Censusing Populations in Algonquin Park

Appendix A. Counting Populations

The censusing of plant and animal populations is central to population ecology, which is basically the study of the patterns of organism abundance and distribution. Ecologists seek explanations for why species such as Black Rat (Rattus rattus) can live almost anywhere and are abundant, when the Karner Blue butterfly (Lycaeides melissa samuelis) is rare and only found in oak savannahs with Lupin bushes (Lupinus perennis).

Censusing a population is usually just the start of broader studies, but it is nevertheless important to do it right. Since total and direct counts of populations are rarely possible (except for the rarest of species), a census entails using sampling methods. This means that we are estimating population size from what we hope are representative samples. By using a method to enumerate a population the observer is influencing the very individuals they are trying to count. How the method used influences the estimates obtained should be understood by the biologist.

A.1. Sampling Methods

Biologists use a variety of sampling methods depending on the type of organism and its natural abundance and distribution. In this exercise we use a variety of methods which fall into two broad categories:

A.2. Quadrat Sampling Method

Quadrat sampling The quadrat method has been widely used in plant studies. A quadrat is a four-sided figure which delimits the boundaries of a sample plot. The term quadrat is used more widely to include circular plots and other shapes.

A common shape used in studies of birds and large mammals is a long, skinny quadrat in which the observer travels a transect and counts individuals within a known area either side of the line. These types of quadrats can be called transect strips. (There are various distance-based methods which use transects and the distance off the line that individuals are seen, but these methods are not dealt with here.)

Quadrat sampling involves counting all individuals within a known area (or volume). Since density (D) and population size (N) are related, as N = D x area, we can estimate the density for the sample and from this compute the total population. This assumes that the area the population occupies is finite and known. In the case of the Algonquin Park species, we take the Park boundaries (in the case of Moose), the Lake Opeongo area (Lake Trout), or the study area boundaries (White-throated Sparrow, Sugar Maple) as the total area.

Normally, a series of samples (quadrats) are counted. We do not know which, if any, of the sample estimates give the true estimate. Instead, we can calculate the average of these samples. The average or mean estimate, while not likely to be the same as the true population size, is nevertheless unbiased. Associated with the mean, we can compute a measure of the variability of the samples (the standard deviation), and this is a measure of the reliability of our population estimate.

A.2.1. Assumptions of Quadrat Sampling

The quadrat method has the following assumptions:

  1. The number of individuals in each quadrat is counted.

  2. The size of the quadrats is known.

  3. The quadrat samples are representative of the study area as a whole.

A.2.2. Worked Example: Estimating Population Abundance from Quadrat Samples

You have used Method A to count Moose in three quadrats (each 25 square kilometres) in Algonquin Park (total area = 7,500 square kilometres). >From these results, you want to determine both a mean estimate of the total Moose population in the Park, and a measure of the reliability of your estimate. The following calculations are required.

Note: In the online simulations, the mean and standard deviation are computed automatically for you for each method.

A.3. Mark-Recapture

The mark-recapture method was first used in the 1890s by C. G. Peterson to estimate fish abundance. Today it is widely used in studies of mobile organisms, such as mammals and insects, and it has been applied to human populations as well.

Peterson equation

The method involves taking a sample from the population, marking those individuals and releasing them back into the population. After the individuals have mixed freely with unmarked individuals, new samples are taken, and for each sample the ratio of marked to un-marked individuals is recorded.

The key principle of sampling applies to this method: the ratio of unmarked to marked individuals in a sample will be the same as the ratio in the population as a whole.

A sample of M animals is collected from the population, marked, then returned to the population. After marked and unmarked animals have mixed, a second sample of n animals is captured and the number of marked recaptures, r, is tallied. We assume that the ratio of marked to unmarked in the recapture sample, is representative of the ratio of marked to unmarked in the whole population. Hence we can obtain an estimate of N.

A.3.1. Assumptions

The mark-recapture method has the following assumptions:

  1. The population is closed (see explanation in boxed text below).

  2. Marked individuals have the same probability of capture as unmarked individuals in the resampling phase.

  3. Marked and unmarked individuals mix randomly between the time of marking and the time of resampling.

  4. Marks are not lost and are always recognizable.

A.3.2. Worked Example: Estimating Population Abundance From Mark-Recapture

Assume that 50 Moose have been marked with radio collars (m = 50) and released to mix in the population. Later, you sample three areas of the Park and count the Moose (n) of which a subset are recaptures (r). From these data you estimate population size, N. Here are some sample data and how population size is calculated.

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