|
<br />910
<br />
<br />HAINES AND MODDE
<br />
<br />TABLE 3.-Simulation results with model M(t) for estimating population size under alternative sampling regimes and
<br />assumptions. Abbreviations are t = day, p = probability of capture, I, = number of unmarked immigrants on day t, N
<br />= true population size, Nl = population estimate with model M(t), SDNl = standard deviation of Nl, aveSE = average
<br />standard error from the individual population estimates, coverage = fraction of the estimates that fall within the 95%
<br />confidence limits, relative bias = IOG.(Nl - NJIN; CV = coefficient of variation (aveSElNl). Each trial is the result
<br />of 200 replications.
<br />
<br />CV
<br />
<br />Model
<br />description
<br />
<br />Trial N Nl
<br />I 5,600 5,920.8
<br />2 2,500 2,579.1
<br />3 5,600 5.635.5
<br />4 2,500 2,548.1
<br />5 5,600 5,731.1
<br />6 2,500 2,563.0
<br />7 11,200 11,507.3
<br />8 11,200 11,291.2
<br />9 5,600 6,411.7
<br />10 11,200 11.790.9
<br />II 11,200 11,353.0
<br />
<br />SDNl
<br />
<br />Relative
<br />aveSE Coverage bias
<br />
<br />Effects of t and p on small sample bias and precision
<br />1,479.34 1,385.99 0.93 5.7 0.23 t = 3, 0.02 < p < 0.05, It = 0
<br />524.57 467.66 0.92 3.2 0.18 t = 3. 0.03 < p < 0.10, It = 0
<br />534.43 468.64 0.91 0.6 0.08 t = 3, 0.07 <p < 0.10, It = 0
<br />333.91 319.22 0.94 1.9 0.13 t = 3, 0.D7 < p < 0.10, I, = 0
<br />904.55 892.69 0.94 2.3 0.16 t = 4, 0.02 <p < 0.05, It = 0
<br />335.37 318.57 0.95 2.5 0.12 t = 4, 0.03 < p < 0.10, I, = 0
<br />2,132.03 1,859.70 0.92 2.7 0.16 t = 3, 0.02 < p < 0.05, I, = 0
<br />724.58 667.13 0.93 0.8 0.06 t = 3, 0.D7 <p < 0.10, I, = 0
<br />
<br />Effects of immigration and emigration on bias and precision
<br />1,653.04 1,593.31 0.98 14.5 0.25 t = 3, 0.02 < p < 0.05.0 < It < 50
<br />1,945.33 1,902.20 0.96 5.2 0.16 t = 3, 0.02 < P < 0.05,0 < I, < 50
<br />719.81 668.82 0.93 1.4 0.06 t = 3, 0.D7 < p < 0.10,0 < I, < 50
<br />
<br />12
<br />13
<br />14
<br />
<br />5,600
<br />5,600
<br />5,600
<br />
<br />Effects of heterogeneity of capture probabilities on bias and precision"
<br />4,817.3 1,255.96 1,081.32 0.74 -14.0 0.22 t = 3, hetero = 1, I, = 0
<br />5,530.6 1,121.67 1,015.50 0.91 -1.2 0.18 t = 3, hetero = 2, I, = 0
<br />4,616.5 575.35 477.44 0.43 -17.6 0.10 t = 3, hetero = 3, It = 0
<br />
<br />"For hetero = 1; 10% of the population had p = 0.01,45% p = 0.03 and 45% p = 0.07; for hetero = 2; 10% of the population had p
<br />= 0.01,45% P = 0.06 and 45% p = 0.07; for hetero = 3; 10% of the population had p = 0.02,45% p = 0.06 and 45% p = 0.14.
<br />Probabilities of capture (p) remain constant within each sampling occasion.
<br />
<br />If the sampling design were modified by dou-
<br />bling the length of the study reach to 32 km and
<br />increasing probability of capture to 0.07-0.10, we
<br />could achieve CV of about 0.06 and reduce relative
<br />bias resulting from small samples and immigra-
<br />tion-emigration to about 1.4% (trial 11).
<br />Another form of bias (heterogeneity) results
<br />when capture probabilities vary among differing
<br />segments of the population (White et al. 1982).
<br />For example, if some backwaters are more effi-
<br />ciently seined than other backwaters (e.g., shallow
<br />versus deep) or if a portion of the population oc-
<br />curs in habitats that are unlikely to be sampled
<br />(e.g., low velocity side channels), the result may
<br />be different capture probabilities for different por-
<br />tions of the population. Simulations incorporating
<br />heterogeneity showed that population estimates
<br />could be low by as much as 17.6% (trial 14). This
<br />bias can be reduced by trying to equalize (e.g.,
<br />more evenly distribute sampling effort among hab-
<br />itats) the probabilities of capture (p) among the
<br />different groups of fish (trials 12, 13).
<br />
<br />Discussion
<br />
<br />The conditions required to apply a closed mark-
<br />recapture population estimate are that marks last
<br />the length of the study effort, survivability an(j
<br />
<br />vulnerability to capture are equal between marked
<br />and unmarked individuals, either marks or effort
<br />are distributed randomly, and negligible immigra-
<br />tion or emigration occurs during the study period
<br />(Ricker 1975). Our laboratory studies concluded
<br />that survival and retention of all three marks met
<br />the minimum length requirement (21 d) for a single
<br />mark-recapture estimate. Fish marked with the tat-
<br />too ink had somewhat elevated initial mortality,
<br />and the mark was not retained well over 3 months,
<br />Fin clips did not cause increased mortality, but
<br />extended mark retention was low. The elastic poly-
<br />mer marks had high survival and retention rates.
<br />When exposed to largemouth bass predation in
<br />experimental tanks, no differences among marking
<br />treatments were observed in the survival of young
<br />Colorado squawfish. However, fish allowed 15 min
<br />for recovery between marking and exposure to pre-
<br />dation showed higher mortality than fish allowed
<br />a 120-min recovery. The difference between times
<br />of recovery but not among treatments suggests that
<br />the source of variation was probably fish handling
<br />rp.ther than the marks themselves.
<br />Fish-handling stress was also evident in the ear-
<br />ly stages ofthe field study when overnight survival
<br />in net-pens was only 68% after marking. Later,
<br />survival increased to 95%, We attribute the im-
<br />
|