A recently developed technique, ‘Astrocladistics’, has been used to analyze a variety of astronomical objects, from galaxies to the satellite systems of the giant planets. The method was originally developed in a biological context, the ‘Tree of Life’, and adapted for use in astronomy. In this work, we use the novel astrocladistical method to examine the relationships between objects in the Jovian Trojan population - two swarms of small Solar system bodies that librate around the L4 and L5 Lagrange points of Jupiter. These objects are of particular interest for researchers as it is thought they were captured to their current location early in the Solar system’s history. Given the importance of such studies, six Trojans are due to be visited by the Lucy spacecraft, launching in 2021. For each Trojan in our astrocladistical analysis, a set of binned characteristics are used, including dynamical properties, albedo, density, along with color ratios from SDSS, WISE, Gaia DR2, and the MOVIS surveys. Not all Trojans are present in each survey, and these differences in available data are accounted for in the algorithm. This highlights one of the advantages of astrocladistics, namely its ability to work with incomplete datasets and return meaningful results. We limit the selection for this study to those Jovian Trojans that have color measurements from at least one survey, including each of the Lucy targets. The results are dendritic trees, which allow us to visualize the relationships between the Jovian Trojans. One of the outcomes of this project is the ability to identify additional, high priority targets for observation. By clustering the population into clans, several mid-sized objects are identified that could provide valuable additional information from follow-up observations. An additional outcome from the analysis is that we are able to make preliminary characterization of objects, even where information is limited. We demonstrate this with some remarks on a recently identified Trojan pair, the first such relationship to be identified in the population. These outcomes highlight two of the potential ways that astrocladistics can be used in a planetary science context.