Recovery Plan for the Northern Spotted Owl - DRAFT

the FWS Breeding Bird Survey on population trends in several species ofhawks and owls. We calculated long-term trends and then estimated thenumber of years required to obtain reliable estimates of these trends. Thisanalysis provides much less detailed results but involves real, rather thansimulated, data. Each analysis provides useful information, but even incombination they provide only preliminary estimates of the sample sizes thatwill be necessary to obtain reliable estimates of long-term trends in spotted owlpopulations.Computer simulations: This investigation required specification of anautocorrelation model describing the process by which the survey data wouldbe obtained. The specific autocorrelation structure of the model is not critical,so an analytically tractable Markov chain model was used. The model insimplest form is defined by the probability 4 that a site is initially occupied, theprobability p that a site occupied in one year will be occupied the next year,and the probability r that a site not occupied in one year will be occupied thenext year. These define a Markov chain on the two states of nature, " 1" foroccupied and "0" for unoccupied, as shown below.Transition probability matrixConditionInitialprobability Condition 1 0f 1 p i-p1-f 0 r I-rThe expected proportion of occupied sites converges to a limiting value, r/( I -p+r), independent of the initial fraction 4 of occupied sites, so if the initialoccupancy rate is less than this equilibrium value then an upward trendoccurs. As an illustration of this phenomenon the trend over an 8-year periodwas calculated for the case p=0.9 and r=0.01 giving a limiting value of .01 /.1 1= .090909 for the fraction occupied after a large number of years. The initialfraction was chosen to be 30 percent smaller than this; namely, f = .070 (TableA.4). During the 8-year interval, this fraction increased 17 percent to 0.082,which is equivalent to an annual, proportional, or multiplicative, change of1.019626 (i.e., 1.0196268 = 1.17). In the analyses below, we would describesuch a change by stating that the population grew at an average annual rate of1.96 percent.Detectability bias and noise were introduced into the model by assuming thatan occupant is detected with probability d, and "detection" is independent fromsite to site and year to year. Only "false negatives" are allowed: i.e., a true 0 isalways recorded as 0 while a true 1 is sometimes (with probability 1 -d) recordedas 0. This has the effect of i) reducing the expected slope by the factord, ii) reducing the variance by the factor d 2 but iii) adding a noise variancecomponent:d(I-d)ac 2 awhere c denotes the contrast year-coefficients and "a" denotes the yearlyexpected true-occupancy per site; i.e.,Expected sample slope = dyca.Stochasticity in the transition probabilities p and r was introduced as randommultiplicative effects. A year-specific, site-specific p became a product of a257