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

• Published in: The American naturalist Vol. 171; no. 3; pp. E102 - E118
• Main Authors: Martin, Tara Laine, Huey, Raymond B.
• Format: Journal Article
• Language: English
• Published: United States The University of Chicago Press 01-03-2008
• Subjects: 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; thermal sensitivity; thermodynamics; thermal preference; optimality; thermoregulation; fitness
• ISSN: 0003-0147; 1537-5323
• DOI: 10.1086/527502

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 (
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) that maximize fitness (r). We develop an optimality model and find that optimal body temperature (T
o) should not be centered at
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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
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depresses fitness more than will aT
bdisplaced an equivalent amount below
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. Our model makes several predictions. The magnitude of the optimal shift (
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) 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
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(“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.