Pathways from marine protected area design and management to ecological success

Qualitative comparative analysis

QCA uses set theory relationships to identify configurations of conditions that, when present, are necessary or sufficient to lead to outcomes of interest (Ragin, 1987; Ragin, 2000; Schneider & Wagemann, 2012). Each case (i.e., one of 121 MPAs in this analysis) is considered as a configuration of causally relevant conditions (i.e., combinations of the presence or absence of NEOLI conditions) and an outcome (i.e., metrics of fish biomass or species richness). QCA comparatively identifies similarities and differences across cases where different, context-dependent paths lead to particular outcomes of interest (Rihoux, 2013). Boolean minimization algorithms in QCA software (Ragin & Davey, 2014) succinctly express causal regularities in the data. Results from analyses are contextual in that the causal power of a condition often depends on the presence of absence of other causal conditions.

To illustrate how QCA can provide information regarding pathways to successful ecological outcomes, consider how contextual social and governance factors influence ecological success in small-scale fisheries in Southeast Asia (Sutton & Rudd, 2015). Among 50 case studies, multiple pathways involving various combinations of social and governance conditions led to local ecological successes, defined on a scale from extremely degraded to thriving local fish stocks. One pathway to success involved the presence of a community organization involved in community-based fisheries management in combination with a degree of autonomy in local governance decision-making at the community level. A second pathway to positive ecological results arose when local fisheries were subsistence oriented, even in the absence of local decision-making powers. Another pathway involved strong local leadership: even with weak local decision-making powers and a market-oriented local fishery, positive ecological outcomes were observed, suggesting local leadership could help mobilize a degree of restraint in local fisheries that helped ameliorate some external stressors. Together these three alternative pathways accounted for 69% of cases where successful ecological outcomes were attained.

Data coding

Case conditions and outcomes may be coded as dichotomous ‘crisp sets’ that dichotomously classify variables as 0 or 1 (fully out of or in a set) or as ‘fuzzy sets’ that exhibit partial membership in the set of an ideal type (Ragin, 2000). Edgar et al. (2014) originally coded the NEOLI conditions into low-medium-high categories for each variable. As the most important differences in their study was between medium and high levels of NEOLI conditions (see Fig. 3, Edgar et al., 2014), and conditions in the middle of a scale provide no additional information useful for differentiating sets in QCA (membership of 50% in a condition’s set is the point of maximum ambiguity in QCA), I aggregated low and medium levels to form crisp set definitions of NEOLI conditions (Table 1). Each condition was thus either fully in or fully out as a member of each set. This aggregation was carried out based on patterns observed in Edgar et al.’s (2014) results and prior to any QCA data analysis.

All ecological outcomes in the Edgar et al. (2014) dataset were measured during reef scuba surveys as biomass or fish species richness per 250 m². I log-transformed (ln[n +1]) them to fuzzy set membership values in a calibration process. If fish species richness or biomass exceeded the 90th percentile for that outcome across all 121 MPAs, they were considered fully in that condition’s set of successful outcomes; if fish species richness or biomass was less than the 10th percentile, they were considered fully out of the set (Table 2). The crossover was the point where an MPA with an overall fish biomass level of 14,765 g per 250 m² would, for example, be assigned 0.50 membership in the set High biomass (and by implication 0.50 in a set NOT[High biomass]). There are no theoretical reasons for defining ‘high’ levels of outcomes at particular levels but some MPAs within the Reef Life Survey dataset were functionally pristine, so full set membership in a positive outcome (i.e., >90th percentile for that condition) should indicate performance that is truly high in the range of possibilities. Note that a biomass of 120,572 g per 250 m² corresponds to approximately 4,800 kg per ha, a figure well in excess of values suggested as baselines to define pristine reef fish biomass (MacNeil et al., 2015).

MPAs with only one or two NEOLI conditions performed poorly and were statistically indistinguishable from fished sites (Edgar et al., 2014). The lower 10th percentile cut-off that defined outcomes as fully outside the set of successful outcomes should thus reflect truly poor levels of MPA performance. Table 3 details the coding for each MPA (starting with MPAs exhibiting all five NEOLI conditions at the top of the table, proceeding through groupings of MPAs with decreasing numbers of NEOLI conditions, and ending with those MPAs that had only a single NEOLI condition; when multiple sites from the 121 international MPA/ecoregion groupings are from a single large MPA, they are denoted, for example, as Galapagos a to Galapagos e).

Truth tables

Truth tables show the connection between all possible configurations of causal conditions that lead to an outcome of interest. The columns represent sets of causal conditions and an outcome, while the rows represent all logically possible intersections among the relevant sets. There is an exponential increase in configuration space as the number of conditions increases, with 2^k ideal types for k conditions. Assignment of an MPA to a configuration was based on the MPA’s membership in each condition’s set and the number of empirical instances of each output of interest was recorded for each configuration. The default inclusion level was set at 0.70 (e.g., a configuration with inclusion = 0.72 would be deemed to ‘usually’ belong to the set High biomass) for testing sufficiency and 0.90 for testing necessity (see Rihoux & Ragin, 2009). In truth tables, outcomes with inclusion levels in excess of the cut-off were coded as successful (inclusion = 1); configurations not meeting the cut-off were coded as unsuccessful (inclusion = 0).

Necessary and sufficient conditions

A truth table forms a Boolean function that can be expressed as a union of fundamental set intersections, each of which corresponds to a successful outcome (Thiem & Duşa, 2013). If a condition is necessary for an outcome, the condition is a superset of the outcome (i.e., the outcome occurs only in the presence of the condition). If a condition is sufficient for an outcome, the condition is a subset of the outcome (i.e., the outcome always occurs only in the presence of the condition but also in its absence).

To give a practical example, suppose that high levels of fish biomass were observed in five MPAs, two of which allowed fishing and three of which prohibited fishing: prohibition of fishing would not be a necessary condition for the positive ecological outcome. However, if in the three cases where fishing was prohibited there were three positive outcomes and no negative outcomes, a prohibition on fishing could be sufficient for achieving the positive ecological outcome.

Boolean logic is used to simplify those set relations from the truth table to as few conditions as are defensible from a theoretical or empirical perspective. The level of Boolean minimization depends on assumptions made regarding the feasibility of the ‘logical remainders’, those configurations for which there are no empirical instances, and the minimum number of empirical instances needed for a configuration to be retained in a model (setting a cut-off level can help dampen noisiness arising from outlying cases). I used a default frequency cut-off of two empirical instances to assess necessary and sufficient conditions. If one assumes that, if observed, none of the logical remainders would result in a positive outcome, the result is the ‘complex solution’. On the other hand, if one assumes that all logical remainders would result in a positive outcome, a ‘parsimonious solution’ with the simplest possible sufficiency conditions results. These two solutions bound the complexity of the Boolean sufficiency conditions.

In QCA models, solution coverage assesses the extent to which a particular combination of causal conditions accounts for empirical instances of an outcome (Schneider & Wagemann, 2012). For example, overall coverage of 0.75 by two sufficient conditions would mean that of all empirical observations of the outcome of interest, 75% could be explained by one or the other (or both) of the conditions. Consistency, on the other hand, refers to the degree to which cases with a shared combination of causal conditions results in an outcome of interest (Schneider & Wagemann, 2012). For example, if a sufficient condition exhibited 0.80 consistency, 80% of all the occurrences of that particular combination of conditions would lead to the outcome of interest.

Models

Sixteen models were estimated in total, one each based on the presence or negation of each of the eight sets of ecological outcomes (species richness; species richness of large (>250 mm) fish; biomass of all fish; biomass of large fish; biomass of damselfish; biomass of jacks; biomass of groupers; biomass of sharks). I used Ragin’s fsQCA software (Ragin & Davey, 2014) for all analyses.

Model 1: High biomass

To illustrate QCA model interpretation, I present detailed results from the High biomass model before briefly summarizing the remaining models. Considering only configurations with two or more empirical instances each, 117 MPAs were represented in 23 NEOLI configurations. Of those, 17 cases in seven configurations exhibited inclusion levels >0.70 and were coded as members of (i.e., ‘usually in’) the set High biomass (Table 6). The High biomass set included the configuration where all five NEOLI conditions were present and one of the two observed configurations with four NEOLI conditions. The other configuration with four NEOLI conditions (No-take, Enforced, Old, Large) fell below the cut-off needed to ‘usually’ belong to the set High biomass.

In the model’s complex solution (Eq. 1.C), five different pathways, derived by Boolean manipulation of the combinations of conditions in rows 1–7 of Table 6, were sufficient to result in high levels of fish biomass. Five conditions in each pathway are combined by logical AND operators; upper case denotes presence of condition and lower case denotes absence of a condition; dash denotes that a condition can be either present or absent; + denotes logical OR. To illustrate, the first condition,-eoLI, can be interpreted as follows: to achieve high levels of overall fish biomass via pathway 1.C1, the MPA can be either fished or not (i.e., N has no effect) AND enforcement is absent AND the MPA is not more than 10 years old AND the MPA is larger than 100 km² AND the MPA is ecologically isolated (note that this corresponds to a total of 5 MPAs in the sample, the configuration represented by rows 2 and 7 in Table 6). In aggregate, the five pathways in the complex solution in combination provided 0.211 coverage and their level of aggregate inclusion was 0.838. The five pathways themselves each provided between 0.049 and 0.078 raw coverage individually; unique coverage for each pathway ranged from 0.021 to 0.055 and inclusion levels ranged from 0.827 to 0.878. ({1.C})${\displaystyle \text{-}eo\mathit{LI}+n\text{-}o\mathit{LI}+ne\text{-}\mathit{LI}+\mathit{NE}\text{-}l\mathit{I}+\mathit{NEO}\text{-}\mathit{I}\to Highbiomass.}$

With the exception of Isolated, the conditions that formed pathways to High biomass could have either positive or negative effects on overall fish biomass depending on the context in which they occurred. While it may at superficially appear that Isolated is necessary for High biomass outcomes (because Isolated appears in each of the five pathways that combine to lead to High biomass), recall that the definition of a necessary condition is that it is a superset of the outcome: the outcome only appears in the presence of the condition. Table 6 showed, however, that row 12 (neO l I) had three empirical instances where High biomass was not achieved even though the MPAs were isolated; if Isolated were a necessary condition, these MPAs would also have exhibited a High biomass outcome. Neither can one say that Isolated is sufficient, on its own, to lead to positive outcomes. Considering only cases where High biomass was observed—the first seven rows of Table 6—Isolated appears in all configurations but never on its own, only in combination with other conditions in the seven distinct MPA configurations that lead to High biomass. Eight of nine logical remainders included Isolated, further highlighting the potential nuance of the role of ecological isolation—the complex solution assumes that none of the logical remainders would, if actually observed, result in high biomass (a point we return to in the Discussion).

Solution (1.C) exhibited configurational complexity in that multiple alternative pathways led to a single outcome of interest. The first three pathways comprising the complex solution highlighted that large, isolated MPAs could compensate, in terms of overall production of fish biomass, for some fishing within MPAs or in the face of weak enforcement, even in young MPAs. Pathways three and four implied that Large and the combination of No-take and Enforced were substitutes in the production of high levels of fish biomass within MPAs.

When the five pathways in the complex solution were simplified as much as possible with Boolean logic (i.e., assuming all logical remainders, if actually observed, would result in High biomass), the parsimonious solution (1.P) consisted of two pathways sufficient for achieving high levels of fish biomass within MPAs: ({1.P})${\displaystyle \mathit{LI}+\mathit{EI}\to Highbiomass}$

Based on the ecological performance of the 17 MPAs that surpassed a reasonable threshold that qualified them as members of the set High biomass, ecological isolation in combination with either large area or effective enforcement were the simplest configurations that led to High biomass on a consistent basis. MPAs needed have only two NEOLI conditions and neither solution involved the presence of either No-take or Old. Moving from the complex to parsimonious solution increased coverage slightly from 0.211 to 0.238 and reduced inclusion from 0.838 to 0.804. The parsimonious pathways did not demonstrate the same level of subtlety as did the more stringent complex model. In the complex solution, a total of 17 specific MPAs were covered by the five sufficient pathways leading to High biomass (Table 7). A total of 20 MPAs were covered under the less stringent parsimonious solution.

There were 14 cases with greater than 0.50 membership in pathway LI [Large AND Isolated], 13 cases with greater than 0.50 membership were covered by pathway EI [Enforced AND Isolated], and an overlap of 7 cases. Figure 1A shows an area-proportional Venn diagram (Micallef & Rodgers, 2014) with the set High biomass normalized to 100%. Solution coverage was 0.238 (0.065 + 0.089 + 0.084): the two solution pathways covered 23.8% of the area the set High biomass and the solution inclusion was 0.804 (i.e., 19.6% of the area of the two sufficient pathways fell outside of the High biomass set, in the set NOT[High biomass]). In Fig. 1B, the MPAs are mapped onto the sets of conditions and outcome. Low coverage left much of the set of High biomass unexplained and implies other conditions and sufficiency pathways are important in explaining high levels of overall fish biomass at the 121 MPAs.

A more stringent consistency cut-off in the model would constrain solution boundaries. For example, increasing the inclusion cut-off to 0.85 in the first stage of the modeling process (i.e., imposing a more stringent definition of ‘usually in’ the set High biomass) would reduce the number of cases used in the Boolean analysis to nine empirical instances (coverage = 0.145) arising from three different configurations of MPA conditions (all still involving Isolated).

Model 2: NOT[High biomass]

In addition to analysis of positive ecological outcomes from MPAs, the QCA analysis in the second model identified sufficient conditions needed to lead to set negation, the set of all MPAs belonging to NOT[High biomass]. Two cases in a single configuration exhibited consistency levels >0.70 and were coded as members of the set NOT[High biomass]. The complex solution could not be simplified, coverage was 0.034, and a single pathway (Eq. 2.C/2.P) described a sufficient condition leading to the absence of high levels of fish biomass: ({2.C/2.P})${\displaystyle \mathit{N}eo\mathit{L}i\to NOT\text{[High biomass]}}$

This pathway consisted of a very specific configuration involving all five conditions (2 present, 3 absent) and had only two empirical instances, the Costa Rican Caletas (row 7) and Camaronal (row 8) MPAs. NEOLI conditions played an extremely limited role in explaining pathways to low levels of overall fish biomass (Fig. 2). Some 97% of low biomass outcomes could not be explained by this solution, implying that other pathways not dependent on either the presence or absence of NEOLI conditions explained low levels of fish biomass (note the striking contrast in low biomass outcomes when comparing all fish species to commercially exploited species—see models 8, 10, and 12 below).

Model 3: High large fish biomass

The complex solution (3.C) consisted of five pathways sufficient to lead to High large fish biomass. Table 8 shows model diagnostics for all parsimonious solutions leading to positive ecological outcomes. The parsimonious solution (3.P) consisted of a single pathway comprised of a single condition, ecological isolation. Three MPAs that were not part of the complex solution (78. Bonaire; 101. Lord Howe Commonwealth MPA b; 115. Seaflower Area Marina Protegida b) were part of the parsimonious solution simply by virtue of their ecological isolation. ({3.C})${\displaystyle ne\mathit{O}\text{-}\mathit{I}+\text{-}eo\mathit{LI}+n\text{-}o\mathit{LI}+\mathit{NE}\text{-}l\mathit{I}+\mathit{NEO}\text{-}\mathit{I}\to Highlargefishbiomass}$ ({3.P})${\displaystyle \text{—-}\mathit{I}\to Highlargefishbiomass}$

Model 4: NOT[High large fish biomass]

In total, seven MPAs were used to calculate a parsimonious solution (4.P) that included two sufficient pathways to membership in NOT[High large fish biomass] (Table 9 shows parsimonious solutions for all negated models; all complex solutions are available from the author upon request). In model 4, the parsimonious and complex solutions (4.C) coincided as no Boolean simplifications were possible. Note that, contrary to received wisdom about MPA size, Large figured in both sufficient pathways to low biomass outcomes; but recall it was also a condition in two pathways to High large fish biomass, demonstrating that the effect of MPA size was highly context dependent. ({4.P/4.C})${\displaystyle \text{-}eo\mathit{L}i+ne\text{-}\mathit{L}i\to NOT\text{[High large fish biomass]}}$

Models 5–16

The remaining models for various ecological outcomes are outlined in Tables 8 and 9. Note that in Model 8 a total of 40 cases in seven configurations were coded as members of the negated set NOT[High grouper biomass]. This was the first model to achieve over 0.50 coverage, where four sufficient pathways in the parsimonious solution accounted for over half of all observed MPAs with low levels of grouper biomass. Similarly, 42 cases (coverage = 0.542) in Model 10 and 54 cases in Model 12 (coverage = 0.706) were coded as members of the negated sets NOT[High jack biomass] and NOT[High shark biomass], respectively. For all three commercially-targeted species, negated solutions had much higher coverage levels compared to more general biomass or species richness outcomes. Lack of ecological isolation was an important factor in virtually all solution pathways (Table 9).