Table of
Contents:

Methods Workshop - UCLA Campus

Counting wild populations can be difficult and time consuming. For this reason the methods below are demonstrated using a variety of beans which represent different species. The beans are manipulated (i.e. marked), sampled and counted to give students experience with four techniques to evaluate populations and spatial trends.

1. Population Estimates

Population estimates are an important part of ecological studies because it is rarely possible to count an entire population. Population estimates allow researchers to estimate the true size of the population (N) by sampling a portion of the population (n). The technique introduced here is the Lincoln-Peterson mark-recapture method.
There are three assumptions associated with this method: (1) closed population, (2) equal capture probability, (3) marks are not lost, gained, or overlooked. The methodology is as follows: a sample of the population (n1) is captured, marked and released. Later, another sample (n2) is captured, a subsample of which is marked (m1). Intuitively, the proportion of marked animals in the second sample should be equivalent to the proportion of animals marked in the entire population so that the number in the entire population can be determined.

N = (n1)(n2)/(m1)

Repeating the resampling effort allows the calculation of variance, and this method, developed by Chapman (1951), reduces the bias over the single recapture method.

UCLA's Sculpture Garden

2. Community Analysis

This research addresses the analysis of species in different habitats, and asks: Are the observed data for these populations different or not. Chi-square tests are useful when comparing matched data by determining if an observed condition differs from and expected distribution. In other words, do these birds all use the habitats the same?
Methods
Three species of birds (represented by different types of beans) are sampled on three streets with different vegetation (represented by different plate colors), and the data are entered into an “observed” table (Table 2). The data table permits calculation of the expected values. Rows and columns are summed to calculate the expected table values (Table 3) for each part of the population with the following formula: (row*column)/total number = expected. A Chi-square table facilitates calculations (Table 4). Degrees of freedom are calculated as follows: (rows-1) multiplied by (columns –1). The Chi-square value and the degrees of freedom are located on a table of critical values to determine the significance level. I am interested in a significance level of 0.05.
Results
The observed relationships between bird species and habitat type differed significantly from the expected relationship (X² =17.32, df = 4, P< 0.001).

Table 2. Observed frequency of 3 species in 3 habitats

Bird Species	Pine	Jacaranda	Ash	Totals
House Finch	9	9	26	44
N. Mockingbird	11	16	6	33
House Sparrow	14	8	7	29
Totals	34	33	39	106

Discussion
This analysis leads me to reject the null hypothesis that bird species and habitat types are independent. There is a strong relationship between bird species and habitat type. The limitations of the Chi-square test, simply the conclusion that the two variables are independent, prevent me from making any further inferences. This demonstrates that the Chi-square test can be used to test for general relationships, and if needed, further analysis can be designed. It should be noted that the results calculated in the field (Green Room X²= 521.09) do not match the results obtained here. This is likely due to some confusion regarding the Chi-square table, and the disparity between the number of calculators and the number of people calling out numbers.

Table 3. Expected frequency of 3 species in 3 habitats

Bird Species	Pine	Jacaranda	Ash
House Finch	14.11	13.70	16.19
N. Mockingbird	10.58	10.27	9.03
House Sparrow	9.30	9.03	10.67

Table 4. Chi-square calculation to determine if observed
distribution is different from the expected distribution.

Species/habitat	O	E	(O-E)	(O-E)²	(O-E)²/E
Finch/Pine	9	14.1	-5.1	26	1.84
Mockingbird/Pine	11	10.6	0.4	0	0.02
Sparrow/Pine	14	9.3	4.7	22	2.38
Finch/Jacaranda	9	13.7	-4.7	22	1.61
Mockingbird/Jacaranda	16	10.3	5.7	32	3.15
Sparrow/Jacaranda	8	9	-1	1	0.11
Finch/Ash	26	16.2	9.8	96	5.93
Mockingbird/Ash	6	9	-3	9	1.00
Sparrow/Ash	7	10.7	-3.7	14	1.28
Chi-square (X²)					17.32
Degrees of Freedom	(3-1)*(3-1)				4

Palm Court, Bunche Hall

3. Environmental Gradient Analysis

This research looks at four species of birds (lima beans, peas, lentils, Pinto beans) on an environmental gradient (plates) and asks if each species is distributed equally across the gradient. This type of analysis can reveal overlap of the elevations used by each species, or indicate the sensitivity of a species to elevation.
Methods
This exercise begins by recording the number of each species that occur at each of six elevation gradients (labeled 1-6). The frequency of occurrence is then plotted against gradient to determine which, if any species exhibit a normal distribution. A normal distribution would mean that the highest frequency of individuals would occur at the middle elevation.
Results
All four species exhibited a different pattern over the environmental gradient. Species A’s pattern could be described as bi-modal because of the high frequency at the lowest elevation, a low frequency at the second elevation class and then high frequencies at the third and fourth elevation classes. Species B shows a linear increase with increasing elevation class. Species C shows a bell curve that is very similar to a normal distribution, except this data shows a skew to the left. Species D also shows a bell curve, highest frequency at mid elevation classes, also with a skew left. (Figure 1)
Discussion
Species C and Species D exhibit a similar pattern in environmental distributions. This could signify that these two species are not in competition with each other. Species B demonstrates some avoidance of the lower elevation classes. This could be because of some habitat requirement such as a nesting tree species preference, which restricts this species to higher elevations. Species A shows a disjunctive pattern. Further analysis is needed to determine the cause of this pattern, but sampling bias or error could be responsible for this result. There was some confusion about the order of the elevation classes (plates) during this exercise.

Figure 1. Environmental Analysis of 4 species of birds over
an elevational gradient

4. Two Variable Analysis and Linear Regression

This method of analysis uses a simple linear regression to evaluate the response of an independent variable (y) to a dependant variable (x). In this case we are interested in determining if there is a relationship, or correlation, between the number of white species and the number of red species in these field sites. The linear regression permits us to measure the strength of the correlation and to test the correlation for significance.
Methods
I counted the number of individuals of two types, white and red, in ten field sites (plates). I recorded the counts in a table and them plotted them. Next I calculated the R² value to determine the strength of the relationship between white and red.
Results
I found a slight positive correlation (r = 0.34) between white species and red species in the ten field sites surveyed. See Figure 2.
Discussion
This data shows that for 34% of the time, you will see an increase in red species when you see an increase in white species. The slope of the line in the regression tells us that for every increase of one in white species we will see an increase of about one tenth in red species. This correlation is not significant because the correlation is weaker than we would expect to find at random, say with a coin toss, 50%.

Figure 2. Results of linear regression between two
species in ten field sites

Regression Statistics
Multiple R	0.34006
R Square	0.115641
Adjusted R Square	0.005096
Standard Error	4.13136
Observations	10

White	Red
3	2
5	4
8	3
7	7
11	9
12	12
9	7
12	15
24	5
34	10

Last updated: April 12, 2004.