WLF 448: Fish & Wildlife Population Ecology 2010

DISTANCE ESTIMATION OF ABUNDANCE

DistanceEstimation_Akepa.ppt

•  The 2 most common distance-sampling methods for estimating abundance of wildlife populations are line transect and point counts (variable circular plot).

Underlying theory

• Density is homogeneous within the area surveyed

• Density estimation for line transects and circular plots (with perfect detection)

                DENSITY = 

                                    For line transect

                                                                         2w = width of transect

                                                                         L = length of transect

                                    For circular plots

                                                                                 w = radius of plot

• But not all individuals will be detected

• We assume that the probability of detecting an individual decreases as its distance from the observer increases

            Therefore,

Detection function to estimate ProportionDetected (PD)

• Detection function: g(x) = Probability of observing and individual at given a distance (x) from the observer.

• The critical assumption permitting estimation from distance data is that all individuals directly on the line (distance = 0) are detected.  So, Actual[g(0)] = 1

                If this assumption holds:

               and we can find the area under the actual detection function by fitting to the observed data...

The main problem in distance estimation involves developing an appropriate model for g(x).

There are a variety of models and associated estimators for g(x) that can be fit to the detection-distance data:

1. Exponential power series
2. Exponential polynomial
3. Negative polynomial
4. Negative exponential
5. Half-normal.
6. Uniform
7. Fourier series (Uniform with cosine expression)
8. Others...

Akaike's Information Criteria can be used to determine the "best" function (model) given the detection-distance data.

 

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 sighting).

3. Distance and angles are measured accurately.

4. Sightings are independent events.

5. Shape criterion: function describing g(x)