When it comes to fitting simple allometric slopes through measurement data, evolutionary biologists have been torn between regression methods. On the one hand, there is the ordinary least squares (OLS) regression, which is commonly used across many disciplines of biology to fit lines through data, but which has a reputation for underestimating slopes when measurement error is present. On the other hand, there is the reduced major axis (RMA) regression, which is often recommended as a substitute for OLS regression in studies of allometry, but which has several weaknesses of its own. Here, we review statistical theory as it applies to evolutionary biology and studies of allometry. We point out that the concerns that arise from measurement error for OLS regression are small and straightforward to deal with, whereas RMA has several key properties that make it unfit for use in the field of allometry. The recommended approach for researchers interested in allometry is to use OLS regression on measurements taken with low (but realistically achievable) measurement error. If measurement error is unavoidable and relatively large, it is preferable to correct for slope attenuation rather than to turn to RMA regression, or to take the expected amount of attenuation into account when interpreting the data.

Mate preferences are important causes of sexual selection. They shape the evolution of sexual ornaments and displays, sometimes maintaining genetic diversity and sometimes promoting speciation. Mate preferences can be challenging to study because they are expressed in animal brains and because they are a function of the features of potential mates that are encountered. Describing them requires taking this into account. We present a method for describing and analysing mate preference functions, and introduce a freely available computer program that implements the method. We give an overview of how the program works, and we discuss how it can be used to visualize and quantitatively analyse preference functions. In addition, we provide an informal review of different methods of testing mate preferences, with recommendations for how best to set up experiments on mate preferences. Although the program was written with mate preferences in mind, it can be used to study any function-valued trait, and we hope researchers will take advantage of it across a broad range of traits.

Study of the genetic and developmental architecture of mate preferences lags behind the study of sexual ornaments. This is in part because of the challenges involved in describing mate preferences, which are expressed as a function of variation in ornaments. We used the function-valued approach to test for genetic and environmental components of variation in female mate preferences in Enchenopa treehoppers (Hemiptera: Membracidae). These insects communicate with plant-borne vibrational signals, and offer a case study of speciation involving sexual selection and environmental change. We focused on female preferences for male signal frequency, the most divergent signal trait in Enchenopa. Obtaining complete, individuallevel descriptions of mate preferences in a full-sib, split-family rearing experiment, we document substantial genetic variation in mate preference functions. Focusing on traits describing variation in the shape of the preference functions, we further document considerable broad-sense heritability and evidence of weak genotype 9 environment interaction in most traits. Against the background of recent and rapid divergence in Enchenopa, these results indicate potent mechanisms that maintain variation and sustain the involvement of mate preferences in sexual selection.

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