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We discuss models for multivariate counts observed at fixed spatial locations of a region of interest. Our approach is based on a continuous mixture of independent Poisson distributions. The mixing component is able to capture correlation among components of the observed vector and across space through the use of a linear model of coregionalization. We introduce here the use of covariates to allow for possible non-stationarity of the covariance structure of the mixing component. We analyze joint spatial variation of counts of four fish species abundant in Lake Saint Pierre, Quebec, Canada. Models allowing the covariance structure of the spatial random effects to depend on a covariate, geodetic lake depth, showed improved fit relative to stationary models.