University of Alaska Fairbanks



Estimating the number of fish in a research survey OR in the McNeil Canyon Elementary School gymnasiumIn fisheries work, we may want to estimate the number of fish in certain area. This could be some place where we need information to managing a fishery. It would be good to have an estimate of the population size so we can determine how many fish would be appropriate to harvest and still leave enough in the ocean for future generations of fisherman to harvest. An example of an area where we might want to could be right here in Kachemak Bay. We can decide on the size of the study area and design a survey to estimate the population size of difference species of fishKachemak BayStudy areaKachemak BayStudy areaFor this exercise, we are going to imagine that we can shrink down this Kachemak Bay study area to the size of the gymnasium here at this school.A population of rockfish in the McNeil Canyon Elementary GymHere we’ve shrunk down our Kachemak Bay study area to the size of the gymnasium and populated it with fish. Later we’ll survey this population just as we’d do in Kachemak Bay and estimate the number of fish in the “gym” population. For now we’ll break down the steps we need to go through to do that. First we need to know the size of the survey area. We’ll use meters for our measurements. The gym is 21 m long and 13 m wide which give us an area of 273 square meters or 273 m2. This isn’t a very large area but if we step back and think of the size of Kachemak Bay and calculate the number of square meters there, we’d end up with a very, very large number. It would be impossible to survey the entire bottom of Kachemak Bay, so we instead “sample” a portion of the bottom and use those samples to “estimate” the number of fish or the population size. This is a very import concept in fisheries work and is used all the time to estimate the number of fish, crabs, clams, or other animals in the population.Next, we’ll divide the long side of the gym up into 23 equally spaced meters. Then, we randomly select 10 of those 23 locations and these will be the locations where we will “sample” our population of rockfish. If we chose all 23, then we’d be surveying the entire population which again, for the size of Kackemak Bay, would be impossible. When we choose our sampling locations randomly, we ensure that each location has an equal probability of been chosen. From each of the 10 randomly chosen locations, we will draw an imaginary line across the gym or the survey area.We will call these lines “transects” and will count the number of fish that we see along these transects to “estimate” our population size. To see how that’s done, let’s start by looking at one transect. Each transect will be 1 meter wide and 13 meters long. If we count 2 fish along the transect line we’d “estimate” that the density of fish in the population was 0.154 fish / sq m and multiplying that by the survey area we’d “estimate the population size at 46 fish. It’s important that we only count fish that are at least halfway inside the transect. If we counted any part of a fish that was inside a transect, we’d be over counting and would overestimate the population size. For our example transect, there are 4 fish that have at least part of their body inside the transect but only 2 that have more than half inside. Now one sample is pretty small and we should really take a lot of samples. Let see what we’d estimate if we took 4 samples.When we take more than one sample we need to average our samples to “estimate” the average density. Here we estimate the average density as 0.096 fish / sq m and the population size as 28.75 fish. This is a different number from before and is an improvement from our first estimate because the “true” population size is actually 28. The more samples we take, the closer to the “true” population size our estimate will be. To demonstrate this, we randomly select one transect at a time until we sample all of the transects, and we estimate our population size as each time we add another sample. Here’s a graph of our results!We see that our estimates are not very good if we take less than 3 samples. We sampled 4 transects and estimated the population size of 26 while the true population size was 27. Not too bad! But as we can see from graph, our estimates go up and down and don’t really stabilize until we take about 11 samples. After that all of our estimates are very similar. ................
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