Species-occupancy distribution removes an excessive parameter from species-area relationship

Aim Although species-occupancy distributions (SODs) and species-area relationships (SARs) arise from the two marginal sums of the same presence/absence matrices, the two biodiversity patterns are usually explored independently. Here, we aim to unify the two patterns for isolate-based data by constraining the SAR to conserve information from the SOD. Location Widespread. Methods Focusing on the power-model SAR, we first developed a constrained form that conserved the total number of occupancies from the SOD. Next, we developed an additive-constrained SAR that conserves the entire shape of the SOD within the power-model SAR function, using a single parameter (the slope of the endemics-area relationship). We then relate this additive-constrained SAR to multiple-sites similarity measures, based on a probabilistic view of Sørensen similarity. We extend the constrained and additive-constrained SAR framework to 23 published SAR functions. We compare the fit of the original and constrained forms of 12 SAR functions using 154 published data sets, covering various spatial scales, taxa and systems. Main conclusions In all 23 SAR functions, the constrained form had one parameter less than the original form. In all 154 data sets the model with the highest weight based on the corrected Akaike's information criteria (wAICc) had a constrained form. The constrained form received higher wAICc than the original form in 98.79% of valid pairwise cases, approaching the wAICc expected under identical log-likelihood. Our work suggests, both theoretically and empirically, that all SAR functions may have one unnecessary parameter, which can be excluded from the function without reduction in goodness-of-fit. The more parsimonious constrained forms are also easier to interpret as they reflect the probability of a randomly chosen occupancy to be found in an isolate. The additive-constrained SARs accounts for two complimentary turn-over components of occupancies: turnover between species and turnover between sites.