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Experimental design
Following five focus groups with SERNAPESCA’s head of enforcement and other personnel, we designed and implemented an online survey that targeted fisheries enforcement officers who are responsible for monitoring IUU activities in Chile. The survey was structured to capture expert knowledge on various aspects of illegal activities, as well as the relative experience of the officers. The survey defined illegal fishing as a fishing activity carried out in national jurisdiction waters by national or international boats that is in violation of the national fishing law, conducted without a legal permit, or activities that involve unreported or misreported captures to the authorities. The Director of SERNAPESCA delivered the survey via email to all SERNAPESCA enforcement officers. The list of officers was constructed by the Director (n = 86). The survey was anonymous in that the officers were not asked to report their name nor any information that could be used for identification (e.g., email). Answers to questions were not mandatory; that is, respondents could opt-out of answering particular questions and continue with the survey. The survey was available online for ten weeks, over which five reminder emails were sent to officers requesting them to complete the survey.
The survey, in Spanish, consisted of two sections. First, we asked respondents to rank the magnitude of illegal activity for twenty fisheries on a nominal scale (1–5), along with their relative experience with each fishery (nominal scale, 1–5). The twenty fisheries were selected a priori based on our focus groups and known information about illegal activity. All fisheries were single species, with the exception of four that included multiple species: skates (2 species, Zearaja chilensis and Bathyraja macloviana), kelp (4 species: Lessonia spicate, L. berteroana, L. traberculata, Macrocystis pyrifera), red algae (3 species: Sarcothalia crispate, Gigartina skottsbergii, Mazzaella laminarioides), and crabs (10 species excluding southern king crab: Cancer edwardsi, C. porter, C. setosus, C. coronatus, Homalaspis plana, Ovalipes trimaculatus, Taliepus dentatus, T. marginatus, Mursia gaudichaudi, Hemigrapsus crenulatus). In the second part of the survey, we asked respondents additional questions for four focal fisheries: South Pacific hake (Merluccius gayi gayi), southern hake (M. australis), loco or Chilean abalone (Concholepas concholepas), and kelp. For each fishery, we asked respondents to score on a nominal scale (1–5),

The frequency of six specific illegal activities in the industrial sector: size, gear, season, area, transshipment, and port.

The frequency of six specific illegal activities in the small-scale sector: size, gear, season, area, transshipment, and port.

The participation of illegal activity for six different stakeholders along the supply chain: fisher, purchaser, processor, wholesaler, exporter, and restaurateur.

The utilization of seven infrastructure types in illegal activities: fishing boats, refrigeration trucks, processing plants, markets, transshipment boats, export vehicles, and restaurants.

This study was approved by the Advanced Conservation Strategies and Pontificia Universidad Católica ethics institutional review boards and followed guidelines established by their ethics committees, which complies with national and international standards. The surveys included a written informed consent approved by all interviewees, which acknowledged research objectives and established that the survey was anonymous and that interviewees were free to choose to not answer questions. While all species have common names in Chile (which were used in the survey), we use Fishbase and Sealifebase as the taxonomic authority and for the common names reported here to facilitate comparisions34,35.
Statistical analysis
For both sections of the survey, we used a Bayesian cumulative multinomial logit model to predict illegal estimates. First, we fitted a model for illegal estimates for each of the twenty fisheries jointly. Second, we fitted models for illegal estimates for various aspects of the four focal fisheries (i.e., activities, stakeholders, and infrastructure) in a single analysis for each aspect. In both models, we included a random intercept term for respondent, along with a fixed effect for fishery. We evaluated the role of experience, as self-reported by the respondents, by comparing the difference between the illegal score by a respondent for a fishery and the model prediction for that fishery across respondents. If higher levels of expertise increased or decreased the value of a respondent’s scoring, there would be a relationship between the size of the differences and the level of experience reported for a fishery. Experience may also affect the difference in mean responses (i.e., bias), potentially due to more personal experience over a longer period of time, which would lead to a correlation between expertise and mean illegality scores. Depending on the patterns observed in the data, there are several ways to control for a respondent’s experience in illegality estimates. In our case, we used experience scores as a covariate in the model.
For the twenty fisheries, we used the following model,

$$Prleft{{S}_{ij}=kright}=phi left({tau }_{k}-left({varvec{beta}}{{varvec{x}}}_{{varvec{i}}}+{{varvec{z}}}_{{varvec{j}}}{{varvec{V}}}_{{varvec{i}}}right)right)-phi left({tau }_{k-1}-left({varvec{beta}}{{varvec{x}}}_{{varvec{i}}}+{{varvec{z}}}_{{varvec{j}}}{{varvec{V}}}_{{varvec{j}}}right)right)$$
(1)

in which the probability that the score for the level of illegal landings ({S}_{ij}) for the ith species by the jth respondent is equal to category k, can be represented as a latent continuous variable which is divided into K categories, by K − 1 thresholds at ({tau }_{k}). This latent continuous variable is represented by the cumulative normal distribution, (phi). For a given observation, the regression equation is composed of coefficients multiplied times predictor variables ({varvec{beta}}{{varvec{x}}}_{{varvec{i}}}) plus a design matrix for the random effect, multiplied times the error term for the jth respondent, ({{varvec{z}}}_{{varvec{j}}}{{varvec{V}}}_{{varvec{i}}}) . The probability of that observation falling in category k, (Prleft{{S}_{ij}=kright}), is thus the probability of it being in a category equal to or smaller than k, (phi left({tau }_{k}-left({varvec{beta}}{{varvec{x}}}_{{varvec{i}}}+{{varvec{z}}}_{{varvec{j}}}{{varvec{V}}}_{{varvec{i}}}right)right)), less the probability of the observation being in a category smaller than k, (phi left({tau }_{k-1}-left({varvec{beta}}{{varvec{x}}}_{{varvec{i}}}+{{varvec{z}}}_{{varvec{j}}}{{varvec{V}}}_{{varvec{j}}}right)right)). Implemented in the R statistical language, using the brms package36, the call to fit this model looks like the following:

$${text{Score}}; , sim ;{text{Species}} + {text{Experience }} + left( {{1}|{text{Respondent}}} right),;{text{ data}} = {text{SurveyData}},;{text{family}} = {text{cumulative}}),$$

where Score is ({S}_{ij}) in (1) above, the fixed effects, ({varvec{beta}}{{varvec{x}}}_{{varvec{i}}}) are the experience of the respondent and the species that was scored, and (1|Respondent) denotes a random intercept model, where each has a different intercept term, drawn from a shared error distribution. For more information on the application of this model to ordinal response data, see Burkner and Vuorre37.
For the estimates for the various aspects of the four focal fisheries, we used the following model,

$${text{Response}}; sim ;{text{Species}} + {text{Experience}} + left( {{1}|{text{Respondent}}} right),;{text{data}} = {text{SurveyData}},;{text{family}} = {text{cumulative}}),$$

which is structured as per (1) above, but with the responses to the various focal species questions (i.e., activities per sector, stakeholders, and infrastructure) substituted for the species scores as in (1).
We compared both models with simpler models, including a single-term null model using leave-one-out cross-validation. We did so in the R statistical language using the loo packages36,38,39. Prior distributions for all regression terms were improper flat priors over the real numbers, the default in the brms package for population parameters. The priors on the intercept and the random effects were student t3,0,10 distributions, as per the default for uninformative priors in the brms package.
We carried out a Principal Components Analysis (PCA) with the four focal fisheries as categorical variables and the illegal activity, stakeholder, and infrastructure estimates from the Bayesian cumulative multinomial logit model. For each fishery, we used 10,000 estimates from the model, along with a qualitative variable that represented the different factors (e.g., restaurateur). The latter has no influence on the principal components of the analysis but helps to interpret the dimensions of variability. Principal Components Analysis is especially powerful as an approach to visualize patterns, such as clusters, clines, and outliers in a dataset40. In our case, we sought to visualize whether there were common illegal factors with similar set of scores and whether there was any association between high or low scores of illegal factors and the focal fisheries. We used the FactoMineR package in the R statistical language41. More

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