Details of the models used in the study.

<p>Details of the models used in the study.</p

Prediction maps of dolphins averaged over 100 models fitted to thinned datasets for each type of model in the Bay of Biscay and the English Channel.

<p>The rows represent the different types of generic models, and the columns represent the number of sightings used to fit the models. The numbers in the right corner of each map represent the number of sightings used to fit the model. The scale is in individuals.km^-2 (Ind/km²) for the NB-GAM, the TW-GAM and the ZIP-GAM and in the probability of presence (Pr.prob) for MaxEnt. This figure only shows the results for which a change was observed compared with the other predictions. All maps are presented in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0193231#pone.0193231.s006" target="_blank">S5</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0193231#pone.0193231.s007" target="_blank">S6</a> Figs. The dotted lines represent the bathymetric strata of the survey area.</p

How many sightings to model rare marine species distributions

<div><p>Despite large efforts, datasets with few sightings are often available for rare species of marine megafauna that typically live at low densities. This paucity of data makes modelling the habitat of these taxa particularly challenging. We tested the predictive performance of different types of species distribution models fitted to decreasing numbers of sightings. Generalised additive models (GAMs) with three different residual distributions and the presence only model MaxEnt were tested on two megafauna case studies differing in both the number of sightings and ecological niches. From a dolphin (277 sightings) and an auk (1,455 sightings) datasets, we simulated rarity with a sighting thinning protocol by random sampling (without replacement) of a decreasing fraction of sightings. Better prediction of the distribution of a rarely sighted species occupying a narrow habitat (auk dataset) was expected compared to the distribution of a rarely sighted species occupying a broad habitat (dolphin dataset). We used the original datasets to set up a baseline model and fitted additional models on fewer sightings but keeping effort constant. Model predictive performance was assessed with mean squared error and area under the curve. Predictions provided by the models fitted to the thinned-out datasets were better than a homogeneous spatial distribution down to a threshold of approximately 30 sightings for a GAM with a Tweedie distribution and approximately 130 sightings for the other models. Thinning the sighting data for the taxon with narrower habitats seemed to be less detrimental to model predictive performance than for the broader habitat taxon. To generate reliable habitat modelling predictions for rarely sighted marine predators, our results suggest (1) using GAMs with a Tweedie distribution with presence-absence data and (2) implementing, as a conservative empirical measure, at least 50 sightings in the models.</p></div

Estimated smooth functions for the selected covariates and predicted distribution of auks in individuals.km^-2 (Ind/km²) for each presence-absence model and in presence probabilities (Pr.prob) for the Maxent model.

<p>The solid line in each plot is the estimated smooth function, and the shaded regions represent the approximate 95% confidence intervals. The y-axis indicates the number of individuals on a log scale, and a zero indicates no effect of the covariate. The best model fits are between the vertical lines indicating the 10^th and 90^th quantiles of the data. The dotted lines represent the bathymetric strata of the survey area.</p

Estimated smooth functions for the selected covariates and predicted distribution of dolphins in individuals.km^-2 (Ind/km²) for each presence-absence model and in presence probabilities (Pr.prob) for the Maxent model.

<p>The solid line in each plot is the estimated smooth function, and the shaded regions represent the approximate 95% confidence intervals. The y-axis indicates the number of individuals on a log scale, and a zero indicates no effect of the covariate. The best model fits are between the vertical lines indicating the 10^th and 90^th quantiles of the data. The dotted lines represent the bathymetric strata of the survey area. The white areas on certain maps represent the absence of predictions beyond the range of covariates used in fitted models.</p

Proportion of experimental models better than a homogeneous spatial distribution.

<p>Each bar represents, the proportion of the experimental models out of the 100 fitted in which the MSE is lower than the MSE_ref for each number of sightings, <i>i</i>.<i>e</i>., the model that is better than a homogeneous spatial distribution. Each colour represents a different model type.</p

Number of sightings contained in the thinned or experimental datasets for each thinning rate and each species group.

<p>Number of sightings contained in the thinned or experimental datasets for each thinning rate and each species group.</p

Environmental predictors used for habitat modelling.

<p>Environmental predictors used for habitat modelling.</p

Flowchart of the methods used in the study.

<p>NB-GAM: generalised additive model with a negative binomial distribution; TW-GAM: generalised additive model with a Tweedie distribution; ZIP-GAM: generalised additive model with a zero-inflated Poisson distribution; MaxEnt: maximum entropy model; GCV: generalised cross-validation; ind: individuals; MSE: mean squared error; stand.: standardised; pred.: prediction; mat.: matrix; ref: reference; AUC: area under the curve.</p

Prediction maps of auks averaged over the 100 models fitted to thinned datasets for each type of model in the Bay of Biscay and the English Channel.

<p>The rows represent the different types of generic models, and the columns represent the number of sightings used to fit the models. The numbers in the right corner of each map represent the number of sightings used to fit the model. The scale is in individuals.km^-2 (Ind/km²) for the NB-GAM, the TW-GAM and the ZIP-GAM and in the probability of presence (Pr.prob) for the MaxEnt model. This figure only shows the results for which a change was observed compared with the other predictions. All maps are presented in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0193231#pone.0193231.s010" target="_blank">S9</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0193231#pone.0193231.s011" target="_blank">S10</a> Figs. The dotted lines represent the bathymetric strata of the survey area.</p