FIU Ecology Webpage



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).

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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 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:

0: species not present

1: 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 point-quarter 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.

-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 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.

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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).

VII. The Quadrat Method

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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 Figure 4: Example of a quadrat,

individuals in the population are clumped in dispersion, there will divided into sub-quadrats.

be a few quadrats with many individuals, and many quadrats with no

individuals (Figure 3C, F).

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.

Table I: Example data -- there are 40 total trees, 44 total individuals, and a mean of 1.1 individuals per tree.

|Number of |Number of |fixi |

|Individuals per tree |trees | |

|(xi) |(fi) | |

| |(O) | |

|0 |9 |9 * 0 = 0 |

|1 |22 |1* 22 = 22 |

|2 |6 |2 * 6 = 12 |

|3 |2 |3 * 2 = 6 |

|4 |1 |4 * 1 = 4 |

|5 |0 |5 * 0 = 0 |

|∑ |40 |44 |

|µ |1.1 |- |

2. Calculate the mean number of individuals per tree.

To calculate the mean value for data in this format use the following equation…

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…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)…

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…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)))

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

(2.718)1.1(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

(2.718)1.1(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.

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 Chi-square 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 |Observed |P(x) |Expected |(O-E)2/E |

|individuals |Frequency | |Frequency | |

|per tree |(O) | |E | |

|(xi) | | | | |

|0 |9 |0.3329 |13.315 |1.398 |

|1 |22 |0.3662 |14.646 |3.693 |

|2 |6 |0.2014 |8.055 |0.525 |

|3 |2 |0.0739 |2.954 |0.308 |

|4 |1 |0.0203 |0.812 |0.043 |

|5 |0 |0.0045 |0.1787 |0.179 |

|∑ |40 |1 |- |6.145 |

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 |Observed |P(x) |Expected |(O-E)2/E |

|individuals |Frequency | |Frequency | |

|per tree |(O) | |E | |

|(xi) | | | | |

|0 |9 |0.3329 |13.315 |1.398 |

|1 |22 |0.3662 |14.646 |3.693 |

|2 |6 |0.2014 |8.055 |0.525 |

|3 | | | | |

|4 | | | |0.226* |

|5 |3 |0.0987 |3.945 | |

|∑ |40 |1 |- |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.

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.

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 |Tally of Trees (fi) |Number of Trees (fi) |

|(xi) |(O) |(O) |

|0 |11111 |5 |

|1-5 |111 |3 |

|6-10 |1111 |4 |

|11-15 |11 |2 |

|16-20 |11111111 |8 |

|21-25 |1 |1 |

|26-more |111 |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 leaf-cutting 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.

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