Biology 160L - 2006
Detecting Patterns of Dispersion and Effects of Sample Unit Size
Patterns of dispersion of organisms
Dispersion is a measure of how individuals of a species are distributed relative to one another. Patterns of dispersion may range from uniform (under-dispersed), to random, to clumped (aggregated, over-dispersed). Patterns of dispersion often suggest ecological mechanisms that cause the observed distributions. These mechanisms can be environmental, such as the distribution of resources (e.g., prey, refuge) or behavioral (e.g., territoriality, mutualism, facilitative recruitment). If organisms are uniformly spaced then intraspecific competition is suggested and experiments testing for it could be devised. Aggregated distributions often indicate that resources are also clumped or responses to some mutualistic intraspecific interaction. Random distributions often indicate the lack of intraspecific interactions. Hence determining the underlying pattern of dispersion of organisms is often a key first step in the study of their ecology.
A complication to the study of the distribution of organisms is the spatial scale over which the organisms are sampled. It is usually the case that the calculated distribution will vary as the spatial scale of the sample increases. For example, consider the distribution of a marine alga (e.g., kelp) that lives on rocky reefs. Within an established stand of algae, individuals are often found in uniform distributions – because of strong intraspecific competition for light. Moving to a scale greater than the size of isolated rocky reefs, the dispersion of algae will be clumped, occurring on rocky reefs and absent on sandy habitats between reefs. At an even larger spatial scale, along the vast stretches of the coast, the distribution might be random since the occurrence of rocky reefs is randomly distributed along the coast. In this field exercise we will estimate the pattern of dispersion of an extremely abundant mudflat snail. We are particularly interested in demonstrating how the size of the sample unit (i.e. quadrat) used to estimate density and dispersion can influence the estimate of these variables and how these variables are calculated.
One commonly used analytical method of determining the dispersion pattern of organisms is based on the variance-to-mean ratio. Recall that the mean is the average number of measurements (here, the numbers of individuals, but could be percent cover, heights of individuals, etc.), and the variance is an estimate of the variability of those same measurements, among replicate samples. Formally, the mean is:
where xi is the number of individuals in sample i, and n is the number of samples
And the variance (s2) is:
where X-bar is the mean among replicate samples and Xi is the measurement of the ith sample.
It turns out that the mean should equal the variance if variates (measurements) are distributed randomly (from the Poisson distribution). So the variance-to-mean ratio (VMR) should be 1. In uniform distributions the number of measurements per sample should all be very similar (theoretically, the same). This means that the mean should be the same as any single sample and the variance should be close to zero (therefore, the VMR should be much less than 1, almost zero). Clumped distributions will have many samples with zeros and a few with large numbers of individuals. Thus, the variance among replicate samples should be great and the VMR should be >1.
Species Background - Battilaria attramentaria is an introduced intertidal snail similar to and competitor with the native horn snail Cerithidea californica. It is a Japanese native snail and was imported in the 1930s with oysters. The distribution on the west coast of N. America is from Elkhorn Slough northward to British Columbia. Batillaria is easily distinguished from Cerithidea because it lacks the welt-like ribs of Cerithidea and because its aperature tends to form a short canal at the base. It occurs in dense aggregations in the mudflats.
Field protocol (also see figures)- We will examine the dispersion patterns of Batallaria along a gradient by sampling continuous 0.0015m2 plots (12.5x12.5cm2). By sampling adjacent quadrats the data can be combined to get values for larger quadrat sizes. We will count the number of Batillaria in continuous 12.5 x 12.5cm2 plots that will equal an overall quadrat area of 8x2m. A transect line will be placed at the edge of the pickleweed, Salicornia, and extend perpendicular out into the mudflats. Along this transect each group will have a designated spot to place their subdivided 0.25m2 quadrat. Buddy pairs will work together counting and recording data on the total number of individuals per 12.5x12.5cm square. Each .25m2 quadrat will be given a C-value (1-16) so that you can properly input the data and recreate the structure of the data set. Each buddy pair will sample 4 of the 0.25m2 quadrats, counting all individuals per square.
See map of quadrat layout
Quad. sizeAreaCODE
12.5x 12.5 cm -0.0015m2 A
25 x 25 cm -0.0625m2 B
50 x 50 cm -0.25m2 C
1m x 1m 1m2 D
4x4 m-4m2 E
Data analysis
We will generate plots of the variance/mean ratios vs. the quadrat size and density versus position down a vertical gradient (away from the Salicornia).
Questions
1)Is there a gradient in the density of individuals as you move away from the edge of Salicornia?
a)Using D’s (which are the 1 meter sq. quadrats) produce a bar graph of density (# per meter sq. versus distance (1 meter increments.)
As an example there are 2 D’s at each vertical level: from Salicornia to the bottom of the grid they are:
E1D1, E1D2 – average these to get density per 1 m sq at the highest vertical level
E1D4, E1D3
E2D1, E2D2
E2D4, E2D3
E3D1, E3D2
E3D4, E3D3
E4D1, E4D2
E4D4, E4D3 the lowest vertical level
b)Using densities from quadrat size C., plot density versus location of quadrat. The idea here is to recreate the spatial arrangement of quadrats in both vertical and horizontal directions (in contrast to what you do by producing the bar graph – which shows variability only in the vertical direction). To do this you should categorize density levels (e.g. 0-10, 11-20 etc.). You should choose intervals that are appropriate for the observed densities we encounter – try to have at least 4 evenly spaced density intervals. Then map density level versus quadrat position in 2 dimensions. One nice way to represent density in a 2-dimensional map is with different scales of gray scale or colors representing levels of density.
c)What other factors (biological or physical) vary along the gradient that may explain the distribution of the snails?
2)Does the pattern of dispersion (random, clumped, uniform) vary with quadrat size?
a)As part of your answer plot the variance to mean ratio as a function of quadrat size.
b)What other factors (biological or physical) vary along the gradient that may explain the observed pattern of dispersion?