This work discusses repertory grid analysis as a tool for investigating the structures of students' representations of biological concepts. Repertory grid analysis provides the researcher with a variety of techniques that are not associated with standard methods of concept mapping for investigating conceptual structures. It can provide valuable insights into the learning process, and can be used as a diagnostic tool in identifying problems that students have in understanding biological concepts. The biological concepts examined in this work are 'natural kinds': a technical class of concepts which "appear" to have invisible "essences" meaning carrying more perceptual weight than being perceptually similar. Because children give more weight to natural-kind membership when reasoning about traits, it would seem pertinent to apply such knowledge to deep-level research into how children reason in biology. The concept of natural kinds has a particular resonance with biology since biological kinds hold the distinction of being almost all natural kinds, such as when the same "stuff or thing" takes many different forms. We have conducted a range of studies using a diversity of biological natural kinds, but in this paper, we wish to explore some of the theoretical underpinnings in more detail. To afford this exploration, we outline one case-study in a small group of secondary school students exploring the concept of "equine"--that is, what is an equine? Five positive examples were chosen to engaged with by the students and one "outlier" with which to compare the construction process. Recommendations are offered in applying this approach to biological education research.