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Unformatted text preview: Exercise 3C Estimating Population Size & Distribution
Parts of this lab adapted from General Ecology Labs, Dr. Chris Brown, Tennessee Technological University and Ecology on
Campus, Dr. Robert Kingsolver, Bellarmine University. Introduction
One of the goals of population ecologists is to explain patterns of species distribution and
abundance. In today’s lab we will learn some methods for estimating population size and for
determining the distribution of organisms.
Measuring Abundance: Quadrats
One of the first questions an ecologist asks about a population is, "How many individuals are
here?" This question is trickier than it appears. First, defining an individual is easier for some
organisms than others. In Canada geese, a "head count" of geese captured on the ground during
their summer molt gives a clear indication of adult numbers, but should eggs be counted as
members of the population or not? In plants, reproduction may occur sexually by seed, or
asexually by offshoots that can remain connected to the parent plant. This reproductive strategy,
called clonal reproduction, makes it difficult to say where one individual stops and the next one
Once the individual is defined, ecologists working with stationary organisms such as trees or
corals can use spatial samples, called quadrats, to estimate the number of individuals in a larger
area. Quadrats are small plots, of uniform shape and size, placed in randomly selected sites for
sampling purposes. By counting the number of individuals within each sampling plot, we can see
how the density of individuals changes from one part of the habitat to another. The word "quadrat"
implies a rectangular shape, like a "quad" bounded by four campus buildings. Any shape will work,
however, as long as quadrats are all alike and sized appropriately for the species under
investigation. For creatures as small as barnacles, an ecologist may construct a sampling frame a
few centimeters across, and simply drop it repeatedly along the rocky shore, counting numbers of
individuals within the quadrat frame each time. For larger organisms such as trees, global
positioning equipment and survey stakes may be needed to create quadrats of appropriate scale.
The number of individuals counted within each quadrat is recorded and averaged. The mean ( x )
of all those quadrat counts yields the population density, expressed in numbers of individuals
per quadrat area (barnacles per square meter, for example, or pine trees per hectare).
Population size can then be estimated using the formula:
N = (A/a) * n where: N = the estimated total population size
A = the total study area
a = the area of the quadrat
n = the number of organisms per quadrat Note: this formula can be used with one quardat or an average of all the quadrats as long as the
area (a) matches the number of organisms/quadrat (n).
Biology 6C 73 An alternative approach is to measure ecological density, expressed in numbers of individuals
per resource unit (numbers of ticks per deer, for example, or numbers of maggots per apple).
Members of a population constantly interact with physical features of their environment, one
another, and other species in the community. Distinctive spatial patterns, describing the
distribution of individuals within their habitat, result from these interactions. Movements, family
groupings, and differential survival create spatial patterns that vary from one population to
another. A population can also change the way it is scattered through space as seasons or
conditions change. As an example, monarch butterflies spread out to feed and reproduce during
the summer, but congregate in dense assemblies during fall migration and winter dormancy. The
physical arrangement of organisms is of interest to ecologists because it provides evidence of
interactions that have occurred in the past, and because it can significantly affect the population's
fate in the future. Analyzing spatial distributions can reveal a lot more about the organism's natural
history than we could ever know from estimates of population size alone. Since it is often impossible to map the location of every individual, ecologists measure features of
spatial pattern that are of particular biological interest. One such feature is the dispersion of the
population. D ispersion refers to the evenness of the population's distribution through space.
(Dispersion should not be confused with dispersal, which describes movement rather than
pattern.) A completely uniform distribution has maximal dispersion, a randomly scattered
population has intermediate dispersion, and an aggregated population with clumps of individuals
surrounded by empty space has minimal dispersion (Figure 3.1). Figure 3.1 Three types of spatial distribution. Individuals spread evenly through
the environment are highly dispersed, individuals clumped together exhibit low
dispersion. How can we measure dispersion in populations? A typical approach again involves quadrat
sampling. By counting the number of individuals within each sampling plot, we can see how the
density of individuals changes from one part of the habitat to another. To get a measure of
dispersion in our population, we need to know how much variation exists among the samples. In
other words, how much do the numbers of individuals per sampling unit vary from one sample to
the next? The sample variance (s2) gives us a good measure of the evenness of our distribution. 74 Exercise 3.C. Estimating Population Size & Distribution Consider our three hypothetical populations, now sampled with randomly placed quadrats (Figure
3.2). Notice that the more aggregated the distribution, the greater the variance among quadrat
counts. To standardize our measurements for different populations, we can divide the variance by
the mean number of individuals per quadrat. This gives us a reliable way to measure aggregation.
Statisticians have demonstrated that the variance/mean ratio,
x , yields a value close to 1 in a
randomly dispersed population, because in samples from a random distribution the variance is
equal to the mean. Any ratio significantly greater than 1 indicates aggregation, and a ratio less
than 1 indicates a trend toward uniformity. We could therefore call the variance/mean ratio an
index of aggregation, because it is positively related to the "clumping" of individuals in the
population. The variance/mean ratio is also called an index of dispersion, even though
dispersion is inversely related to
x . It is good to remember: a high value of
x means high
aggregation, but low dispersion. Bear in mind that the size of the sampling frame can significantly influence the results of this kind
of analysis. A population may be clumped at one scale of measurement, but uniform at another.
For example, ant colonies represent dense aggregations of insects, but the colonies themselves
can be uniformly distributed in space. Whether we consider the distribution of ants to be patchy or
uniform depends on the scale of our investigation. Figure 3.3 illustrates a population that would be
considered uniformly distributed if sampled with large quadrats, but aggregated if sampled with
smaller quadrats. For organisms distributed in clusters, the
x ratio will be maximized when the
size of the sampling frame is equal to the size of the clusters. Biology 6C 75 The significance of aggregation or dispersion of populations has been demonstrated in many
kinds of animal and plant populations. Intraspecific competition, for example, tends to separate
individuals and create higher dispersion. Territorial animals, such as male robins on campus
lawns in the spring, provide an excellent example. As each male defends a plot of lawn large
enough to secure food for his nestlings, spaces between competitors increase, and the population
becomes less aggregated. Competition can also create uniform plant distributions. In arid habitats,
trees and shrubs become uniformly distributed if competition for soil moisture eliminates plants
growing too close together.
If organisms are attracted to one another, their population shows increased aggregation.
Schooling fish may limit the chance that any individual within the group is attacked by a predator.
Bats in temperate climates conserve energy by roosting in tightly packed groups. Cloning plants
and animals with large litter sizes create aggregation as they reproduce clusters of offspring. For
example, the Eastern wildflower called mayapple generates large clusters of shoots topped by
characteristic umbrella-like leaves as it spreads vegetatively across the forest floor. By setting up
quadrats, and calculating the variance/mean ratio of the quadrat counts, you can gain significant
insights about the biology of your organism.
Check your progress: 76 Exercise 3.C. Estimating Population Size & Distribution Exercise 3C: Population Size Estimate and Dispersion of Plants in a Lawn
What is the population size of the lawn species of interest? What can we infer about the natural
history of a lawn species from its spatial distribution?
Before laboratory, carefully examine lawns on campus. Regardless of maintenance efforts, few
lawns are actually monocultures. Almost all lawn communities include some broad-leaved plants
such as dandelions, plantain, or clover growing among the grasses.
Materials (per laboratory team)
1 large nail
1 meter stick
1 piece of nylon string, about 1-1/2 m long
1. Make quadrat sampler by tying one end of the string around the nail, tightly enough to stay on,
but loosely enough to swivel around the head (Figure 3.4). Then using the meter stick, mark a
point on the string 56 cm from the nail by tying an overhand knot at that position. Repeat the
procedure to make a second knot 80 cm from the nail, then a third knot 98 cm from the nail,
and a fourth knot 113 cm from the nail. The distance to the first knot represents the radius of a
circle of area 1 m2. (Try verifying this calculation using the formula Area = Br2 for a radius of
.56m.) The knots further along the string will be used to sample circles of areas 2 m2, 3m2 and
4m2, respectively. Take your sampler to a lawn area.
2. Choose one lawn species exhibiting an interesting spatial pattern and common enough to find
some specimens growing less than a meter apart. Decide what vegetative unit of this plant you
will designate as an individual for the purpose of counting plots. For non-cloning plants such as
dandelions, one rosette of leaves constitutes one individual. For cloning plants such as violets,
choose a unit of plant growth, such as a shoot, as an arbitrary unit of population size.
3. Choose an area of lawn for sampling in which this species is relatively common. Before taking
any samples, observe physical features of the habitat such as shade, soils, or small dips or
mounds affecting water runoff that might help you interpret the pattern you see. Develop
hypotheses relating the reproductive history of your species and habitat features with the
distribution you are measuring.
4. Next, you must select sites for quadrat samples within your study area. You can obtain a fairly
unbiased sample by tossing the nail within the sample area without aiming for any particular
spot, and then pushing it into the soil wherever it lands. Hold the string at the first knot and
stretch it out taut from the nail.
5. Now move the string in a circle (Figure 3.4). The length marked by your closest knot becomes
a radius of a circular quadrat with area 1 m2• If this circle is too small to include several
individuals, move out to the second knot for a 2-m2 quadrat, the third knot for a 3-m2 quadrat,
or the fourth knot for a 4-m2 quadrat, as needed. After you decide on the appropriate scale,
use the same size quadrat for all your samples.
Biology 6C 77 Figure 3.4 A string tied to a large nail, with knots tied at specified distances, can be used to sample
a fixed area of lawn. Put the nail in the ground and pull the string taut. Moving the knot around the
nail, count how many of your organisms fall within the circle. 6. As you move the string in a circle, count how many individuals fall within this quadrat. When
the circle is complete, record this number in Table 3.1. Pull out the nail, make another toss to
relocate your circular plot, and repeat for a total of 20 samples. Your sampling is complete
when you have recorded 20 quadrat counts. Data Analysis: Population Size Estimate
Calculate N for the quadrat data using the formula:
N = (A/a) * n 78 where:
N = the estimated total population size
A = the total study area
a = the area of one quadrat
n = the mean number of organisms/quadrat Exercise 3.C. Estimating Population Size & Distribution Data Analysis: Determination of Dispersion
j 2 2 S 2 x
By comparing the variance of your 20 quadrat counts with the mean, you will determine
whether the plants you sampled are aggregated, random, or uniformly dispersed. Biology 6C 79 Table 3.1 Quadrat Sampling of Lawn Species: _______________________________ 80 Exercise 3.C. Estimating Population Size & Distribution Discussion
1. Based on the variance/mean ratio, what can you conclude about the spatial pattern of your
population? How might you explain this pattern, given observations you made as you were
sampling? 2. Random sampling is very important if the data you collected are meant to represent a larger
population. In retrospect, do you have any questions or concerns about the validity of the
sampling method? If bias exists, how might you alter your method to randomize your samples? 3. An index of aggregation is maximized in patchy distributions if the size of the quadrat is the
same as the size of the organism's aggregations. Might a larger or smaller sampling unit (or a
different sized resource unit) have affected your results? 4. Would you expect another organism from the same biological community to exhibit a similar
index of dispersion? Is spatial pattern a property of the organism, or of its habitat? Biology 6C 81 ...
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