Table 1 Main hypotheses relating effects of Marine Protected Areas (MPA) on site (alpha) stability, species stability and asynchrony, compared to open areas (OA)

Within sites (communities)

MPA → alpha stability

MPA are more stable than OA.

Greater stability (lower fluctuations) in abundance of individual species and greater functional richness increases stability in MPA compared to OA.

^{13,15,16,17,18,22}

MPA → species stability → alpha stability

Stronger positive relationship between alpha stability and species stability in MPA than OA.

MPA increase alpha stability by maintaining more stable populations compared to OA.

^13,22,23,24

§MPA → asynchrony → alpha stability

The contribution of asynchrony to stability is stronger (weaker) in MPA than OA.

MPA increase (decrease) asynchrony if relieve from fishing and direct human disturbances induce divergent (coherent) temporal fluctuations in fishes.

^10,11,34,35

MPA → MHW → species and alpha stability

Alpha and species stability decline more abruptly with intensifying MHW in OA than MPAs.

MPA buffer reef fishes from MHW by maintaining greater population abundances, functional richness and asynchronous fluctuations, all of which contribute to increase stability.

¹⁸

MPA → Remoteness → species and alpha stability

Stronger positive relationship between alpha and species stability with remoteness in MPA than OA.

Remote MPA are relieved from both fishing and direct human impacts, whereas fishing can still impact remote sites in OA, decreasing alpha and species stability.

⁴⁰

MPA → temperature niche

Stronger positive relationship between the abundance of thermally resistant species with intensifying MHW in MPA than OA.

MPA support higher fish abundances and promote stability by allowing thermally resistant species to attain large population sizes under intensifying warming conditions.

^18,61,62

Among sites (metacommunities)

MPA → gamma stability and underlying mechanisms

Greater asynchrony and stability in MPA than OA at the metacommunity scale.

Local effects of MPA on species stability and asynchrony scale-up at the metacommunity level.

^44,45,65

Size of MPA network → gamma stability and underlying mechanisms

Differences between MPA and OA increase with the size of MPA networks.

Gamma stability and the underlying mechanisms operate more strongly in large MPA networks embracing a wide range of habitats and environmental conditions.

^44,45,65