Cross correlation maps: A tool for visualizing and modeling time lagged associations

It has long been recognized that arthropod populations fluctuate with changes in environmental conditions and these changes occur at various spatial and temporal scales. Empirical studies that have explored associations between vector abundance and the environment often considered meterological events as leading indicators with their effects traditionally restricted to single points in time, such as precipitation 12 days prior to trapping. Field experience, however, suggests that the duration of these environmental effects on vectors often extends over a range or interval of time. Such a scenario is not directly interpretable from cross correlation plots routinely employed to visualize and identify time lag associations. Cross correlation maps are introduced as a way to generalize cross correlation plots and to visualize the effects of environmental conditions over intervals of time. This graphical method is flexible and can include different characterizations of environmental effects, as well as interactions among environmental variables. A time series of daily trapped female Ochlerotatus sollicitans mosquitos and leading meterologic conditions were used for demonstration. Associations shown in cross correlation maps were consistent with the arthropod biology and trapping efficacy and were also stronger than those identified at single time points using cross correlation plots. Poisson regression models for vector abundance built using meterological variables with both single and interval based leading time lags were compared. The approach based on the leading meterological events allowed to extend over time intervals reproduced the Oc. sollicitans daily population dynamics better than the traditional approach.