Evol Ecol Res 7: 421-434 (2005)     Full PDF if your library subscribes.

Likelihood models for discriminating alternative phenotypes in morphologically dimorphic species

J. Mark Rowland1* and Clifford R. Qualls2

1Department of Biology and  2Department of Mathematics and Statistics, University of New Mexico, Albuquerque, NM 87131, USA

Author to whom all correspondence should be addressed.
e-mail: rowland@unm.edu


Question: How can we numerically discriminate with explicit confidence the alternative phenotypes in dimorphic species with bimodal threshold traits?

Mathematical method: A bimodal distribution of a dimorphic trait is parameterized by mixture distribution models for normal and gamma distributions. Likelihood ratios of the alternative phenotypes for a given trait size are computed from the mixture models. The likelihood models are tested in several horn-dimorphic beetles and compared with existing piece-wise linear regression methods.

Key assumptions: The bimodal distribution represents a mixture of two discrete distributions. The alternative phenotypes have normal or gamma distributions.

Conclusions: Likelihood methods effectively model the way in which alternative phenotypes are expressed in taxa with bimodal trait size frequency distributions. New likelihood models estimate the probability that a given trait size represents a given phenotype in normal to skewed bimodal frequency distributions. These prove theoretically and empirically superior to linear regression methods. Likelihood methods model the behaviour of threshold mechanisms in natural populations and will enhance exploration of the evolutionary significance of intraspecific conditional phenotypes.

Keywords: alternative tactics, horn dimorphism, intrasexual polyphenism, likelihood models, threshold traits.

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