1. Estimating Population Size
Density Abundance
Relative Absolute
Density – individuals per unit area

2. Estimating Abundance {Chapters 3 & 4}
Change-in-Ratio:
Most often used by wildlife biologists for estimating density of big game species.
Assumes:
The population is comprised of two distinct {often requires morphologically distinct} types of individuals within the population.
There is a differential change in the numbers of the two types of organisms.
E.g., ungulates:

3. Catch per unit effort or removal method
Assumptions:
The population is closed.
All individuals have an equal probability of being captured between samples.
All individuals have the same probability of being captured within a sample.
Sampling intensity is sufficient to cause a decline in density.

6. This technique is often applied to aquatics, in particular fish.
Removal can also include known marked individuals.
Program CAPTURE can also be applied to removal methods using MLE.

7. Transects: Are not necessarily a special type of quadrat.
Line transects only sample a line, i.e., no area and consequently no density. If standardized, very useful for absolute abundance.
Examples:
Point contact for plants.
Random or standardized intervals for animals.

8. Belt transects can sample an area and are most often applied to plants.
For animals, if sighting distance, sighting angle, and perpendicular distance can be obtained, it is possible to estimate density.

9. Accuracy becomes a function of detection probability:
D = n / 2La
D = density
n = number of individuals observed
L = length of transect
a = half the effective viewing distance
n = 32, L = 25 km, a = 0.2 km
D = 32 / ((2)(25)(0.2)) = 3.2 indv/km2
Anderson et al. (1979) give nine recommendations for transect sampling, page 120 in Krebs.

10. Distance – Plotless Sampling Methods:
Useful for estimating density of animals and, in particular, plants that move very little; e.g., trees.
Two broad approaches:
Select random organisms and measure the distance to their nearest neighbors.
2. Select random points and measure the distance from each point to the nearest organism.
To estimate density, assume individuals are randomly distributed.
If density is known, can be used to determine spatial patterns.

13. Number of Trees in Sample
N = Number of distance measurements
∑D = sum of distance measurements
D = mean point-to-plant distance
D2 = the mean area occupied by an average tree
1 ÷ D2 = density in trees per square meter
Trees / m2 10,000 = density in trees per hectare
Species
Number of Trees in Sample
Relative Density
Trees / Hectare

14. Quadrats
Similar to plotless sampling, best applied to individuals that are relatively sessile.
Shape:
Long, narrow quadrats increase area to perimeter ratio – potentially increasing edge effects.
Long narrow quadrats take into account more habitat heterogeneity.
Two approaches, Wiegert’s method and Hendricks’ method incorporate cost analysis into determinations of sampling intensity.
An alternative approach is to simply plot a species area curve.

15. Number of Quadrats
Number of Species

16. Number of Species
Number of Quadrats

17. Mark-and-Recapture {MR} Techniques (Chapter 4)
Closed population – assumes no immigration or emigration.
Open population – assumes immigration and emigration.
Population
Closed
Open – Jolly-Seber
{requires multiple markings}
Peterson Schnabel
{single marking} {multiple markings}

18. In its simplest form, MR assumes a single marking and single recapture sampling: Lincoln-Peterson {LP} or Peterson method.
N = C
M R
M = number of individuals marked in the first sample.
C = total number of individuals captured in the second sample.
R = the number of individuals in the second sample that are marked.
N = estimated population size.

19. Example:
82 fish are netted and fin clipped.
One week later the population is resampled and 70 fish are captured, 28 of which are marked.
N = 70 N = 205
82 28
However, for small sample sizes, the LP method produces biased estimators.
Bailey developed an unbiased estimate:
N = M(C + 1) / R + 1
N = 82 (70 + 1) / = 200.7

21. Potential biases: What happens if some animals lose their marks?
What if there was emigration?
What if there was immigration?
Marked animals have higher mortality?
How would trap-shy and trap-happy individuals influence the estimate?
What if marked individuals were more sluggish?

22. If there are multiple samples, the Schnabel method may be applied.
The Schnable method may be viewed as a series of multiple LP samples that are averaged.
Both the LP and Schnabel approach assume:
Capture probabilities are constant over time.
Capture probabilities do not vary by individual animal.
Capture probabilities do not vary due to behavioral
responses.

23. By incorporating multiple recaptures it is possible to test for violations of the above assumptions.
Program MARK can test for deviations from the above assumption and, in turn, fit the correct model.
Manual and software can be downloaded for free:

24. In practice, Maximum Likelihood Estimators {MLE} are used to calculate N and test for violations of the above assumptions.
If the above assumptions are violated, a variety of different models can be applied, such as Zippin for behavior and Darroch for time.
An alternative approach for multiple samples in a closed population is catch per unit effort or removal sampling.

25. Maximum Likelihood Estimations {MLE}
MLE are based on a likelihood function – the joint probability density function of the sample data.
The LP formula for MLE is:
N = n1n2 m2

26. Open Population Models
Jolly-Seber {Jolly-Seber-Cormick} {JS}
Allows for immigration and emigration.
Requires multiple samples.
Similar to the closed population models, uses MLE.
Has the same assumptions as the closed models.
As with the closed models, variations have been developed for unequal catchability.

27. Total Enumeration
Assumes all individuals in the population are marked.
If an individual skips a census, it back-counted and included in the total density of the skipped census.
There have been major debates whether estimation techniques or enumeration is the most appropriate approach.