BIOLOGY AND CONSERVATION OF THE COMMON MURRE 123 



Appendix H 



Summary of regression analyses 

 (prepared by J. L. Yee and H. R. Carter) 



We conducted the following three types of 

 regression analysis: (1) Simple linear regression to 

 demonstrate major trends in the log-transformed annual 

 sums of whole-colony counts for populations of 

 common murres (Uria aalge californica) in central 

 California, northern California. Oregon, southern 

 Washington, northern Washington, and Washington 

 (referred to as "Sum Regressions"); (2) Poisson 

 Regression to demonstrate major trends in annual sums 

 of whole-colony counts for colony complexes in central 

 California and Washington: and (3) Averaged Poisson 

 Regressions for colony complexes over a certain period 

 within central California to derive "Route Regressions" 

 for comparison with Sum Regressions over the same 

 period (Geisslerand Sauer 1990; Link and Sauer 1994). 

 For either regression method (Sum Regression or Route 

 Regression), trends can be fit with Poisson Regression 

 directly on counts or simple linear regression on log- 

 transformed counts. Both approaches fit a linear relation 

 between time and population size on a log-scale, 

 allowing percent per annum change to be derived from 

 the exponent of the slope of log(N). Further, the log- 

 transformation helps the data to better meet the constant 

 variance assumption of simple linear regression 

 (Rawlings 1988: Neter et al. 1990). Both approaches 

 provide consistent results when counts are large. 

 However, they differ in assumptions regarding the 

 distribution of errors in the model and there are problems 

 in the simple regression approach when counts are too 

 close to zero. We chose to use simple linear regression 

 on the log-scale for the Sum Regression method since it 

 is a more accessible approach and the data sums involved 

 were large enough to make the two approaches 

 comparable. The Poisson Regression was selected for 

 the Route Regression method because some individual 

 colony complex counts reached zero. To examine 

 possible violation of independence in using a series of 

 years of available data for regression analyses, we 

 performed Durbin-Watson tests (Durbin and Watson 

 1 950, 1 95 1 ) but did not find evidence of autocorrelation. 

 All regressions were performed using SAS 7 (SAS 1997), 

 and graphs were prepared using Microsoft Excel 97. 



With regard to the practical application of linear 

 regression techniques, we have not assumed that true 

 linearity exists in the data examined since different 

 results can be obtained by merely considering slightly 



different samples of years. A wider class of models able 

 to reflect nonlinear relations between population size 

 and time would produce better fitting models but, for 

 our objective, this exercise probably would produce 

 needlessly complex models. We instead used the 

 approach that reasonable line approximations to 

 nonlinear functions can be taken over subset ranges of 

 data. To standardize the use of regression analyses in 

 this chapter, we conducted regressions over three time 

 periods (1) data throughout the 1979-95 period that 

 used all years of standardized whole-colony count data 

 when all colonies were surveyed; (2) a subset of 

 population data confined roughly to the first half of 

 this period (i.e.. between 1979 and 1989) with a 

 consistent trend of decrease, increase, or no change 

 during this period: and (3) a subset of population data 

 confined roughly to the second half of this period (i.e., 

 between 1984 and 1995) with a consistent trend of 

 decrease, increase, or no change. Subsets were based on 

 trends evident from inspection of sums of whole-colony 

 counts. For Poisson and Route Regressions of colony 

 complexes, the same range of years of data was applied 

 (as for Sum Regressions of the larger population), but 

 additional years of data for colony complexes were 

 included if available. All regressions were presented in 

 tables. 



To perform Sum Regressions, we collated 

 population sums for each geographic area from available 

 data in Appendixes C, D. E. F. and G. Population sums 

 are summarized in Table H- 1 , including sums for ( 1 ) all 

 colonies in central California between 1980 and 1995; 

 (2) all colonies, except Castle Rock, in northern 

 California between 1979 and 1989: (3) 15 sample 

 colonies in Oregon between 1988 and 1995; (4) all 

 colonies in southern Washington between 1979 and 

 1995; (5) all colonies, except Tatoosh Island and 

 associated rocks, in northern Washington in 1979-95; 

 and (6) all colonies, except Tatoosh Island and 

 associated rocks, in Washington between 1 979 and 1 995. 

 The regressions were conducted by examining the 

 relation of N on year where N is the sum of whole- 

 colony counts for all colonies (or all sample colonies) 

 in a geographic area. To describe Sum Regressions for 

 three time periods, we presented in Table H-2 ( 1 ) me 

 slope of ln(AO with standard error and 95% confidence 

 limits; (2) the percent per annum change, with 95% 



