A Course in Quantitative Ecology

Cox's method depends on tallying observed distances within f ixed intervals away from the transect line. Thus all of the observations within a dis tance,∆ , on either side of the line are added up and used to estimate the t r u e proportion of all observations, denoted p(0,∆ ), that fall in that interval. H e n c e if there are k1 observations within the distance ∆ , we estimate p(0,∆ ) = k 1 /m . Similar estimates are constructed for p(∆ ,b∆ ), the next pair of parallel b e l t s (Fig. 5.9) and p(b∆ ,d∆ ). Cox's original method used only two intervals, but a n extension to three or more intervals is readily obtained (Eberhardt 1979). However, it appears that the variance of the resulting density es t imate increases as the number of intervals is increased (Eberhardt 1979), so we w i l l limit the present discussion to two intervals. An estimator for two intervals is (Eberhardt 1979): ( 1̂ μ) = (b2 1 ) p̂( 0 , ∆ ) p̂(∆,k∆ ) b(b-1)∆ (5.9) where ∆ is the width of the inner interval and b∆ is the width of the inner two intervals (Fig. 5.9). The quantities p̂ (0,∆ ) and p̂ (∆ ,b∆ ) are estimated a s described above, i.e., p̂(0,∆) = k1 m and p̂(∆ ,b∆) = k2 m (5.10)