Undesirable Consequences Of Neglecting Nonlinearity: Response To Comments By Liefting Et Al. (2013) On Rocha & Klaczko (2012)

In response to our previous study, Liefting et al. argue, in defense of their work on latitudinal variation of developmental-rate reaction norms (RNs), that (1) developmental rate (the reciprocal of development time: rate = time-1) is a more biologically relevant variable than development time; (2) the linear RN model is a valid approximation; and (3) three experimental points suffice to estimate RN parameters. Here, we reply to their comments. First, we give evidence that the complexity of actual development challenges the appealing simplicity of developmental rate. Using the same analysis as Liefting et al. to test their hypothesis with development time, instead of rate, reveals a pattern that is the opposite of their conclusion. Second, we show that a quadratic model is consistent with the whole development-time RNs and explains this contradiction. Third, with the quadratic model, we introduce two parameters to study plasticity: the RN shape (the quadratic coefficient) and RN local plasticity (the derivative of the RN function). The first showed a statistically significant correlation with latitude; and the second showed a continuous variation pattern where all localized patterns can be found (positive, negative, or nonsignificant correlations with latitude) but certainly cannot be generalized. © 2014 The Author(s). Evolution © 2014 The Society for the Study of Evolution.68515481551Box, G.E.P., Cox, D.R., An analysis of transformations (1964) J. R. Stat. Soc. Series B Stat. Methodol., 26, pp. 211-252Davidowitz, G., Nijhout, H.F., The physiological basis of reaction norms: the interaction among growth rate, the duration of growth and body size (2004) Integr. Comp. Biol., 44, pp. 443-449Davidowitz, G., D'amico, L.J., Nijhout, H.F., Critical weight in the development of insect body size (2003) Evol. Dev., 5, pp. 188-197Folgueraa, G., Menscha, J., Muñoz, J.L., Ceballosa, S.G., Hasson, E., Bozinovic, F., Ontogenetic stage-dependent effect of temperature on developmental and metabolic rates in a holometabolous insect (2010) J. Insect Physiol., 56, pp. 1679-1684Liefting, M., Hoffmann, A.A., Ellers, J., Plasticity versus environmental canalization: population differences in thermal responses along a latitudinal gradient in Drosophila serrata (2009) Evolution, 63, pp. 1954-1963Liefting, M., Hoffmann, A.A., Ellers, J., Measuring the plasticity of developmental rate across insect populations: comment on Rocha and Klaczko (2012) (2014) Evolution, 68, pp. 1544-1547Mensch, J., Carreira, V., Lavagnino, N., Goenaga, J., Folguera, G., Hasson, E., Fanara, J.J., Stage-specific effects of candidate heterochronic genes on variation in developmental time along an altitudinal cline of Drosophila melanogaster (2010) PLoS One, 5, pp. e11229Mensch, J., Lavagnino, N., Carreira, V.P., Massaldi, A., Hasson, E., Fanara, J.J., Identifying candidate genes affecting developmental time in Drosophila melanogaster: pervasive pleiotropy and gene-by-environment interaction (2008) BMC Dev. Biol., 8, p. 78Rocha, F.B., Klaczko, L.B., Connecting the dots of nonlinear reaction norms unravels the threads of genotype-environment interaction in Drosophila (2012) Evolution, 66, pp. 3404-3416Rocha, F., Medeiros, H.F., Klaczko, L.B., The reaction norm for abdominal pigmentation and its curve in Drosophila mediopunctata depend on the mean phenotypic value (2009) Evolution, 63, pp. 280-287Rohlf, F.J., (2010) tpsDig, version 2.16 digitize landmarks and outlines. Department of Ecology and Evolution, , State University of New York at Stony Brook, N