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Methods of Estimating Population Sizes

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To estimate population sizes when the individuals are hidden or too numerous to count in a given area, it is ideal to estimate these numbers with a random selection of samples taken in the given area with quadrats. Using a given and later chosen area, we will then toss the quadrats and record the number of individuals in that area to estimate the population density.


Experiment A- Using a model in the lab

The equipment that was used for measuring the population and the dimensions of the model were:

A quadrat of 0.1m x 0.1m or 100 cm2

A marked area on bulky paper where drawn crosses indicate organisms

A 100cm ruler

Using a quadrat to estimate the populations of small stationary organisms

First, we measured of the dimensions and area of the paper using the ruler, which are best represented in the diagram below, whose uncertainty is 0.005 cms:

To find the area of the marked area, I first have to calculate areas A, B and C with some basic formulas:

Area of Rectangle= width x length

Area of Triangle= (width x length) /2

Area A= 98 x 79 –> 7742 cm2

Area B= (130-80) x 70= 50 x 70 –> 3500 cm2

Area C= (98-70)x (130-80)= 28 x 50 –> 1400 cm2

Area A + Area B + Area C= Total Area

7742 cm2 +3500 cm2 +1400 cm2 = 12642 cm2 or 1.26 m2

Number of random throws

In order to randomly throw our quadrat in area we decided to turn around at an initial point. The subject turns away from the area so that she could not see where she was aiming and then throws the quadrat behind her into the area. Then from the position where it landed, the same process is repeated. We chose to choose this method instead of throwing it from the same initial point to avoid biased results. If any quadrat landed out of the selected area, but significantly close to the perimeter it was moved in the same perpendicular line until it was completely in the area. This process can be shown in the following diagram:

If it was far off the chosen area, as we encountered in two occasions during experiment B, we decided to invalidate the throws.

The quadrat for experiment A consisted of four wooden sticks whose dimensions were 10 cmx10 cm or 0.1mx0.1m, covering an area of 100 cm2 or 0.01 m2 each time it landed.

The total number of crosses found was 80 which will be divided between:

i) the average number of crosses per throw

= 80 crosses / 1.2642 m2

=63.282 crosses per m2

ii) The number of throws to find an average of crosses per throw/quadrat . This is achieved by the following formula:

Number of crosses / number of throws= 80/20

4 crosses per throw or 4 crosses per 0.1 m2.

From these two results, we can find the absolute population and the population density:

Population density (in agriculture standing stock and standing crop) is a measurement of population per unit area or unit volume. The population density is the number of individuals per meter square; therefore we have to multiply the average of the population per 0.1m2 times a hundred since each quadrat represents a hundredth of a meter square. Thus, it is calculated the following way:

Pop. Density= 4 crosses x 100 = 400 crosses

To calculate the estimated absolute population of the area we must use the following formula:

Absolute population= Population density (individuals per square metres) x area (square metres)

=400 crosses per m2 x 1.2642 m2505 crosses

The population density of the marked area was 400 crosses per metre square and the absolute population was 505 crosses.

Experiment B- Using a quadrat on a grass sport field

In experiment B, we went to a selected field in the school grounds and repeated a similar process than that in Experiment A with a few variations in order to estimate the population of dandelions growing in the area.

The dandelion is “a perennial, herbaceous plant with long, lance-shaped leaves. They’re so deeply toothed, they gave the plant its name in Old French: Dent-de-lion means lion’s tooth in Old French.” The images of dandelions below help illustrate the above description:

Fig. 2: A group of dandelions Fig.3: A single dandelion at close


The equipment that was used for measuring the population and the dimensions of the model were:

A football

A quadrat of 50 cm2

A measuring tape

The area from where we withdrew our results was a rectangular area located behind the school’s coliseum. The following sketch describes the area in greater detail:

As we can see, the selected area for our experiment had dimensions of 1000 cm in width and 2050 cm in depth. In order to fin the area we need to use the following formula:

A (cm2) = length (cm) x width (cm)

From this formula we can deduce our selected area is 2050000 cm2 or 205 m2. Out quadrat’s measures were 50 cm so that the covered and area of 2500 cm2 each time they were threw.

We must note before starting with the description of our method that the locations of the dandelions is unevenly distributed as the north west corner of the selected grass field has a higher concentration of dandelions is concentrated as shown in our diagram, whilst the rest of the field has more sparsely distributed organism, which is why it can be predicted that our measurements, depending in the area where our football initially landed may vary significantly.

It is equally important to note that though our method to randomly throw the quadrat suffered some slight variations. For experiment B, we could not directly throw our quadrat as it got slightly deformed and slanted due to the force of fall, which could ultimately bias our results. For this reason, we would throw a football to indicate the location where our quadrat would have landed and then locate our quadrat around our football as accurately as possible to then withdraw the latter to count the dandelions captured in the area.

If the dandelions button was inside this quadrat it was considered inside the area, but if only the petals were seen, it was not counted, applying the same method as in experiment B.

Absolute population is: 3.4 dandelions m-2 x 205m2 697 dandelions

There are some random errors of measurement as we cannot be certain of the exact measurement of the dimensions of an area, but it has been approximated as much as possible. If was measured to the nearest centimetre so in this case it was 1000 cm 0.5 cm and 2050 cm 0.50 cm. The random error is half the nearest unit. In this case:

This method is suitable for organisms which will not move, from the plantae kingdom as well as organisms from the fungi kingdom. It is also recommendable to practice this method in a population of organisms which will not be considerably damaged when the quadrat or football lands on them, which is the case of dandelions, since that are rarely depleted in such cases. If this method were to be applied in populations that can mobilize, such as animals, especially fast moving ones, the numbers of individuals would be ever-changing even during the experiment as chances of them escaping when we approach or eventually migrating could bias the results and leave the experiment inconclusive.

This method to calculate population sizes proved to be the closest and most accurate in the case where individuals in a selected area are numerous and unable to be counted individually as seen on experiment B. We tried to get out sample numbers from a random throw of our quadrats but this cannot be assured to be a random method despite our efforts to equalize the unsystematic up taking of samples. On a couple of occasions when the quadrat fell outside the area, the data was changed which could have affected our results and the uneven distribution of the dandelions in experiment B could have biased the data collecting and eventual calculation of population size. As well, the measuring of the area, especially in experiment B is not accurate and may be a little off since the measuring tape had to be used several times at one side as it only covered around 500 cm. During the measuring process errors of measurements may have occurred.

To reduce and eliminate the inaccuracies of this experiment, we could measure the area several times and in case of getting different measurements we could average them in order to get a more exact area and thus population density. Furthermore, a field where the dandelion population was not clearly unevenly distributes would have been ideal and a higher amount of throws would have given us a far more accurate idea of the estimation for the dandelion population. Perhaps our method for random throws was a bit biased a major efforts were not purposefully taken to make sure the throws landed in distributed areas of the area in order to maintain randomness, but maybe a systematic collection would have proven to be more precise.

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