WLF 448: Fish & Wildlife Population Ecology

Lab 6: LINE TRANSECT

I. Definitions and Concepts (see Braun: 107-110)

Abundance -

Density -

Population parameter -

Population estimate -

Population index -

Bias -

Accuracy -

Precision -

Confidence interval (CI) -

II. Distance Sampling Methods

III. Basic Concepts of Line-Transect Sampling

1. Data collection (overview)

L = transect line

Z = position of observer

X = position of object

W = strip width (1/2)

ri = sighting distance (flushing distance)

0i (theta) = sighting angle

yi = perpendicular distance (note: yi = ri sin 0i )

2. Underlying theory

3. Detection function

4. Estimating density

How can we use a detection function g(x) to estimate density (D^)?

where n = number of objects observed 
      L = total length of transect 
      w = strip width 

where a = one-half the effective strip width (ESW).

The constant a is simply the total area under the detection function g(x):

Underlying any continuous random variable, such as detection distance, there is a probability density function (pdf), denoted f(x). ...f(x) can be thought of as the underlying pdf from which the observed distance data were generated (e.g., normal pdf, negative exponential pdf). It can be shown that f(x) and g(x) are related by:

As noted by Burnham et al. (1980), this equation shows that f(x) is simply g(x) scaled to integrate to 1 (and hence be a valid pdf).
If g(0)=1, then f(0) = 1/â. If we can estimate f(0), then we can estimate a as:

The equation for estimating density (D = n/2La) can be rewritten in terms of f(0):

There are a variety of models and associated estimators, f(0), that can be used to fit the pdf to the detection-distance data:
  1. Fourier series
  2. Exponential power series
  3. Exponential polynomial
  4. Negative polynomial
  5. Negative exponential
  6. Half-normal.
  7. Others...
The Fourier series estimator is the most robust estimation model but it only works with perpendicular-distance data.

IV. Software for Analyzing Line-transect Data

V. Assumptions (in order from most to least critical):

  1. Objects directly on the line will never be missed, i.e., g(0) = 1.

  2. Points are fixed at the initial sighting position (i.e., no movement before or after).

  3. Distance and angles are measured exactly.

  4. Sightings are independent events.

  5. For clustered populations, the probability of sighting a cluster (e.g., flock, covey, etc.) is independent of cluster size.

VI. Field Procedures

Appropriate versus Inappropriate populations or sampling areas

Guidelines for line-transect studies (Anderson et al. 1979):

Proper estimation of density via line transect sampling schemes involves a mix of basic statistical-sampling theory and biological knowledge of the population under study. Ten important points to consider in designing a survey were suggested:

  1. The center line of the transect(s) must be straight and well marked. The observer must be able to determine the position of the line at all times. In some cases, a series of straight line segments will suffice.

  2. Care must be taken to assure that objects on the center line of the transect are seen with probability equal to one. In practice, this often can be met if the observer walks carefully along the center of the line transect at all times.

  3. Width of the transect should be treated as quite large, or effectively unbounded. Outlier data can be deleted, if necessary, during the analysis.

  4. All measurements of distances and angles must be accurate. Use a steel tape or other appropriate device to assure a high degree of accuracy. Careless measurements and rounding errors lead to poor estimates of density and sampling variances.

  5. All three basic measurements should be taken: right-angle distance (perpendicular distance), sighting distance (flushing distance), and sighting angle (flushing angle). Note: sighting distance and sighting angle are the measurements most commonly recorded in wildlife studies because the observer does not have to move from the original sighting position to obtain these data (and thus is less likely to "flush" additional animals during the measurement process). However, guideline #4 still applies.

  6. Measurements should be recorded separately for each segment of the total transect length.

  7. As a practical minimum, studies should be designed to assure that at least 40 objects are seen (n > 40), and it might be preferable if the length (L) were sufficient to allow the location of at least 60-80 objects (n > 60-80 best).

  8. A pre-survey is recommended to aid in planning the survey design. Often, a simple visit to the area to be surveyed, along with basic biological information about the animal and its habits and habitat, will be sufficient to design an adequate survey to estimate density.

  9. Attention should be given in designing the survey to assure that the population to be surveyed is not correlated with the sample line transects. For example, avoid transects running along roads, ridgetops, and streambottoms.

  10. The survey should be conducted using competent, interested, and trained personnel. This point is particularly important concerning points 1,2 and 4 above.

VII. Program DISTANCE

Analysis considerations/options:

  1. Ungrouped versus grouped data (a priori or a posteriori). Note: program DISTNACE provides frequency histograms to help evaluate the potential for a posteriori grouping of data.

  2. Choosing the appropriate sampling unit: individuals versus social groups (clusters) such as coveys or flocks.

  3. Examining the data for possible outliers. You can remove outliers by specifying a truncation distance. Note: as a general rule of thumb, do not truncate >3% of the data points.

  4. Use of replicate transect lines. It is very desirable to have some form of replicate lines (to get a more accurate estimate of variance) but this requires an adequate sample size for each line.

  5. Asymmetry of the detection function.

  6. Selecting the appropriate model/estimator for your data.

  1. Determined by using "simulations"
  1. "Shoulder" at f(0).
  2. Asymptotic tail.
  1. sample variance
  2. coefficient of variation (CV = SD/mean).
  3. precision of density estimate
  1. Ho: model provides good fit to the data.
  2. Based on a posteriori grouping of data ("cut points"  can be specified for evaluation).
  3. Failure to reject the null hypothesis (see above) is not valid evidence that the model is the "true" model for the data.
  4. Do not use the goodness-of-fit tests as the sole criteria for selecting an estimator.

Output from Program DISTANCE

  1. Introduction

  2. Symbol definitions

  3. Model selection

  4. Data description, including summary statistics and list/plot of data.

  5. Density estimation narrative.

  6. Density estimate(s) for each model/estimator chosen.

7.  Summary of estimation results

VIII. In-class Exercise

IX. Problem set

X. Selected References:

 

Revised: 11 September 2007