Ralph and Miller 



Chapter 33 



Offshore Population Estimates in California 



Analyses 



Murrelet Distribution From the Shoreline 



We used the following method to determine the 

 relationship between the number of birds at varying distances 

 from shore and the total number of birds at the three intensive 

 survey areas. We assumed the relationship was similar for 

 the three areas. Differences in coastal habitat types (sandy 

 beach, rocky shoreline, and offshore rocks) and relative 

 numbers of birds (low, medium, and high densities) at the 

 three areas did not affect the distribution of birds out from 

 the shoreline, as determined by plots of the residuals from a 

 regression analysis. 



The following four steps were used to establish the 

 relationship between the distribution of murrelets from shore 

 and the total population in an area. 



Monthly Mean Counts 



The datum used for analyses was derived from the total 

 number of birds detected in each 2-km segment on each 

 survey day at each distance from shore. Surveys from April 

 through October for all years were included in the data set. 

 Monthly mean counts were calculated for each transect 

 distance (400, 800, 1400, 2000, 3000, and 5000 m). An 

 example would be the following: during April, at Crescent 

 Beach in the two 1400-m 2-km segments combined, a total 

 of 235 birds were seen over all years. We surveyed a total of 

 133 of the 2-km segments at that distance during April. The 

 average was then 235 birds/133 2-km segments or 1.77 birds 

 per 2-km segment for all years. 



Not all distances were sampled in all years during each 

 month at each survey area. For example, surveys were not con- 

 ducted at 400 m at Pebble Beach because of the unsafe rocky 

 shoreline, nor at 5,000 m at any survey area prior to 1990. 



Where possible, the missing monthly mean counts were 

 estimated with regression equations constructed with the 

 non-missing monthly mean counts. We assumed that nearby 

 distances would provide the best predictive ability for missing 

 mean counts, and only those models were examined for each 

 distance. For example, when estimating the 400-m count, we 

 looked only at two models: one with the 800 m monthly 

 mean and another with both the 800 m and the 1,400 m 

 monthly means. The mean monthly count from October 

 1990 at 800 m offshore did not fit the distinct pattern found 

 with all other sample points and was excluded from the 

 analysis. The regression equations were chosen to have up to 

 two independent variables and the results were as follows: 



400 



= 0.228 + 0.6824- 



std. err. of estimate = 2.775 

 r 2 = 0.414; n = 20 



*20oo = - 2605 + 0-23003 x 140Q + 1.6631 x 

 std. err. of estimate = 1.205 

 r 2 = 0.738; n = 36 



x 3000 = 0. 1 205 + 0.20603 x 2000 

 std. err. of estimate = .5375 

 r 2 = 0.441 ;n = 36 



* 5000 = 0.009026 + 0.942065- * 3000 -0.121016 x 2000 

 std. err. of estimate = 0.2290 

 r 2 = 0.668; n= 12 



The missing values were estimated with the regression 

 equations, and any negative estimates were replaced with 

 zero. Because some counts could not be predicted because 

 not all of the independent variables were available, repeated 

 use of the equations was performed until no more missing 

 values could be estimated. Months with remaining missing 

 values were excluded from the next step of the analysis. 



Murrelets Per 2-km Intensive Coastal Segment 



The total mean numbers of murrelets per 2-km coastal 

 segment (fig. 7) of intensive survey area were then 

 calculated from the actual and estimated mean monthly 

 counts for all survey distances (400, 800, 1400, 2000, 

 3000, and 5000 m). Counts associated with 200-m wide 

 and 2-km long survey strips (fig. 1) starting (and centered) 

 at 200 m from shore, and ending with a 200-m wide strip 

 centered at 6,000 m from shore, were interpolated or 

 extrapolated using the surrounding or closest observed 

 counts. For example, the 200-m estimate was found with 

 a linear extrapolation of the 400-m and the 800-m count 

 (fig. 3). This extrapolated distribution closely resembled 

 results of surveys conducted from shore-based stations 

 (Ralph and others 1990), where we found the peak numbers 

 of birds occurred beyond 400 m from the shoreline. The 

 3,200-m strip count was estimated with linear interpo- 

 lation of the 3,000-m and 5,000-m count. If any linear 

 interpolation resulted in a negative number, then zero was 

 used instead. The total number of murrelets between 100 

 m from shore and 6,100 m from shore was then found by 

 summing the contribution of the 200-, 400-, 600-,..., 6000- 

 m strips (fig. 3). 



The Total Birds From 800- and 1, 400-m Counts 



The total number of murrelets from the intensive surveys 

 was then regressed against the mean counts at 800 m and 

 1,400 m. The resulting equation: 



Coastal segment total = 

 6.758 + 4.6102- x 



S<KI 



+ 4.6241 x 



1400 



represents the relationship between the counts at these two 

 distances and the total number of birds in a 2-km coastal 

 segment of coastline, from 100 m to 6100 m offshore. 



Estimates of Murrelet Numbers for Each Coastal Section 



The extrapolated distribution of birds, from 100 m to 

 6,100 m out from the shoreline at our intensively surveyed 

 areas, was used to estimate the numbers of birds in the 



USDA Forest Service Gen. Tech. Rep. PSW-152. 1995. 



357 



