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ABSTRACT Even as numerous studies have documented that the red and yellow coloration resulting from the deposition of carotenoids serves as an honest signal of condition, the evolution of condition dependency is contentious. The resource trade‐off hypothesis proposes that condition‐dependent honest signalling relies on a trade‐off of resources between ornamental display and body maintenance. By this model, condition dependency can evolve through selection for a re‐allocation of resources to promote ornament expression. By contrast, the index hypothesis proposes that selection focuses mate choice on carotenoid coloration that is inherently condition dependent because production of such coloration is inexorably tied to vital cellular processes. These hypotheses for the origins of condition dependency make strongly contrasting and testable predictions about ornamental traits. To assess these two models, we review the mechanisms of production of carotenoids, patterns of condition dependency involving different classes of carotenoids, and patterns of behavioural responses to carotenoid coloration. We review evidence that traits can be condition dependent without the influence of sexual selection and that novel traits can show condition‐dependent expression as soon as they appear in a population, without the possibility of sexual selection. We conclude by highlighting new opportunities for studying condition‐dependent signalling made possible by genetic manipulation and expression of ornamental traits in synthetic biological systems.
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Concavity of solutions to semilinear equations in dimension two
Abstract We consider the Dirichlet problem for a class of semilinear equations on two‐ dimensional convex domains. We give a sufficient condition for the solution to be concave. Our condition uses comparison with ellipses, and is motivated by an idea of Kosmodem'yanskii. We also prove a result on propagation of concavity of solutions from the boundary, which holds in all dimensions.
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- Award ID(s):
- 2005311
- PAR ID:
- 10420131
- Publisher / Repository:
- Oxford University Press (OUP)
- Date Published:
- Journal Name:
- Bulletin of the London Mathematical Society
- Volume:
- 55
- Issue:
- 2
- ISSN:
- 0024-6093
- Page Range / eLocation ID:
- p. 706-716
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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