BIOS 3010: ECOLOGY
Laboratory 10: Dispersion Analysis
Dr. Stephen Malcolm
Introduction:
Spatial and temporal patterns of distribution and abundance of
individuals within populations or metapopulations is an important consequence of
their responses to the distributions of resources and conditions as well as to
different ecological processes such as competition and predation. Description of
these patterns is necessarily the first step to the determination of how the
processes that underlie such patterns actually work.
Organisms often show characteristic distributions in time or space that
may be random, regular or aggregated and we can measure these distributions
and analyze them statistically. Distributions can be analyzed either as numbers
per unit area using plots or quadrats, or with the use of plotless techniques that
analyze distances among individuals.
Begon, Harper and Townsend (1996)
In this laboratory exercise we would like you to use both quadrat and
plotless techniques to examine the distribution of tree species in the typically
mixed forests of south west Michigan.
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Laboratory 10: Dispersion
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Tree species likely to be encountered:
(bold = most common)
Broadleaf trees:
Red maple
Sugar maple
Box elder
Dogwood
Black locust
Red oak
White oak
American beech
Hickory
Butternut
Black walnut
Sassafras
Tulip tree
Red mulberry
Osage orange
White ash
Sycamore
Black cherry
Choke cherry
Quaking aspen
Eastern cottonwood
American basswood
American elm
Hackberry
Acer rubrum
Acer saccharum
Acer negundo
Cornus florida
Robinia pseudoacacia
Quercus rubra
Quercus alba
Fagus grandifolia
Carya spp.
Juglans cinerea
Juglans nigra
Sassafras albidum
Liriodendron tulipifera
Morus rubra
Maclura pomifera
Fraxinus americana
Platanus occidentalis
Prunus serotina
Prunus virginiana
Populus tremuloides
Populus deltoides
Tilia americana
Ulmus americana
Celtis occidentalis
Aceraceae
Aceraceae
Aceraceae
Cornaceae
Fabaceae
Fagaceae
Fagaceae
Fagaceae
Juglandaceae
Juglandaceae
Juglandaceae
Lauraceae
Magnoliaceae
Moraceae
Moraceae
Oleaceae
Platanaceae
Rosaceae
Rosaceae
Salicaceae
Salicaceae
Tiliaceae
Ulmaceae
Ulmaceae
Conifers:
White pine
Red pine
Eastern hemlock
White spruce
Northern white cedar
Pinus strobus
Pinus resinosa
Tsuga canadensis
Picea glauca
Thuja occidentalis
Pinaceae
Pinaceae
Pinaceae
Pinaceae
Cyperaceae
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Laboratory 10: Dispersion
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Hypotheses to be investigated:
Ho: Trees are randomly distributed in space.
H1: Trees are evenly distributed.
H2: Trees are aggregated in space:
H21: Aggregated by tree species
(possible competitive effects)
H22: Aggregated by location
(possible effect of exposure to abiotic conditions)
The logic behind these hypotheses is based on the simplest (most
parsimonious) explanations for observed patterns. For example, random
distributions are likely if biological interactions are not important.
Even
distributions may be the product of strong intraspecific competition for resources
and aggregated distributions may be a product of strong interspecific competition
or the impact of natural enemies such as herbivores or pathogens. While you
are considering this problem it would be valuable to think about these ecological
processes, especially while you are in the field.
Methods:
Organize yourselves into working groups of 3 or 4 and measure the
distribution of trees in two ways:
(1) Quadrat samples:
Used with predictions of the Poisson distribution to measure the fit of
the observed pattern to a random pattern. This is especially appropriate for
relatively low density distributions.
You should investigate the hypotheses listed above at different spatial
scales. To do this you should count the numbers of trees in replicated quadrats
of different sizes. Mark out five quadrats of 25 m2 (5 x 5 m) that are randomly
selected (stand in the forest and throw a marker over your shoulder and set that
as the NW corner of your quadrat) and count all trees within the quadrat. Then
do the same for 5 replicated quadrats of 100 m2 (10 x 10 m) each, and again for
5 replicated quadrats of 2,500 m2 (50 x 50 m) each. In your lab notebook,
tabulate your data by quadrat area and replicate, as follows:
(a)
(b)
Sum of all data
By tree species
(2) Plotless samples:
In order to avoid problems associated with the choice of appropriate
quadrat size it is often easier to analyze dispersion with plotless techniques that
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Laboratory 10: Dispersion
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measure either the distance from a random point to all individuals, or the
distance to the nearest neighbor of an individual.
Each group should choose 50 single trees throughout an area of forest
and measure the distance to the nearest neighbor as follows:
(a)
(b)
Nearest neighbor of same species
Nearest neighbor of a different tree species (record
details).
Data Analysis:
There are two statistical techniques to determine the type of
distribution a population shows. First, one can calculate the variance/mean ratio
and plot a frequency histogram of the distribution. Second, one can use statistical
software to compare the fit of the data to a distribution. Each of these is
explained below.
1) When describing the distribution characteristics of a population, there are two
important statistics: the center (“average,” “mean” or “median”) and the spread
(“variance” or “standard deviation”). These characteristics can be graphically
seen by plotting a frequency histogram, where the distance to nearest neighbor
is the x-axis and the frequency is the y axis (see below).
A: Random Distribution
B: Aggregated Distribution C: Regular Distribution
Note that these distributions can be described by their centers (means)
and spread (variances). The random distribution (A) has a mean frequency of
about 3.7 and a variance of about 3.9 (its Variance to mean ratio, or VMR, is thus
about 1 corresponding to a random or Poisson distribution). The aggregated
distribution (B) has a mean frequency of about 3.4 and a variance of about 8.2
(VMR is significantly greater than 1, corresponds to an aggregated or negative
binomial distribution). The regular distribution (C) has a mean frequency of about
3.5 and a variance of about 0.58 (VMR is significantly less than 1, corresponds to
an even distribution).
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2) The data you collect in lab can also be compared directly to a
theoretical distribution using statistical software. The programs “negbinom.exe”
and “poisson.exe” from Krebs (1989; see references below) can be used to
compare the fit of the data to the Negative Binomial and Poisson distributions,
respectively.
In this case you can compare the fit of your data to both the Poisson
and Negative Binomial distributions using the programs “negbinom.exe” and
“poisson.exe” in the Ecology folder, or the programs in ECOSTAT.
“Negbinom.exe” and “poisson.exe” are programs from:
Krebs, C.J. 1989. Ecological methodology. Harper & Row, New York
ECOSTAT is from:
Young, L.J., & J.H. Young. 1998. Statistical Ecology. Kluwer Academic
Publishers, Boston.
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Trees commonly found in Kalamazoo county (courtesy of Dr. David Karowe)
Black Oak
This oak grows on upland sites with well-drained soils. It generally
becomes established in open fields and is intolerant of shade. Seedlings cannot
survive in the shade cast by mature black oaks. They are susceptible to fire, but
the root system will send up new shoots when the tops are killed. This may
result in dense brushy thickets. Their maximum height is about 23 m.
White Oak
White oaks grow on a wide variety of soils. Seeds will germinate and
survive in open fields but they are more shade tolerant than black oaks, and will
grow under and displace black oaks. They are susceptible to fire and do not
sprout back very well. White oaks grow to a height of 26-33 m.
Sugar Maple
Maple seedlings do not germinate and survive well in open areas with full
sun and competing weeds and grasses. They do germinate and grow (or at least
hang on) in the dense shade of other trees. Adult trees have such dense foliage
that no direct sunlight reaches the ground. Trees of all ages are very susceptible
to fire. Sugar maples grow to a height of 33 m.
Red Maple
Red maples are generally considered trees of lowland forests. Like those
of sugar maples, their seeds do not germinate and grow in open habitats, but
they do well in the damp cool partial shade of other trees. Mature red maples
cast a shade that is too dense for their own seedlings to survive. They are very
fire susceptible. Full grown trees reach a height of 26 m.
Black Cherry
Black cherry seedlings are fairly shade tolerant, but older trees are not.
Consequently, in forests they seldom reach the canopy. Occasionally a seedling
will establish and reach the canopy if a larger tree dies. Most often this tree
starts to grow in open areas and is one of the first tree species to colonize old
fields. Black cherry seldom grows to heights greater than 20 m.
Pin Cherry
The pin cherry life history is similar to black cherry, but pin cherry is a
smaller tree and often colonizes after fires.
Pignut Hickory
This tree prefers well-drained sites and generally becomes established in
areas where there is plenty of sunlight. Mature trees reach a height of 23 m.
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Flowering Dogwood
This is a true understory tree. Dogwoods can grow in the open, but most
often they become established in forests where mature oaks form a canopy at
about 26 m. The mature flowering dogwoods reach a height of 3 to 13 m.
Sassafras
Sassafras is a weedy tree. Seeds only germinate in sunny locations and
they grow quickly into a scraggly or brushy tree 7 to 10 m in height. The shade
of sassafras is sparse and many forest trees can displace them.
American Beech
Like the sugar maple, young beeches are extremely shade tolerant and
are often a codominant canopy tree with sugar maples to form a beech-maple
climax forest. Unlike maples, beeches often send up shoots from roots, and in
some cases most of the new trees develop from root sprouts instead of seeds.
Beeches make large trees up to 33 m tall with a trunk more than 1 m in diameter.
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Laboratory 10: Dispersion
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Photographic guide to commonly found trees at Asylum Lake Preserve.
Black oak (Quercus velutina)
White oak (Quercus
alba)
Sassafras (Sassafras
albidum)
BIOS 3010: Ecology
American beech (Fagus grandifolia)
Pignut hickory (Carya
glabra)
Flowering dogwood (Cornus florida)
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