Increased nitrogen loading to rivers due to human activities was blamed for the rise in abundance of algae in coastal waters. For example, the Neuse River Estuary fishkills in the 1990s were attributed to the increased algae due to increased nitrogen loading from the Neuse River basin, especially from concentrated animal farming in Eastern North Carolina. Conclusions like this are often made from analyzing crosssectional or metadata. Cole et al. [1993] assembled a data set including many large river systems in the world to study the effect of human activities on nitrogen loadings to rivers (data file nitrogen.csv). They included nine variables in the data set: (1) discharge (DISCHARGE), the estimated annual average discharge of the river into ocean (in m3/sec); (2) runoff (RUNOFF), the estimated annual average runoff from watershed (in liters/(sec×m2 )); (3) precipitation (in cm/yr) (PREC); (4) area of watershed (in km2 ) (AREA); (5) population density (in people/km2 ) (DENSITY); (6) nitrate concentration (in µ mol/L) (NO3); (7) nitrate export (EXPORT), the product of runoff and nitrate concentration; (8) deposition (DEP), nitrate loading from precipitation – product of precipitation and precipitation nitrate concentration; and (9) nitrate precipitation (NPREC), the concentration of nitrate in wet precipitation at sites located near the watersheds (in µ mol/(sec×km2 )). In the paper, the authors used nitrate concentration (NO3) and nitrate export (EXPORT) as measures of human impact on rivers. The authors looked at these two response variables separately to determine whether the impact of human activities in river nitrogen level is a result of direct pollutant discharge input to the river or discharged indirectly through atmospheric pollution. They suggested that population density in the watershed can be used as a measure of direct discharge and nitrate precipitation can be served as a measure of indirect discharge.

Fit a regression model for each of the two response variables and discuss whether anthropogenic impact of river nitrogen is more through direct discharge or through indirect atmospheric deposition. Note that the two factors are correlated and their effects are unlikely to be additive.

Although Schoener [1968] reported four species of Anolis lizard in the paper, only two species were included in the data set. A Poisson regression does not constrain the total number of lizards in a given habitat condition, which may be misleading because the number of lizard cannot be unlimited. A different way of analyzing the same data is using logistic regression. Assuming that there are only two competing species, we can model one species habitat preference as the probability of seeing one species over the other. The data set we used has two parts. The first 24 rows are the number of times of species A. opalinus and the second 24 rows are the number of times of species A. grahamii. Use logistic regression to predict the probability of seeing one species (e.g., A. grahamii). That is, use response of A. grahamii as success and the response of A. opalinus as failure, and develop a model to predict the probability of success. If the probability of success is high for one condition, the habitat defined by this condition is preferred by A. grahamii; if the probability is low, the habitat is preferred by A. opalinus; if the probability is close to 0.5, the habitat is shared by both. Discuss whether your interpretation of species habitat preference changes from the results using a Poisson regression model.