Section 3 Model Development

3.1 Model Definition

The occupancy model uses a logistic linear mixed effects model framework for estimating the probability of occupancy in each catchment (Bolker et al., 2009; Zuur et al., 2009).

The model includes one fixed effect representing the estimated mean July stream temperature (see Stream Temperature), and a random effect intercept that varies by HUC8. The random effect is included to account for spatial variations in observed occupancy that are not explained by the mean July stream temperature.

The model is fit using the glmer() function of the lme4 R package (Bates et al., 2015) using the following formula and parameters.

lme4::glmer(
  presence ~ mean_jul_temp + (1 | huc8),
  family = binomial(link = "logit"),
  data = model_data,
  control = glmerControl(optimizer = "bobyqa")
)

3.2 Model History

The original development of this model was based on a similar brook trout occupancy model that was developed using a Bayesian hierarchical framework to evaluate associations between various catchment and riparian characteristics as well as climate inputs and the occupancy probability in catchments within the state of Connecticut (Kanno et al., 2015).

Prior to version 2.0.0, the EcoSHEDS northeast brook trout occupancy model included a number of independent variables (i.e., covariates) representing land use (forest, agriculture, high intensity development), climate (summer precipitation), and drainage area. The earlier model versions also included the mean July stream temperature as estimated by the EcoSHEDS northeast stream temperature model. However, because the stream temperature model depended on a number of the same independent variables, the estimated effects in the occupancy model were often counter-intuitive due to cross-correlations between some covariates and the estimated stream temperature.

Therefore, beginning with version 2.0.0, the brook trout occupancy model uses only the mean July stream temperature as the sole fixed effect. This change resulted in a small decrease in model accuracy, but provides more intuitive results and can be more easily applied for evaluating alternative climate or land use change scenarios.

References

Bates, D., Mächler, M., Bolker, B., and Walker, S. (2015). Fitting linear mixed-effects models using lme4. Journal of Statistical Software, 67(1), 1–48.

Bolker, B. M., Brooks, M. E., Clark, C. J., Geange, S. W., Poulsen, J. R., Stevens, M. H. H., and White, J.-S. S. (2009). Generalized linear mixed models: A practical guide for ecology and evolution. Trends in Ecology & Evolution, 24(3), 127–135.

Kanno, Y., Letcher, B. H., Rosner, A. L., O’Neil, K. P., and Nislow, K. H. (2015). Environmental Factors Affecting Brook Trout Occurrence in Headwater Stream Segments. Transactions of the American Fisheries Society, 144(2), 373–382.

Zuur, A. F., Ieno, E. N., Walker, N., Saveliev, A. A., and Smith, G. M. (2009). Mixed effects models and extensions in ecology with R. New York, NY: Springer New York.