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<br />18 <br /> <br />The lower catch ability of bottom dwelling ani- <br />mals and in vegetated areas has been mentioned. <br />The animals will often be immobilized out of sight <br />of the fisherman. It may then be advantageous to <br />use constant rather than pulsed direct current. <br />This will shorten the attraction radius, but is <br />partly compensated for by a reduction in the <br />immobilization radius. Thus the possibility of <br />getting the animals out of their cover before they <br />are immobilized will increase. When catching (or <br />affecting) large decapodes like crayfishes it is also <br />advantageous to use constant direct current as the <br />risk of the animals loosing their claws will be <br />reduced. An interesting combination unit for <br />catching bottom dwelling animals have been con- <br />structed by Phillips and Scolaro (1980). They <br />used constant direct current to make the animals <br />leave cover, after which alternating current <br />(0.1 V /cm) was used to immobilize the attracted <br />animals. <br /> <br />Population estimation <br /> <br />Introduction <br /> <br />This section and the next concern estimating <br />population size and population changes from elec- <br />trofishing data. In this section we review some <br />widely used - and useful - methods of assessing <br />the number of fish in a closed site of a stream or <br />the litoral zone of a lake, and in the next this <br />theme is continued with the next question - how <br />to select these sites and how to make more general <br />statements about stocks. <br />Unfortunately the methods of population esti- <br />mation are not easily accessible for people not <br />trained in statistics. We have therefore tried to <br />make the presentation as clear as possible. The <br />calculations require only a pocket calculator with <br />preprogrammed functions for mean and standard <br />deviation, and th examples provided are intended <br />to faciliate the use of the methods. <br />Before these are presented, however, it might be <br />useful to recall some basic statistical concepts. <br /> <br />Statistical and systematic errors <br /> <br />There are seldom opportunities to obtain exact <br />measurements of the size or density of fish popu- <br />lations. Rather, the true population size y is esti- <br />mated as y, more or less close to the true but <br />generally unknown y. <br />As an estimate with unknown error is quite <br />useless, several ways of expressing and estimating <br />these errors have been developed. The types of <br />error that may arise can be illustrated by firing a <br />rifle at a target (Fig. 7). If the shot group is tight <br />but its center at a distance from the bullseye, the <br />statistical error or sampling error is small, but the <br />systematic error large and represented by the dis- <br />tance between the center of the shot group and the <br />bullseye. This distance is the bias. If the sampling <br />error of an estimate is small, the precision is good, <br />and if the bias is small, the accuracy is good. <br />A biased method of estimation will, on the <br />average, yield either over- or underestimation <br />(positive or negative bias). There are usually no <br />easy ways to assess the bias of estimates of natural <br />populations. Occasionally it is possible to apply a <br />specific method to populations of known size, e.g. <br />marked members, and thus get an idea of the bias. <br />Further, if two methods are applied to the same <br />population of unknown size, at least one of them <br />is biased if the estimates, on the average, differ. <br />Finally, a critical look at the assumptions on <br />which the method is based will often reveal at <br />least the direction of the bias. <br />The sampling error has the effect that the esti- <br />mate y would fluctuate around a mean E(y) if, <br />hypothetically, the estimation were repeated many <br />times under identical conditions. This fluctuation <br />can be measured as the sampling variance V(y) of <br />y, which is the average value of the squared <br />deviations E (y) - y. The square root of V(y) is <br />called the Standard Error of y, or SE(y). This <br />can be viewed as a direct measure of this (hypo- <br />thetical) fluctuation (Fig. 7). <br />Another useful measure of the sampling error is <br />the coefficient of variation C = SE(y )/y, indicating <br />the relative sampling error. <br />In addition it may sometimes be possible to <br />estimate the sampling error (or its effects) as a <br /> <br />I' <br />i <br />r <br /> <br /> <br />\ <br />I <br /> <br />) <br />r <br />I <br />r <br />Ii <br /> <br />\: <br />I <br />:: <br /> <br />( <br />r <br />