Topical discussion networks (TDNs) are networks centered around a discourse concerning a particular concept, whether in real life or online. This paper analogises the population of such networks to populations encountered in mathematical ecology, and seeks to evaluate whether three metrics of diversity used in ecology - Shannon's $H'$, Simpson's $λ$ and $E_{var}$ proposed by Smith and Wilson - give valuable information about the composition and diversity of TDNs. It concludes that each metric has its particular use, and the choice of metric is best understood in the context of the particular research question.