24Habitat use and distribution is a critical aspect in the management and conservation of a species, shortcomings of conventional HSIs: 1) the abundance indices from survey catch data typically 58 incorporated in these models do not account for changes in catchability over a time series; and 2) 59 the commonly used abundance indices, and therefore HSIs, are unable to incorporate surveys 60 from multiple gear types which sample different segments of the population and likely cover 61 different types of habitat. These issues need to be addressed in order to produce an unbiased 62 evaluation of spatio-temporal changes in habitat quality for a species over its distributional 63 range. Conventional HSIs use available data from sampled locations, hereinafter referred to as sample-
78based HSIs, which are often restricted to the locations of occurrence and typically processed to 79 assume that the samples are representative (i.e., the species is effectively sampled) and are 80 comparable through time (i.e., no changes in sampling distribution and efficiency). Therefore, 81 the sample-based HSIs might not be appropriate in at least the following two situations: 1) the 82 survey misses a significant portion or type of the species' habitat; and 2) sampling efficiency 83 (i.e., catchability) changes over space and/or through time due to density-dependent processes.
84Density-dependent habitat selection is a likely process for species in decline (MacCall 1990).
85When a species population is high, individuals move into previously marginal habitat because 86 high quality habitat is saturated; thus, the overall suitability of all occupied habitat declines on 87 average (MacCall 1990 Cusk (Brosme brosme) in the Gulf of Maine is one species where assessment is difficult using 104 conventional HSIs. It is a data-limited species, with low abundance and low catchability. central GOM to better sample species that primarily reside in complex habitat (Hoey et al. 2013).
146Six survey strata were selected for the LLS from ten offshore and four inshore strata from the The study area was divided into 5,710 cells (0.05º x 0.05º) for predicting grid-based densities, The second stage of the model approximates positive catches (c):
199The probability density function Gamma (c, x, y) is evaluated at c given a gamma distribution, knots that are generated based on the proportional density of survey data over the defined 208 domain (i.e., the 0.05º x 0.05º grid; Thorson et al. 2015). The spatial (ω) and spato-temporal (ε) 209 random effects were used in both spring and fall density estimates.
211Encounter probability p and positive catch rates λ are approximated using linear predictors
212( Thorson et al. 2015):
215where and ߣ are the expected probabilities of an occupied habitat and positive catches given 216 occupied habitat for sample i at a given location; ݀ ் () is the average reference density
217(encounters/positive catch rates) in year ܶ () ; ܳ is catchability for each survey; w i is the area 218 swept for sample i;...