An alternative method of estimating the number of individuals in marine populations by echo integration is presented. The method was published almost two decades ago by the same author and here it is reviewed and developed. The method is based on just two defined concepts, the Echo Abundance and the mean Echo-Value Constant, respectively. The ratio of these quantities is equal to the number of scattering individuals within a covered area. As the Echo Abundance is estimated by interpolating echo-integrator values over selected areas, the mean Echo-Value Constant can be estimated from representative resolved echoes and their detection angles from individuals in the population, as obtained by the split-beam echosounder system. Two types of estimators for the mean Echo-Value Constant are given and discussed theoretically with respect to their properties. The approach is described and discussed in relation to the conventional theory of abundance estimation by echo integration.
Estimators of mean Echo Value Constant (the ratio between echo abundance and the number of fish) in an alternative echo-integrating method were tried with the SIMRAD EK 60 split-beam echosounder. The mean fish-density estimates of NE Arctic cod were compared with corresponding estimates by the classical echo-integration method; the two methods gave similar results. The alternative method uses integrated single-fish echoes, and a new algorithm to extract and integrate single-target echoes is introduced and used. This algorithm uses echo shape and angle stability, not echo amplitude, to test for the presence of single-target echoes. Apparent single-target echoes with a dynamic range of 60 dB in integrated echo intensity were extracted.
A finite number of colonies, each subject to a simple birth-death and immigration process is studied under the condition of migration between the colonies.
Kolmogorov's backward equations for the process are solved for some special cases, and a sequence of functions uniformly converging to the p.g.f. of the process is given for the general case. Further, a set of algebraic equations for the extinction probabilities are studied for the process without immigration, and a necessary and sufficient condition that the extinction probability be one is obtained.
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