Freshwater fisheries conservation can increase biodiversity

and ethnic heterogeneity) and, finally, a preliminary discussion regarding willingness in changing the way that local fisheries are managed. It also includes the clarification of whether deep pools exist (as the creation of FCZ hinges on its existence). This step typically involves one or more visits by WWF staff (facilitated by local government authorities), from which then emerges a final list of eligible villages. The next steps involve the drafting and re-drafting of local regulations. The approval of these regulations at local level (including informing neighbouring villages and government bodies, such as police, of their existence) precedes the formal approval by the District Gover- nor. The process ends with the advertising of the new fishing regulations as well as the limits of the newly created FCZ (usually, through the use of public signboards). Statistical analysis We follow Rubin’s potential outcome model of causal inference [24] and start by stating that each unit of analysis in the population of interest (village) has two potential biodiversity out- comes (number of species), one when ComFishIII is implemented (Yi(1)) and another one in its absence (Yi(0)). The actually observed outcome (Yobs) can be expressed as a combination of these two potential outcomes according to the expression: Yobs ¼ TiYið1Þ þ ð1 TiÞYið0Þ ð1Þ where Ti = {0, 1} indicates treatment status (= 1 if participating in program, 0 otherwise), mak- ing clear that we cannot observe counterfactual potential outcomes—for example, [Yi(0)jTi =

1] defined as the outcome of a treated unit had it not been treated. If nothing can be done at individual level, at population level we can quantify the Average Treatment on Treated (ATT) as ATT ¼ E½Yið1Þ Yið0Þ j Ti ¼ 1� ¼ E½Yið1Þ j Ti ¼ 1� E½Yið0Þ j Ti ¼ 1� ð2Þ where E[.] is the expectation operator and Ti = 1 indicates that the unit participated in the pro- gram. If a program is randomly placed then, by design, units participating in the program will be (on average) identical to those that do not participate, hence E½Yið0Þ j Ti ¼ 1� ¼ E½Yið0Þ j Ti ¼ 0� ð3Þ and the ATT takes the simple form of E[Yi(1) j Ti = 1] − E[Yi(0) j Ti = 0]. When the program is purposefully placed and/or participation is voluntary, there is no a priori certainty that Eq 3 is satisfied, raising the need to consider quasi-experimental designs that adequately address this problem—see [25] for a review of different approaches in the context of environmental programs. Matching, the approach used here, aims to eliminate the effect of any imbalance in the dis- tribution of potential outcomes (and the effect of confounders on potential outcomes) on the estimates of ATT. In these designs, the counterfactual is then expressed as E½Yið1Þ j Ti ¼ 1; X� ¼ E½Yið0Þ j Ti ¼ 0; X� ð4Þ which formalizes the Conditional Independence Assumption (CIA), ie, that once we account for the effect of all potential confounders X, program participation is as if random in the sense that it is independent of potential outcomes. [26] shows that the effect of X can be summarized

by an appropriate specification of the probability of participating in the program, also known as the propensity score. Given that the allocation of many environmental programs is not usu- ally randomized, matching on the propensity score is a widely supported alternative approach PLOS ONE FCZ and biodiversity PLOS ONE | https://doi.org/10.1371/journal.pone.0233775 May 27, 2020 3 / 14