Journal Article

Why “Suboptimal” Is Optimal: Jensen’s Inequality and Ectotherm Thermal Preferences

Martin, Tara Laine, Huey, Raymond B.

2008

Overview

Body temperature (T b) profoundly affects the fitness of ectotherms. Many ectotherms use behavior to controlT bwithin narrow levels. These temperatures are assumed to be optimal and therefore to match body temperatures ( \\documentclass{aastex} \\usepackage{amsbsy} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{bm} \\usepackage{mathrsfs} \\usepackage{pifont} \\usepackage{stmaryrd} \\usepackage{textcomp} \\usepackage{portland,xspace} \\usepackage{amsmath,amsxtra} \\usepackage[OT2,OT1]{fontenc} \\newcommand\\cyr{ \\renewcommand\\rmdefault{wncyr} \\renewcommand\\sfdefault{wncyss} \\renewcommand\\encodingdefault{OT2} \\normalfont \\selectfont} \\DeclareTextFontCommand{\\textcyr}{\\cyr} \\pagestyle{empty} \\DeclareMathSizes{10}{9}{7}{6} \\begin{document} \\landscape $T_{r_{\\mathrm{max}\\,}}$ \\end{document} ) that maximize fitness (r). We develop an optimality model and find that optimal body temperature (T o) should not be centered at \\documentclass{aastex} \\usepackage{amsbsy} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{bm} \\usepackage{mathrsfs} \\usepackage{pifont} \\usepackage{stmaryrd} \\usepackage{textcomp} \\usepackage{portland,xspace} \\usepackage{amsmath,amsxtra} \\usepackage[OT2,OT1]{fontenc} \\newcommand\\cyr{ \\renewcommand\\rmdefault{wncyr} \\renewcommand\\sfdefault{wncyss} \\renewcommand\\encodingdefault{OT2} \\normalfont \\selectfont} \\DeclareTextFontCommand{\\textcyr}{\\cyr} \\pagestyle{empty} \\DeclareMathSizes{10}{9}{7}{6} \\begin{document} \\landscape $T_{r_{\\mathrm{max}\\,}}$ \\end{document} but shifted to a lower temperature. This finding seems paradoxical but results from two considerations relating to Jensen’s inequality, which deals with how variance and skew influence integrals of nonlinear functions. First, ectotherms are not perfect thermoregulators and so experience a range ofT b. Second, temperature‐fitness curves are asymmetric, such that aT bhigher than \\documentclass{aastex} \\usepackage{amsbsy} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{bm} \\usepackage{mathrsfs} \\usepackage{pifont} \\usepackage{stmaryrd} \\usepackage{textcomp} \\usepackage{portland,xspace} \\usepackage{amsmath,amsxtra} \\usepackage[OT2,OT1]{fontenc} \\newcommand\\cyr{ \\renewcommand\\rmdefault{wncyr} \\renewcommand\\sfdefault{wncyss} \\renewcommand\\encodingdefault{OT2} \\normalfont \\selectfont} \\DeclareTextFontCommand{\\textcyr}{\\cyr} \\pagestyle{empty} \\DeclareMathSizes{10}{9}{7}{6} \\begin{document} \\landscape $T_{r_{\\mathrm{max}\\,}}$ \\end{document} depresses fitness more than will aT bdisplaced an equivalent amount below \\documentclass{aastex} \\usepackage{amsbsy} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{bm} \\usepackage{mathrsfs} \\usepackage{pifont} \\usepackage{stmaryrd} \\usepackage{textcomp} \\usepackage{portland,xspace} \\usepackage{amsmath,amsxtra} \\usepackage[OT2,OT1]{fontenc} \\newcommand\\cyr{ \\renewcommand\\rmdefault{wncyr} \\renewcommand\\sfdefault{wncyss} \\renewcommand\\encodingdefault{OT2} \\normalfont \\selectfont} \\DeclareTextFontCommand{\\textcyr}{\\cyr} \\pagestyle{empty} \\DeclareMathSizes{10}{9}{7}{6} \\begin{document} \\landscape $T_{r_{\\mathrm{max}\\,}}$ \\end{document} . Our model makes several predictions. The magnitude of the optimal shift ( \\documentclass{aastex} \\usepackage{amsbsy} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{bm} \\usepackage{mathrsfs} \\usepackage{pifont} \\usepackage{stmaryrd} \\usepackage{textcomp} \\usepackage{portland,xspace} \\usepackage{amsmath,amsxtra} \\usepackage[OT2,OT1]{fontenc} \\newcommand\\cyr{ \\renewcommand\\rmdefault{wncyr} \\renewcommand\\sfdefault{wncyss} \\renewcommand\\encodingdefault{OT2} \\normalfont \\selectfont} \\DeclareTextFontCommand{\\textcyr}{\\cyr} \\pagestyle{empty} \\DeclareMathSizes{10}{9}{7}{6} \\begin{document} \\landscape $T_{r_{\\mathrm{max}\\,}}-T_{\\mathrm{o}\\,}$ \\end{document} ) should increase with the degree of asymmetry of temperature‐fitness curves and withT bvariance. Deviations should be relatively large for thermal specialists but insensitive to whether fitness increases with \\documentclass{aastex} \\usepackage{amsbsy} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{bm} \\usepackage{mathrsfs} \\usepackage{pifont} \\usepackage{stmaryrd} \\usepackage{textcomp} \\usepackage{portland,xspace} \\usepackage{amsmath,amsxtra} \\usepackage[OT2,OT1]{fontenc} \\newcommand\\cyr{ \\renewcommand\\rmdefault{wncyr} \\renewcommand\\sfdefault{wncyss} \\renewcommand\\encodingdefault{OT2} \\normalfont \\selectfont} \\DeclareTextFontCommand{\\textcyr}{\\cyr} \\pagestyle{empty} \\DeclareMathSizes{10}{9}{7}{6} \\begin{document} \\landscape $T_{r_{\\mathrm{max}\\,}}$ \\end{document} (“hotter is better”). Asymmetric (left‐skewed)T bdistributions reduce the magnitude of the optimal shift but do not eliminate it. Comparative data (insects, lizards) support key predictions. Thus, “suboptimal” is optimal.

• Publisher: The University of Chicago Press
• Subject: Animals / Body temperature / Body Temperature Regulation / Darwinism / Datasets / Ecological competition / E‐Article / Invertebrates - physiology / Lacertilia / Lizards / Lizards - physiology / Modeling / Models, Biological / Personality traits / Predictive Value of Tests / Speed / Temperature dependence / Thermoregulation