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.  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.

 

 

Tree species likely to be encountered:

 

(bold = most common)

 

Broadleaf trees:

Red maple                           Acer rubrum                       Aceraceae

Sugar maple                       Acer saccharum               Aceraceae

Box elder                              Acer negundo                      Aceraceae

Dogwood                              Cornus florida                      Cornaceae

Black locust                         Robinia pseudoacacia      Fabaceae

Red oak                                Quercus rubra                    Fagaceae

White oak                            Quercus alba                      Fagaceae

American beech                Fagus grandifolia               Fagaceae

Hickory                                 Carya spp.                           Juglandaceae

Butternut                              Juglans cinerea                 Juglandaceae

Black walnut                       Juglans nigra                      Juglandaceae

Sassafras                            Sassafras albidum            Lauraceae

Tulip tree                              Liriodendron tulipifera       Magnoliaceae

Red mulberry                       Morus rubra                         Moraceae

Osage orange                     Maclura pomifera                Moraceae

White ash                             Fraxinus Americana           Oleaceae

Sycamore                             Platanus occidentalis         Platanaceae

Black cherry                       Prunus serotina                 Rosaceae

Choke cherry                      Prunus virginiana              Rosaceae

Quaking aspen                   Populus tremuloides          Salicaceae

Eastern cottonwood           Populus deltoides               Salicaceae

American basswood          Tilia Americana                   Tiliaceae

American elm                      Ulmus Americana              Ulmaceae

Hackberry                             Celtis occidentalis              Ulmaceae

 

 

Conifers:

White pine                           Pinus strobus                     Pinaceae

Red pine                               Pinus resinosa                   Pinaceae

Eastern hemlock               Tsuga Canadensis            Pinaceae

White spruce                      Picea glauca                       Pinaceae

Northern white cedar       Thuja occidentalis             Cyperaceae

 

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)

 

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)     Sum of all data

(b)        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 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)       Nearest neighbor

(b)       Nearest neighbor of a different tree species (record details).

 

Data Analysis:

 

Please compare the fit of your data to both the Poisson and Negative Binomial distributions using the programs Ònegbinom.exeÓ and Òpoisson.exeÓ in the Ecology folder on drive H (H:\301Ecology), 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.