Algorithm for white whales number estimation on data of aerial survey

16 April 2014

In accordance with the program «Beluga – White Whale» IPEE RAS aerial survey of belugas by sample transects have been made in the 5 survey regions of White Sea in 2005-2011 and also in the Sakhalin Bay and Amur estuary of Okhotsk Sea in 2009-2010.

The same extrapolation algorithm was used for beluga number estimation in each of these regions. Mathematical basis of the algorithm has been worked out by Chelintsev N.G. Arena of extrapolation of sample survey for each of the regions has been determined by its geo-location and by the position of sample transects.
Calculations were conducted using the computer program «БЕЛУХА» for survey data in the White Sea and the program «БЕЛУХА-2» for survey data in the Sea of Okhotsk. Comparing to the «БЕЛУХА», the «БЕЛУХА-2» program provides additional data-processing of continuous aerial survey with aerial observation of the whole area occupied by surveyed population, and extrapolation is not conducted.

Correction of distance undercount for an optimal truncated strip width. If it is assumed that the probability of beluga location at different distances from the axis of the transect have the uniform distribution, and at the same time, the probability of beluga detection decreases with increasing distance from the axis of transect, the correction of the distance undercount by the data of beluga detection distance is conducted. Observed width on each side of the strip W for the each region is determined by the greatest beluga detection distance in this region. The whole strip W is divided into 20 equal intervals and for each strip, made up of t intervals, the completeness of beluga detection is estimated by the formula based on the integrated lognormal (LN) detection function.


In contrast to detection function model LN in the «БЕЛУХА» program, in the program «DISTANCE» are used as key the half-normal (HN) and Hazard-rate (HR) models. As demonstrated by the comparative analysis, the detection function model LN in its optimal truncation, on average better corresponds to the actual data of the distribution of beluga detection distances compared with models HN and HR. The half-normal model (HN) because of the too short plateau often brings to underestimation of the value of the completeness of beluga detection and to overestimation of the beluga number, and the model Hazard-rate (HR) sometimes brings to overestimation of the value of the completeness of beluga detection and to underestimation of the beluga number because of a too long plateau.

Fairly frequently, when the program «DISTANCE» is applied, appear the systematical errors in the estimate of the completeness of the beluga detection due to an unsubstantiated addition of adjustment terms of the detection functions caused by random deviation of the actual distribution of the detection distances from the key model. In this case an addition of adjustment terms will increase a statistical error in the estimate of the completeness of the animal detection and in some cases requires the «monotonization» of the estimated detection function, that brings to increasing of statisti-cal error.

Another difference of the algorithm of the «БЕЛУХА» program in the method of correction of distance underestimate consists in the fact that the estimate of the completeness of animal detection in the survey strip is conducted directly on the distribution of the detected beluga individuals. In the program «DISTANCE» the estimate of the completeness of animal detection is calculated by the distribution of the distances of the detected beluga groups. The extrapolation is also conducted on data of the detected animal groups. In order to transfer the estimated value of the animal group number in the region into the number of animal individuals, it is necessary to estimate the mean size of the animal groups in the population. In «DISTANCE» program is proposed to apply 4 different methods without well-defined criteria of selecting a better method.


These methods of calculation can lead to significantly different (up to 1.5-2 times) estimates of mean size of animal groups and as a result to different estimates of the animal individual numbers.


Extrapolation. If in region is applied the regular location of parallel survey transects then the use of a standard formula of calculation of statistical error based on the model of random location of the sample transects, yields an overestimation of the statistical error of extrapolation when there is a substantial trend of population density in the direction perpendicular to the transects.


For the case when all parallel survey transects with unequal intervals between them can be divided into some groups in each of which the intervals between transects are equal, the method of separate extrapolation for each group with equal intervals between transects is proposed. In this method instead the population density on
each of survey transects is used the number of detected animals, that limits the application of this method when there is the substantial difference of the lengths
of the survey transects.

The algorithm of separate extrapolation for each of the parallel transects applied in the program «БЕЛУХА» is enough universal and can be used if survey transect
lengths are unequal and intervals between the parallel transects in the survey region are also unequal. The presented algorithm of separate extrapolation on separate sections of the survey route can be used also for the saw-toothed or zigzag route. In this case, the lines forming separate extrapolation sectors are  conducted at equal distance between separate straight sections of the survey route.

When the continuous aerial survey of belugas is conducted then as the estimation of the beluga number in the region is assumed the total number of detected animals. The statistical error of beluga number estimate is determined by the fact that each beluga has only a certain probability of being on the surface and of being detected from air.


Chelintsev N.G.


Moscow, Russia




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