}}}}}}}}{n}} \right)}} }},} \hfill \\ {{{\overline r}_{{{P_y},{P_z}}}} = {r_{{{\mathrm{in}}{{\mathrm{d}}_{{0y}}},{\mathrm{in}}{{\mathrm{d}}_{{0z}}}}}}\frac{{\sqrt {{{v_{{{\mathrm{in}}{{\mathrm{d}}_{{0y}}}}}}{v_{{{\mathrm{in}}{{\mathrm{d}}_{{0z}}}}}}}} }}{{\sqrt {{\left( {{v_{{{\mathrm{in}}{{\mathrm{d}}_{{0y}}}}}} + \frac{{{v_{{{e_{{0y}}}}}}}}{n}} \right)\left( {{v_{{{\mathrm{in}}{{\mathrm{d}}_{{0z}}}}}} + \frac{{{v_{{{e_{{0z}}}}}}}}{n}} \right)}} }} + \frac{{{r_{{{e_{{0y}}}{e_{{0z}}}}}}}}{n}\frac{{\sqrt {{{v_{{{e_{{0y}}}}}}{v_{{{e_{{0z}}}}}}}} }}{{\sqrt {{\left( {{v_{{{\mathrm{in}}{{\mathrm{d}}_{{0y}}}}}} + \frac{{{v_{{{e_{{0y}}}}}}}}{n}} \right)\left( {{v_{{{\mathrm{in}}{{\mathrm{d}}_{{0z}}}}}} + \frac{{{v_{{{e_{{0z}}}}}}}}{n}} \right)}} }},} \hfill \\ {{{\overline r}_{{{P_y},{P_z}}}} = {r_{{{\mathrm{in}}{{\mathrm{d}}_{{0y}}}{\mathrm{in}}{{\mathrm{d}}_{{0z}}}}}}\sqrt {{\left( {\frac{{{v_{{{\mathrm{in}}{{\mathrm{d}}_{{0y}}}}}}}}{{{v_{{{\mathrm{in}}{{\mathrm{d}}_{{0y}}}}}} + \frac{{{v_{{{e_{{0y}}}}}}}}{n}}}} \right)\left( {\frac{{{v_{{{\mathrm{in}}{{\mathrm{d}}_{{0z}}}}}}}}{{{v_{{{\mathrm{in}}{{\mathrm{d}}_{{0z}}}}}} + \frac{{{v_{{{e_{{0z}}}}}}}}{n}}}} \right)}} + \frac{{{r_{{{e_{{0y}}},{e_{{0z}}}}}}}}{n}\sqrt {{\left( {\frac{{{v_{{{e_{{0y}}}}}}}}{{{v_{{{\mathrm{in}}{{\mathrm{d}}_{{0y}}}}}} + \frac{{{v_{{{e_{{0y}}}}}}}}{n}}}} \right)\left( {\frac{{{v_{{{e_{{0z}}}}}}}}{{{v_{{{\mathrm{in}}{{\mathrm{d}}_{{0z}}}}}} + \frac{{{v_{{{e_{{0z}}}}}}}}{n}}}} \right)}}, } \hfill \\ }<!end array> $$

where the latter equation reveals that the phenotypic correlation of individual means is not only a function of the between-individual correlation (\( {r_{{{\mathrm{in}}{{\mathrm{d}}_{{0y}}}{\mathrm{in}}{{\mathrm{d}}_{{0z}}}}}} \)) but also of the within-individual correlation (\( {r_{{{e_{{0y}}},{e_{{0z}}}}}} \)). The extent to which \( {\overline r_{{{P_y},{P_z}}}} \) reflects \( {r_{{{\mathrm{in}}{{\mathrm{d}}_{{0y}}}{\mathrm{in}}{{\mathrm{d}}_{{0z}}}}}} \) depends on the number of observations per individual (n). Typically, n is relatively low (2–5) in behavioural syndrome research, implying that \( {\overline r_{{{P_y},{P_z}}}} \) might often reflect \( {r_{{{e_{{0y}}},{e_{{0z}}}}}} \) rather than the behavioural syndrome (i.e. \( {r_{{{\mathrm{in}}{{\mathrm{d}}_{{0y}}}{\mathrm{in}}{{\mathrm{d}}_{{0z}}}}}} \)) that was meant to be quantified by using this method.

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Dingemanse, N.J., Dochtermann, N.A. & Nakagawa, S. Defining behavioural syndromes and the role of ‘syndrome deviation’ in understanding their evolution. Behav Ecol Sociobiol 66, 1543–1548 (2012).

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