Beissinger 



Chapler37 



Population Trends Projected from Demographic Analyses 



post-breeding population model was used. Similar ratios 

 have been used to examine population trends in a variety of 

 other wildlife studies (Hanson 1963, Lambeck 1990, Paulik 

 and Robson 1969, Roseberry 1974). 



At-sea surveys should be conducted before subadults 

 and adults begin to molt into winter plumage and become 

 difficult to distinguish from young-of-the-year (Carter and 

 Stein, this volume). In most years, molting adults and subadults 

 are first detected in mid- to late August (Carter and Stein, this 

 volume: Ralph and Long, this volume). Therefore, I used 

 survey data collected on or before 16 August, and pooled 

 results for two week periods to yield reliable sample sizes. 

 How ever, fledging of young can occasionally occur until late 

 September i Hamer and Nelson, this volume a). When the at- 

 sea surveys were conducted, it is likely that some young had 

 not yet fledged (and thus would not be detected), but most 

 adults were censused since they were in the ocean gathering 

 food to feed young. Therefore, this ratio will tend to 

 underestimate recruitment. To correct for this problem, I 

 used the cumulative frequency distribution for estimates of 

 "known" fledging dates for all nests or young found throughout 

 the range (Hamer and Nelson, this volume a). From this 

 distribution. I determined what proportion of young would 

 have fledged by the end-point of the census date and then 

 adjusted the juvenile ratio upwards by this factor. 



There is one problem with using juvenile ratios to estimate 

 fecundity. Fecundity is the number of female young per adult 

 female produced annually. But during the censuses, subadults 

 can not be distinguished from adults that are capable of 

 breeding. Therefore, just using the ratio of juveniles to after- 

 hatch-year birds from the censuses will tend to underestimate 

 fecundity because the proportion of adults will be 

 overestimated. This can be seen by conducting a deterministic 

 projection of a population for 25 years and looking at the 

 proportion of the population that fledglings comprise. Just 

 using the value from the ratio usually results in a lower ratio 

 of young-of-the-year birds to older birds than expected. 

 Fortunately, the ratio can be corrected by increasing it 

 incrementally until the population projection yields the proper 

 starting ratio of juveniles to older birds. 



Alcids typically exhibit delayed ages of first breeding 

 (Croxall and Gaston 1988, Hudson 1985). One of the earliest 

 recorded ages of first breeding is for Cassin's Auklet 

 (Ptychoramphus aleuticus) where some birds begin at 2 

 years but most start at 3 years of age (Croxall and Gaston 

 1988). Hudson (1985) estimated 5 years in general for 

 Atlantic alcids. The age of first breeding of individuals, 

 however, ranged between 3 and 15 years (Harris and others 

 1994). Given its small body size, it is unlikely that the 

 murrelet would require 5 years to reach sexual maturity, 

 although it could require longer to obtain a nest site if sites 

 were limiting. On the other hand, nest sites were probably 

 much more abundant historically than they are today as a 

 result of deforestation. Thus, in comparison to most other 

 seabirds, which nest colonially on islands where obtaining 

 a breeding site can sometimes be difficult (Hudson 1985), 



it seems likely that the Marbled Murrelet would have a 

 young, rather than old, age of first breeding. I suspect that 

 an age of first breeding would be 3 years, but explored ages 

 from 2 to 5 in the model. 



Once demographic traits were selected, values were 

 used to calculate lambda (the expected annual growth rate of 

 the population) and the stable stage distribution. Populations 

 decline when lambda is less than 1 and increase when lambda 

 exceeds 1 . The stable stage distribution is the proportion of 

 the total population that is comprised of each stage class and 

 can be used to yield an expected juvenile ratio. Lambda and 

 the proportion of juveniles in the stable age distribution 

 were calculated: (1) analytically by constructing Leslie 

 matrices and solving for the dominant eigenvalue and right 

 eigenvector (Caswell 1989) using MATLAB (1992); and (2) 

 numerically using spreadsheets to project population changes 

 over 25 years (Burgman and others 1993). I used these same 

 methods to explore what levels of adult survival and fecundity 

 are required to yield estimates of lambda equal to 1 for 

 different ages of first breeding and the juvenile ratios that 

 these combinations would produce. A sensitivity analysis 

 was conducted by determining the partial derivative of lambda 

 with respect to each element in the Leslie matrix (Caswell 

 1989, McDonald and Caswell 1993). 



Results 



Estimating Fecundity 



Reproduction in the marbled murrelet appears to be highly 

 asynchronous. The cumulative frequency distribution for 

 estimated dates of fledging throughout the range of the murrelet 

 shows a regular increase during the breeding season (fig. 2). 

 Fledging has occurred as early as the first week in June and 

 very rarely as late as September, although 94 percent of the 

 nests had fledged by the end of August. Fledging finished by 

 the end of August in Alaska, British Columbia, and 

 Washington, but in Oregon and California, it extended into 

 September (see fig. 3 in Hamer and Nelson, this volume a). A 

 linear model fit the data well, especially through the middle 

 portions of the range of fledging dates (fig. 2). This model 

 was used to estimate the cumulative proportion of nests that 

 had fledged to adjust juvenile ratios for differences in the 

 date of surveys. 



Table 1 summarizes the ratio of juveniles for different 

 localities, survey periods, and years for surveys made from 

 shore or from a boat cruising only through kelp beds, which 

 juveniles appear to frequent preferentially (Sealy 1975a). 

 Similar data are shown for the juvenile ratio from boat 

 surveys at sea (table 2). Several trends are evident. First, the 

 proportion of juveniles encountered was much greater near 

 shore (<800 m from shore) and on kelp bed surveys (table 

 1), than on boat surveys (table 2) of near shore (500-800 m) 

 and distant waters (from 1400 m up to 5 km off shore in 

 some cases). All at-sea surveys had adjusted ratios of juveniles 

 of less than 5 percent, while onshore surveys typically had 

 adjusted ratios of 9-16 percent juveniles. Juveniles were 



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



387 



