ABSTRACT: The legacy of the 'SL > SS principle', that a single or a few large habitat patches (SL) conserve more species than several small patches (SS), is evident in decisions to protect large patches while down-weighting small ones. However, empirical support for this principle is lacking, and most studies find either no difference or the opposite pattern (SS > SL). To resolve this dilemma, we propose a research agenda by asking, 'are there consistent, empirically demonstrated conditions leading to SL > SS?' We first review and summarize 'single large or several small' (SLOSS) theory and predictions. We found that most predictions of SL > SS assume that between-patch variation in extinction rate dominates the outcome of the extinction-colonization dynamic. This is predicted to occur when populations in separate patches are largely independent of each other due to low between-patch movements, and when species differ in minimum patch size requirements, leading to strong nestedness in species composition along the patch size gradient. However, even when between-patch variation in extinction rate dominates the outcome of the extinction-colonization dynamic, theory can predict SS > SL. This occurs if extinctions are caused by antagonistic species interactions or disturbances, leading to spreading-of-risk of landscape-scale extinction across SS. SS > SL is also predicted when variation in colonization dominates the outcome of the extinction-colonization dynamic, due to higher immigration rates for SS than SL, and larger species pools in proximity to SS than SL. Theory that considers change in species composition among patches also predicts SS > SL because of higher beta diversity across SS than SL. This results mainly from greater environmental heterogeneity in SS due to greater variation in micro-habitats within and across SS habitat patches ('across-habitat heterogeneity'), and/or more heterogeneous successional trajectories across SS than SL. Based on our review of the relevant theory, we develop the 'SLOSS cube hypothesis', where the combination of three variables - between-patch movement, the role of spreading-of-risk in landscape-scale population persistence, and across-habitat heterogeneity - predict the SLOSS outcome. We use the SLOSS cube hypothesis and existing SLOSS empirical evidence, to predict SL > SS only when all of the following are true: low between-patch movement, low importance of spreading-of-risk for landscape-scale population persistence, and low across-habitat heterogeneity. Testing this prediction will be challenging, as it will require many studies of species groups and regions where these conditions hold. Each such study would compare gamma diversity across multiple landscapes varying in number and sizes of patches. If the prediction is not generally supported across such tests, then the mechanisms leading to SL > SS are extremely rare in nature and the SL > SS principle should be abandoned.
