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In many countries, biodiversity compensation is required to counterbalance negative impacts of development projects on biodiversity by carrying out ecological measures, called offset when the goal is to reach "no net loss" of biodiversity. One main issue is to ensure that offset gains are equivalent to impact-related losses. Ecological equivalence is assessed with ecological equivalence assessment methods taking into account a range of key considerations that we summarized as ecological, spatial, temporal, and uncertainty. When equivalence assessment methods take into account all considerations, we call them "comprehensive". Equivalence assessment methods should also aim to be science-based and operational, which is challenging. Many equivalence assessment methods have been developed worldwide but none is fully satisfying. In the present study, we examine 13 equivalence assessment methods in order to identify (i) their general structure and (ii) the synergies and trade-offs between equivalence assessment methods characteristics related to operationality, scientific-basis and comprehensiveness (called "challenges" in his paper). We evaluate each equivalence assessment methods on the basis of 12 criteria describing the level of achievement of each challenge. We observe that all equivalence assessment methods share a general structure, with possible improvements in the choice of target biodiversity, the indicators used, the integration of landscape context and the multipliers reflecting time lags and uncertainties. We show that no equivalence assessment methods combines all challenges perfectly. There are trade-offs between and within the challenges: operationality tends to be favored while scientific basis are integrated heterogeneously in equivalence assessment methods development. One way of improving the challenges combination would be the use of offset dedicated data-bases providing scientific feedbacks on previous offset measures.

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, +33476762846 Acknowledgments We are thankful to Marie-Eve Reinert for her useful comments on an earlier draft of this article. We are grateful to the researchers from IRSTEA who participated in the working group on the framework development. We also thank Agnes Barillier and Frederick Jacob for relevant comments and advice on the choice of indicators, and all the organizations that collected the data on the study sites. This research was financed by the French government "CIFRE" grant for PhD students and Electricité de France (EDF).

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