As a first approach, we focused on a single site, SOCAL N, and limited the response variables to the presence of 1) blue whale D calls and 2) beaked whale clicks in 1-min segments. To eliminate potentially confounding issues in responses among different species, we conducted the analysis separately for these two signal types.
terms Sonar lag sonarlag Integers: number of segments since last sonar ping Each 1-min segment = 0 where spres = 1 (see above); otherwise as lag in minutes since last 1-min segment with sonar. Periods after no sonar effort are NA until first sonar ping Peak-to-peak received level maxpprl Maximum ppRL per 1-min segment. 0 if no pings, if multiple pings fall in 1-min segment, result is the maximum To segments without pings we used with spres Sound exposure level (SEL) cumsel Cumulative sound exposure level in dB for 1-min segment Adding up values (SEL) from different pings in the same segment: bels= SEL/10 intensity=10^bels cumsel = 10 * log10 (sum(intensity)) for 1-min segments without pings we used with spres Proportion of sprop Proportion of 1-min segment with sonar Sum of duration of all sonars (secs) that fall within 1-min segment / 60 secs Noise measurement RLD_dB Received level within the frequency band of blue whale D calls Provided in 1-min segments Only for blue data Day-night DN Binary (1=day, 0=night) Using sunrise and sunset information MSR Length in minutes since sunrise Integers: 0 for 1-min segment in which sunrise occurred MSS Length in minutes since sunset Integers: 0 for minute in which sunset occurred Julian date jd Date in integers Consecutive day of year: Year year Year of recording Cumulative
Sonar presence over 1 hour spres.1hr Binary (1/0): Presence/absence of sonar pings 0 if no sonar in the preceding 60 and current 1-min segments, 1 if at least 1 sonar ping Only used for with other terms >1 ping over 1 hour scount2plus.1hr Binary (1/0): Presence/absence of sonar pings 0 if 0 or 1 sonar ping detected in the preceding 60 and current 1-min segments, 1 if more than 1 Only used for with terms Cumulative SEL_dB over 1 hour (unweighted) cumsel.1hr Same as cumsel above except over 60 minutes for 1-min segments without pings in previous 60 minutes we use with spres.1hr Cumulative SEL_dB over 1 hour (weighted) cumsel.1hrw Lag is time lag in minutes between sonar pings and 1-min segment. Using exp(-lag*3/60) as a weight ensures that after 60 minutes weight is negligible bels <- SEL/10 intensity <- 10^bels cumsel.1hrw <- 10 * for 1-min segments without pings in previous 60 minutes we use with spres.1hr Variability Standard deviation of SEL_dB (unweighted) sdsel.1hr Standard deviation of all SEL values that occurred within the last hour (each with equal weight) sd(SEL of pings that fall within 60 minutes before respective 1-min segment) for 1-min segments with 0 or only 1 ping in previous 60 minutes we use
with Standard deviation of SEL_dB (weighted) sdsel.1hrw Standard deviation of all SEL_dB values that occurred within the last hour (weighted by time lag) weighted sd(SEL of pings that fall within 60 minutes before respective 1-min segment) using sqrt(Hmisc:wtd.var()). Same lag-based weighting as applied to individual SEL values for calculating cumsel.1hrw where 1-min segments with greater lag contribute less than 1-min segments with smaller lags. for 1-min segments with 0 or only 1 ping in previous 60 minutes we use with Standard deviation of over 1 hour sdsprop.1hr Standard deviation of over 60 minutes 5. Methods for generalized estimating equations Modeling approach for GEEs The relationship between the coefficients and the response (presence of calls or clicks) is modeled using a logit-link function that can be expressed as , where p is the probability of presence, 1-p is the probability of absence, and β represent the intercept and coefficients associated with the k covariates x. We fitted GEEs using the geeglm function of the geepack package in R (). We added smoothing terms of 3 to 5 degrees of freedom using the bs function of the splines package. We used the default correlation structure ‘independence’ where correlated observations were grouped using a block identifier (argument id from the geeglm function). Each block consisted of consecutive observations of 1-min segments. The size of the blocks was determined using the acf function from the stats package. This function estimates the autocorrelation between consecutive residuals for various lags. We chose sizes of 20 and 41 for the blue whale and beaked whale models, respectively. Model selection for GEEs Our methods for selecting the final model included three main steps: 1) elimination of collinear covariates; 2) stepwise backwards selection based on marginal p-values; and 3) stepwise backwards selection by inspecting 95% confidence intervals around partial fit plots.