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Ecological techniques and Distribution patterns
Field sampling
I. Introduction to ecological systems
Ecologists frequently refer to their subject of study as a system that they investigate (O'Neill
2001). A group of potentially interbreeding individuals of the same organism (a population) is a system;
an assemblage of different species in a given area (a community) is a system; and a large area of land
containing many populations of organisms arranged in different local communities over areas with unique
abiotic environments is also a system (an ecosystem). All ecological systems share two important traits,
structure and function. The structure of a system is defined by its measurable traits at a single point in
time and can include living (biotic; ex: tree height, species density, tree canopy vs open savannah) and
non-living (abiotic; ex: mountainous vs flat, soil depth, water depth, nutrient composition) components.
Ecological systems function as the component parts exchange energy through time (ex: a small fish eats
algae then the fish is eaten by bigger fish which die and leave the nutrients accumulated by the algae and
small fish in the soil as the bigger fish decomposes).
Figure 1: Prescribed fire in a Miami-Dade County pine rockland community.
A significant challenge to ecologists is to measure components of structure and function. In the
example below we can see how many different kinds of components need to be measured in order to
adequately describe and understand how the ecosystem functions.
Following a fire, the structure of a fire-dependent plant community like pine
rocklands (Figure 1) could be described by the biomass of vegetation, the number of
species and their relative abundances, and the soil chemical properties (e.g., nutrient
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content and pH). These same variables could be measured annually for two decades. By
measuring these variables repeatedly through time, we could gain insight into how this
plant community functions. After a fire, initial plant biomass will be low, but then it will
rise slowly for a few years and then will rise quickly. Eventually plant biomass will
stabilize and remain stable until the next disturbance. The number of species will follow a
similar pattern for the first few years following a fire. After reaching its peak, species
number in the pine rockland will decline to fewer species that remain present until the
next fire; however, seeds of the declining species generally remain in the soil waiting for
the next fire to create the specific environment needed for germination and establishment.
Meanwhile, soil nutrient content and pH are also changing with plant biomass and
species number. By making such detailed measurements in a pine rockland community
through time, we can understand the emergent functional properties of this ecological
system.
II. Field sampling and measurement of biomass
As in the above example, ecologists collect data, often in a natural setting, to understand the
structure and function of the systems that they study. Field sampling is one of the most important aspects
of ecological investigation, and it is important that you gain an understanding of some common methods
that ecologists use to describe ecological systems. In this lab you will learn and employ sampling
techniques that are widely used in ecology. Not surprisingly, there can be large differences in the methods
used to sample plants and animals or even different communities of plants or animals. However, there are
several techniques that can be used in a wide variety of situations. The first step in choosing a sampling
technique is to determine what question you are interested in. Do you want to learn about the distribution
and abundance of a particular species? Are you interested in understanding patterns of community
composition? It is important to keep in mind that you must pick the best sampling technique for a given
ecological system, and that not every method will work in every situation. Two basic ecological sampling
techniques are reviewed below.
Plot (quadrat) sampling
Plot (or quadrat) sampling is commonly used to sample populations/communities of plants and
animals with limited mobility in a variety of aquatic and terrestrial ecosystems. Plot sampling is used to
intensively sample a subset of the system in question to obtain a representative sample. Plot data should
be replicated a number of times, in a random way, to ensure that the data represent an unbiased picture of
the system. When true randomness cannot be obtained, haphazardly selecting plot locations is often used.
Determining where to place a sample of plots is critical to a good study, and there are a variety of
techniques available. Some of these include “over the shoulder tosses,” randomly generated positions, and
stratified samples.
Once a plot has been selected, the total number of individuals of each species can be counted to
determine densities and species composition. While this method is objective, it can be extremely time
consuming, especially when some species are very abundant. Some species do not lend themselves well
to the count method because it is hard to differentiate individuals (e.g., plants that exhibit vegetative
reproduction, corals, etc.) or individuals are too numerous to easily count. A measure of the percentage of
area within the plot covered by these species (percent cover) is often used. Accurately estimating percent
cover can be very difficult, although advances in digital cameras and imaging software have alleviated
some of the problems. Because of the difficulties involved with obtaining accurate values for percent
cover, the Braun-Blanquet method is often used for these species. This method involves delineating a
specific area (the plot or quadrat), identifying all species in that area, and then assigning a code to each
species based on its percent cover. An example of Braun-Blanquet codes is:
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0: species not present
1: species <5% of total
2: species 5-10% of total
3: species 10-25% of total
4: species 25-50% of total
5: species 50-90% of total
6: species >90% of total
Clearly, these are subjective classifications, so it is important that the same observer make code
classifications whenever possible.
Transect sampling
Transect sampling is one of the most widespread ecological techniques for sampling both plants
and animals. To implement this technique, the investigator establishes a line (i.e., the transect line)
between two points. There are three major types of transects: belt transects, line-intercept, and strip
census (or line transect). In a belt transect all individuals within a specified distance from the transect line
are counted. Based on the length and width of the transect, densities of species can be calculated. During
line-intercept transects, only individuals that come in contact with the transect line are counted and the
length of the transect line they occupy is often measured. This type of transect is mainly used by plant
ecologists. Strip censuses are typically used for mobile organisms. The researcher walks along the
transect, recording individuals encountered. The data collected represent an index rather than a density.
Densities can be estimated if the distance to each observed individual is measured. As with plot and pointquarter samples, it is important to have replicate transects within the same area.
III. Designing ecological experiments
In future labs, we will discuss the hypothesis testing method. At this point, you should be aware
that, in order to test a hypothesis, you must design appropriate experiments and sampling methods.
Making inferences (i.e., deciding whether or not to reject a hypothesis) requires experiments designed
with statistical tests in mind. Design your observations in order to explain variability in the system of
study so that you understand its structural and functional properties. Excellent experiments usually require
familiarity with basic biological principles in addition to the properties of specific systems. Keep in mind
that there are many different experimental and sampling designs, and your selection of the appropriate
design depends on the objective(s) of the experiment.
IV. Are your results representative of the population?
As we will see this week there are myriad sources of error that can intrude into estimation of
population parameters. Often times these are intrinsic to the methodology that you are using. For example
some methods consistently overestimate parameters while in other cases human error is the source of
biased or erroneous estimates. One way to evaluate your results and/or evaluate your samples is to
consider them in the context of precision and accuracy (Figure 2).
-Precision refers to the degree of repeatability of a single measurement. Imprecise measurements
are made, for example, when someone does not consistently read a ruler correctly.
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-Accuracy refers to the degree to which single measurements reflect the true value of the object
being measured.
Accurate but not precise
Both precise and accurate
Precise but not accurate
Figure 2: Examples of accuracy and precision
There is often a tradeoff that ecologists must make when investigating populations and
ecosystems. Time, space, technology and often money represent significant barriers to gaining estimates
that are both accurate and precise. As a result of these limitations, the investigator may sacrifice precision
or accuracy when choosing a methodology. These compromises can be cause for consternation among
scientists; however, the ability to compromise when designing experiments or field studies is often a large
part of ecological studies. Because different methodologies often produce accurate, yet biased results,
comparing estimates collected by different methods (or observers) can be problematic.
Population ecology
Population distribution patterns
V. Introduction to population distribution patterns
The distribution of individuals in a population describes their spacing relative to each other.
Different species and different populations of the same species can exhibit drastically different
distribution patterns. Generally, distributions can follow one of three basic patterns: random, uniform
(evenly spaced or hyper-dispersed), or clumped (aggregated or contagious; see Figure 4). Species traits
such as territoriality, other social behaviors, dispersal ability, and allelochemistry will shape individual
dispersal (i.e., movements within a population), emigration, and immigration, all of which affect
population distribution patterns. In addition to species traits, the distribution of resources or microhabitats
links population distribution patterns to the surrounding abiotic environment.
VI. Measuring population distribution
Population distribution is commonly quantified by population ecologists. With mobile organisms,
this requires intensive sampling. Therefore, we will measure the distribution patterns of less mobile
species. Analyses of population distribution patterns usually follow a standard method in which observed
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distribution patterns are compared to predicted, random distribution patterns. As such, the following
steps are followed:
1. A particular method of field sampling is chosen, which will allow the ecologist to quantify the
distribution of individuals within a population of a given species. – This is the observed
distribution pattern.
2. A standardized technique is used to determine what values would have been obtained if the same
sampling techniques was used for a randomly distributed population (e.g. the Poisson
distribution). – This is the predicted, random distribution pattern.
3. A statistical test is used to evaluate the hypotheses:
HO: There is no significant difference between the observed distribution pattern and the
predicted, random distribution pattern.
Ha: There is a significant difference between the observed distribution pattern and the
predicted, random distribution pattern.
4. If p > 0.05, then we fail to reject the null hypothesis and therefore state that the observed
population is randomly distributed.
If p < 0.05, then we reject the null hypothesis and therefore state that the observed population is
not randomly distributed. It is therefore uniform or clumped.
5. If the population is not randomly distributed, we then use a method to determine whether it is
uniform or clumped.
C
A
B
D
E
F
Figure 3: Common dispersion patterns are represented above. Figures A, B, and C represent the spacing
of individuals within a population relative to each other. The entire square indicates the entire quadrat,
and each small square indicates one sub-quadrat. Figures D, E, and F indicate the number of individuals
within each sub-quadrat. Note that Figure D is derived from a randomly dispersed population, and that it
indicates a Poisson distribution (example data and figure from S. Whitfield).
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VII. The Quadrat Method
The quadrat method involves counting the frequency of
occurrences of the species of interest in each of the 100 individual
sub-quadrats that compose the quadrat. The example on the right
shows a quadrat made up of 36 sub- quadrats. Each sub-quadrat
contains 1 individual.
If the individuals within the population are randomly
dispersed, there will be a random number of individuals in each
quadrat, centered about the mean (Figure 3A, D). If the individuals
in the population are uniformly dispersed, there will be the same
number of individuals in each sub- quadrat (Figure 3B, E). If the
individuals in the population are clumped in dispersion, there will
be a few quadrats with many individuals, and many quadrats with no
individuals (Figure 3C, F).
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Figure 4: Example of a quadrat,
divided into sub-quadrats.
In today’s lab, we will modify the quadrat method. We will be assessing the distribution of epiphytes
growing on trees on campus. Each tree will represent one quadrat. Within each tree, all epiphytes,
Tillandsia usneoides and Tillandsia recurvata, will be counted. To analyze the data from this we will use
a chi-square test to evaluate our proposed hypotheses:
HO: There is no significant difference between the observed distribution pattern and the predicted,
random distribution pattern.
Ha: There is a significant difference between the observed distribution pattern and the predicted,
random distribution pattern.
The chi-square test compares a given (observed) distribution to the Poisson (random)
distribution. The Poisson distribution basically allows us to determine the probability of obtaining “x”
number of individuals within a tree, if the population is randomly distributed. For example, if the
population of interest is randomly distributed, what is the probability of obtaining 3 individuals in a tree?
To do this, follow these steps:
1. Determine the observed distribution pattern.
This information is collected in the field and then used to complete the table below, where “x” is
the number of individuals found in a tree and “f” represents the number of trees that contained x number
of individuals (This column is also labeled “O” meaning “observed distribution”). For example, suppose
we sample 40 trees to determine the distribution of the individual epiphyte species. We may get the
following results: Nine trees have 0 individuals each, 22 trees have 1 individual each, 6 trees have 2
individuals each, 2 trees have 3 individuals each, 1 tree has 4 individuals and none of the trees have 5
individuals or more (Table I).
We can then calculate the total number of individuals recorded within the tree. This is done in the “fx”
column.
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Table I: Example data -- there are 40 total trees, 44 total individuals, and a mean of 1.1 individuals per
tree.
Number of
Individuals per
tree
(xi)
Number of
trees
(fi)
(O)
fixi
0
1
2
3
4
5
9
22
6
2
1
0
40
1.1
9*0=0
1* 22 = 22
2 * 6 = 12
3*2=6
4*1=4
5*0=0
44
-
∑
µ
2. Calculate the mean number of individuals per tree.
To calculate the mean value for data in this format use the following equation…
…in which, f is the number of trees and x is the number of individuals per tree for each row in Table I. In
the given example, µ = 44/40 = 1.1
3. Calculate the Poisson probability values.
Once the mean is calculated, we can then calculate the Poisson probability values. To do this we use the
‘Poisson expression’ (Cox 2001)…
…where e = the base of the natural log = 2.7182818, µ = mean, and x = the number of individuals per
tree.
You can do this calculation in Excel, by using the following formula:
=(µ^x)/((EXP(µ))*(FACT(x)))
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We use the Poisson probabilities to determine the probability of obtaining “x” number of individuals
within a tree, if the population is randomly distributed. We can calculate these probabilities for each row
in Table I as shown below:
P(x0) =
(1.1)0
=
1
= 0.3329
(2.718)1.1(0!)
3.0038
P(x1) =
(1.1)1
= 1.10 = 0.3662
1.1
(2.718) (1!)
3.0038
P(x2) =
(1.1)2
= 1.21 = 0.2014
(2.718)1.1(2!)
6.0076
P(x3) =
(1.1)3
= 1.31 = 0.0739
(2.718)1.1(3!)
18.0228
P(x4) =
(1.1)4
= 1.4641 = 0.0203
1.1
(2.718) (4!)
72.0912
P(x5) =
(1.1)5
= 1.6105 = 0.0045
(2.718)1.1(5!)
360.456
These values can now be used to calculate the expected number of trees that would obtain “x” individuals,
if the population was randomly distributed. For example, the results above show that, if the population
was randomly distributed, then 33% of the trees should each have 0 individuals, 7% of the trees should
each have 3 individuals and 0.4% of the trees should each have more than 5 individuals.
4. Calculate the expected values.
We can now use these probabilities to calculate expected values using the equation below (essentially,
multiply each probability above by the total number of trees, in this case, 40.):
E(xi) = P(xi)∑fi
E(x0) = P(x0)∑fi = 0.3329*40 = 13.316
E(x1) = P(x1)∑fi = 0.3662*40 = 14.6463
E(x2) = P(x2)∑fi = 0.2014*40 = 8.055
E(x3) = P(x3)∑fi = 0.0739*40 = 2.954
E(x4) = P(x4)∑fi = 0.0203*40 = 0.812
E(x5) = P(x5)∑fi = 0.0045*40 = 0.1787
Based on the results above, we can see that if our population was randomly distributed, we would expect
13.3 of the 40 trees to have 0 individuals, 2.9 of the trees to have 3 individuals and .17 of the trees to have
more than 5 individuals.
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5. Compare the Observed values to the Expected values using the Chi-squared test (χ2).
We can now compare our observed values and our expected values to see whether or not there is a
significant difference between them. To calculate our Chi-square value, we use the following equation:
χ2 = ∑(O – E)2
E
Please note that you must calculate this equation for each row, and THEN sum all the values to obtain
your Chi-square value.
In this example, the expected values for trees with three or more individuals are combined for the Chisquare analysis because those trees have expected values that are less than 1. If the expected frequency for
any category or set of categories is less than 1 then your Chi-square value is under-estimated; therefore,
you must combine the values from this category and the one preceding it, and then use the combined fi
value to calculate Chi-square (see Table 2).
In the example below, because the Expected values for rows 4 and 5 are less than 1, the values for these
two rows were added to the row preceding them. Therefore:
The combined Observed frequency = 3
The combined Probability = 0.0987
The combined Expected frequency = 3.945
The combined Chi-square value is therefore: (3-3.945)2/3.945 = 0.226
Table II. Example of a completed Poisson Table
Number of
individuals
per tree
(xi)
Observed
Frequency
(O)
0
1
2
3
4
5
∑
9
22
6
2
1
0
40
P(x)
Expected
Frequency
E
(O-E)2/E
0.3329
0.3662
0.2014
0.0739
0.0203
0.0045
1
13.315
14.646
8.055
2.954
0.812
0.1787
-
1.398
3.693
0.525
0.308
0.043
0.179
6.145
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Table IIb. Example of a Poisson Table -- Asterisk (*) denotes that the categories for 3, 4, and 5
individuals per tree were combined into one class in order to better meet assumptions of the Chi-square
test.
Number of
individuals
per tree
(xi)
0
1
2
3
4
5
∑
Observed
Frequency
(O)
P(x)
Expected
Frequency
E
(O-E)2/E
9
22
6
0.3329
0.3662
0.2014
13.315
14.646
8.055
1.398
3.693
0.525
3
40
0.0987
1
3.945
-
0.226*
5.841
6. Determine the adjusted number of categories and calculate the degrees of freedom.
Once you have calculated the Chi-square statistic, you will then need to calculate one other value in order
to obtain your p-value, the degrees of freedom.
The degrees of freedom (df) is used to locate the χ2statistic on a Chi-square table:
df = k-2
…where k is the number of categories remaining after you perform any necessary adjustments to the
number of rows in the table. In the example above, after adjusting the table, we end up with 4 categories
(instead of the original 6). Therefore the degrees of freedom = 4 – 2 = 2.
7. Use the Chi-square statistic and the degrees of freedom to obtain the associated p-value.
The χ2 statistic for our example is 5.841. You can locate this value on the Chi-square table and then find
the associated p-value, or use the following Excel formula to get a precise p-value:
=CHIDIST(χ2,df)
…where χ2 is the test statistic you calculated and df are the degrees of freedom.
Using the following equation in Excel: =CHIDIST(5.841,2), we get an associated p-value of 0.75.
8. Based on the p-value, determine whether to reject or fail to reject your null hypothesis.
If p > 0.05, then we fail to reject the null hypothesis and therefore state that the observed population is
randomly distributed.
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If p < 0.05, then we reject the null hypothesis and therefore state that the observed population is not
randomly distributed. It is therefore uniform or clumped.
Using our example, the p-value was 0.75 which is greater than 0.05. Therefore the population is randomly
distributed.
If our p-value was less than 0.05, meaning that the population is not randomly distributed, we would then
have to plot our observed data on a graph to determine whether it is uniform or clumped, based on the
pattern of the graph.
VIII. Objectives
In this lab, we will use two field sampling methods to measure the density of organisms.
The objective is to compare two field sampling methods: Plot (quadrat) and Transect, and test for sources
of bias in the data that your class collects.
Then you will be collecting data on the dispersion pattern of populations of epiphytic species
chosen by your TA. The objective is to determine if the dispersion patterns of the populations you
investigate are random, uniform, or clumped.
VIIII. Instructions
Before you leave the lab to go to your field site for today’s exercise, be sure to do the following:
1) Generate several hypotheses as a class that you can test with today’s exercise (Hint: the objective,
above, may help with this).
2) Discuss how to keep track of the data that you record at your field site and set up data sheets.
3) Divide into groups and work as teams. Work should be divided so that all team members get to
experience each aspect of the exercise.
4) Gather all the equipment that you will need for the lab exercises. Equipment that you will need is
measuring tapes, flags, 1m ruler, aluminum tags, and a notebook. Read the activity descriptions
below.
FIELD SAMPLING METHODS
With the help of your TA the entire class will pick a green area big enough for the activity. The area could
be 30m x 30m, and you will have to mark its limits with flags. Before start with the exercises, randomly
distribute the aluminum forestry tags within your pre-established area. Notice that each tag has a letter,
and there are 4 letters in play: A, B, C, and D and represent 4 different species.
The following exercises will be performed by each field team (group):
1) The first method you will use is quadrats. Toss a 1m2 quadrat blindly over your shoulder to locate
it in a haphazard position within the pre-established area. In the quadrat, count the number of
individuals of each species (A, B, C or D) found in each plot. Do this 30 times per group.
2) Within the same pre-establish area now you will conduct a strip census. Establish a 15m long
transect line across a given area (randomly picked). At each 1m interval, count the number of
individuals of each species (A, B, C or D) that fall within each 1m of your transect (like a belt
transect). Do this two times per group.
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EPIPHYTE DISTRIBUTION SAMPLING
You will be collecting data on 40 trees (10 trees per group) assessing the epiphytic species
distribution of the entire population. Count the number of individual epiphytes within each tree.
Record data as shown below, using a tally for each row:
Number of Individuals per
Tree
(xi)
Tally of Trees (fi)
(O)
Number of Trees (fi)
(O)
0
1-5
6-10
11-15
16-20
21-25
26-more
11111
111
1111
11
11111111
1
111
5
3
4
2
8
1
3
You will then use this data to complete your chi-square calculations. To perform the calculations, use the
following number of individuals per tree as your xi value for each category above:
0=0
1-5 = 3
6-10 = 8
11-15 = 13
16-20 = 18
21-25 = 23
26-more = 28
Literature Cited
Cox, G. W. 2001. General Ecology Laboratory Manual, 8th edition. McGraw-Hill, New York.
O'Neill, R. V. 2001. Is it time to bury the ecosystem concept? (With full military honors, of course!).
Ecology 82:3275-3284.
Further Reading
Cornell, H. V. 1982. The notion of minimum distance or why rare species are clumped. Oecologia
52(2):278-280.
Johnson, P. T. J. 2003. Biased sex ratios in fiddler crabs (Brachyura, Ocypodidae): A review and
evaluation of the influence of sampling method, size class, and sex-specific mortality. Crustaceana
76:559-580 Part 5.
Williams, M. S. 2001. Performance of two fixed-area (quadrat) sampling estimators in ecological surveys.
Environ metrics 12(5):421-436.
Zavala-Hurtado, J. A., P. L. Valverde, M. C. Herrera-Fuentes, A. Diaz-Solis. 2000. Influence of leafcutting ants (Atta mexicana) on performance and dispersion patterns of perennial desert shrubs in an
inter-tropical region of Central Mexico. Journal of Arid Environments 46(1):93-102.