**Statistical**Failure

Population estimation

Introduction

Estimates of population size play a vital role in many fisheries management decisions. The numbers of fish in a stock are used to identify influences of environmental factors, human exploitation, and ultimately to identify the effectiveness of management strategies. (Van Den Avyle & Hayward 1999) The three most common methods of population estimation among biologist are sample plots, mark and recapture, and removal.

Counts on sample plots is based on the principle that an estimate of population size can be obtained by determining the average density of animals per unit area and multiplying its value by the total area covered by the population. This procedure is done by setting up a pre-determined number of circular, square, or rectangular plots. These plots should be randomly placed and should not over lap. "This method is used when all members of the target population can be counted with reasonable certainty"(Van Der Avyle & Hayward 1999). The formula used with this method is:

Where A is the size of the study area, a is the size of the plot, and n is the average number of animals counted per sample plot (Van Der Avyle & Hayward 1999).

The mark and recapture method is simply preformed by collecting fish, marking them, releasing them, and at a later time collecting fish from the same area and examining them for marks. This is based on the principle that the number of marked fish in the second sample is proportional to the total number of fish in the population. This is called the Peterson method and the equation is as follows:

Where M is the number of fish initially marked and released, C is the number of fish collected, and R is the number of recaptures (Van Der Avyle & Hayward 1999). The Peterson index can give biased estimates when the numbers of fish sampled are low; so several modifications have been made to correct this. One being Bailey\'s modification which is used when sampling during the recapture period is conducted with replacement. The Chapman method is used if replacement is not taking place. The differences in these three methods would be of little significance if the recapture number exceeds 7 (Van Der Avyle & Hayward). All three of these variations are based on the assumptions that: 1. Marked fish don\'t lose their marks. 2. Marked fish are not over looked in the recapture sample. 3. Marked and unmarked fish are equally vulnerable to recapture. 4. Marked and unmarked fish have equal mortality. 5. Following release marked and unmarked fish become randomly mixed. 6. There are no additions to the population during the study. If any of these conditions are not met over estimation will most likely occur (Van Der Avyle & Hayward 1999). The third and final method of population estimation is the removal method. This is based on the idea that the number of fish caught per unit of effort will progressively decline as members of the population are removed. The population can be estimated from data on fishing effort and catch rates. The assumptions with this method are: 1. All members of the target population are equally vulnerable to capture. 2. Vulnerability to capture is constant over time. 3. There are no additions to the population or losses other than the removal itself (Van Der Avyle & Hayward). The Leslie and DeLury methods are used in cases when sampling effort my vary among periods. They are used on large populations where the probability of catching an individual fish is low (Kohler 138). The Leslie method assumes that the number of fish caught per unit effort is proportional to the number of fish present at the beginning of the interval. The DeLury method differs in that the population estimate is based on total effort rather than cumulative data. The Zippin method is used where the catchability is high and equal effort is expended in each sample period. This is most commonly used in small mountain streams in conjunction with electrofishing as the removal method.

Materials & Methods

On September 13, 2000 we went to Mull Creek. We set up two stop nets spanning 75m one upstream and one downstream to keep the population contained. We made three runs with electrofishing gear to remove the fish. Once removed

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