1. Estimating Animal Numbers
Uses
Definitions
Types of methods and analyses

2. Estimating Animal Numbers
Populations vs. Experimental Units N N N N N N N N N

3. Estimating Animal Numbers
Population
Abundance or population size (N)
Density
Relative abundance/density

4. Estimating Animal Numbers
Types of methods
Estimation methods
Censuses
All individuals observed
Complete
Sample plots
Surveys
All individuals not observed
Indices
Pros & cons
Cost
Precision & Accuracy

5. Estimating Animal Numbers
Indices
Estimating Animal Numbers
Censuses
Surveys
DISTANCE
METHODS

6. Estimating Animal Numbers Censuses
Aerial photography/counts
Waterfowl
Deer
Large animals

7. Estimating Animal Numbers Censuses
Thermal IR
Large homeotherms

8. Estimating Animal Numbers Censuses
Drive counts
Large animals

9. Estimating Animal Numbers Censuses
Total mapping of territories
Spot or Territory mapping

10. Estimating Animal Numbers Censuses
Radar

11. Estimating Animal Numbers Censuses
Point counts

12. Estimating Animal Numbers Censuses
Various total counts on plots

13. Estimating Animal Numbers Surveys
Mark-recapture
Distance sampling
Line transects & point counts
Distance methods
Removal methods

14. Estimating Animal Numbers Mark-Recapture
Used to estimate abundance and density for many different species
Some methods also allow the estimation of survival, population change, and harvest effects
Many methods
Lincoln-Peterson
Schumacher
Jolly-Seber
Other

15. Estimating Animal Numbers Mark-Recapture
All methods require capturing, marking, and recapturing individuals
Capture and marking may not require making contact with animals
Natural markings, e.g., jaguars
Electronic or photo sensors for recapture
Radio-telemetry

16. Estimating Animal Numbers Mark-Recapture
Sample Size & Precision
# captures & capture probability
# marked
# sampling occasions
Population size
Survival rates

17. Estimating Animal Numbers Mark-Recapture
Lincoln-Peterson
Simplest method
Mark animals on 1 occasion and record the proportion of animals recaptured on second capture occasion
Assumptions
Equal catchability among animals and trapping occasions
Animals do not lose their marks
Marking does not influence survival
All marks are correctly recorded
Closed population (i.e., no B, D, I, or E during study)

18. Estimating Animal Numbers Mark-Recapture
Lincoln-Peterson
Original model
N = CM/R
Better model
N = ((M+1)(C+1)/(R+1))-1
95% CI = ….
With and without* replacement
where: N = population size at time of marking.
M = number of animals marked as a result of the first trapping occasion.
R = number of marked animals captured during the second trapping occasion.
C = total number of animals (marked and unmarked) captured during the second t rapping occasion.

19. Estimating Animal Numbers Mark-Recapture
Lincoln-Peterson
Example: In July, 27 box turtles were marked and released. In September, 23 were recaptured, of which 17 had been marked. Therefore: M = 27, C = 23, and R = 17.
Density (N) = ((M+1)(C+1)/(R+1))-1 = ((27+1)(23+1)/(17+1))-1 = 36.3 turtles
95% CI = 31.8 – 45.4 turtles

20. Estimating Animal Numbers Mark-Recapture
Schumacher Method
Variation of the Lincoln-Peterson method, using several mark and recapture occasions
Assumptions similar to L-P method

21. Estimating Animal Numbers Mark-Recapture
Schumacher Method
Model
where: Mi = # marked in population prior to the ith day.
Ci = # captured (total) on the ith day.
Ri = # captured with marks (recaptures) on ith day.
Ui = # marked for first time and released on ith day (needed to calculate Mi)
N = Σ (CiMi2)
Σ RiMi
95% CI = …

22. Estimating Animal Numbers Mark-Recapture
Schumacher Method
A frog population sampled over 5 days
Day Ci Ri
Ui (# newly marked less deaths) Mi 1 32 2 54 18 36 3 37 31 6 68 4 60 47 13 74 5 41 87
N = 93.1 frogs
95% CI = 81.7 – 108.1

23. Estimating Animal Numbers Mark-Recapture
Jolly-Seber Method
Animals are marked and recaptured on several occasions
Population can be open
Each animal must carry a unique mark so it can be determined when each individual was last captured
Allows estimation of N & survival (Φ)

24. Estimating Animal Numbers Mark-Recapture
Jolly-Seber Method
Assumptions
Animals do not lose their marks
Captured animals are correctly recorded as marked or unmarked
Marking does not affect survival and all animals have the same survival during intervals between samples
Equal catchability*
Very important & testable
Sampling time is negligible in relation to intervals between samples
Assumptions can be changed (e.g., survival constant vs. survival different between sampling occasions).

25. Estimating Animal Numbers Mark-Recapture
Jolly-Seber Method
Field voles sampled on 11 days
Time of capture
Time of last capture 1 2 3 4 5 6 7 8 9 10 11 15 37 61 75 77 69 14 19
Total marked (mt) 16 64 79 81 76
Total unmarked (ut) 22 26 32 45 25 12
Total caught (nt) 41 48 82 89
101
107 91 27
Total released (st) 21 46 88 99
106 90 m6

26. Estimating Animal Numbers Mark-Recapture
Jolly-Seber Method
Sample
Prop. marked
Size of marked pop. N
95% CI of N
Prob. of Φ
95% CI of Φ 1
0.832 2
0.381
17.5
45.9
0.395 3
0.347
17.2
49.5
0.862 4
0.458
40.7
88.8
0.824 5
0.722
70.5
97.7
0.925 6
0.784
87.5
111.6
0.853 7
0.759
91.7
120.8
0.651 8
0.837
76.0
90.8
0.104 9
0.450
9.3
20.7
0.738 10
0.571
15.0
26.2 11
0.870

27. Estimating Animal Numbers Mark-Recapture
Tests of equal catchability
Zero-Truncated Poisson
Leslie, Chitty, and Chitty
Others
Causes of unequal catchability
The behavior of individuals in the vicinity of the trap
Learning by animals already caught (trap-shy or trap-happy)
Unequal opportunity to be caught because of trap position

28. Estimating Animal Numbers Mark-Recapture
Zero-Truncated Poisson Test of Equal Catchability
Snowshoe hares captured during 7 days
# of times caught (x)
# of hares caught (fx)
Expected frequency 1
184
174.6 2 55
66.0 3 14
16.7 4
3.2 5
0.5 6
0.1 7

29. Estimating Animal Numbers Mark-Recapture
Zero-Truncated Poisson Test of Equal Catchability
Snowshoe hares captured during 7 days
Χ2 Goodness of fit test
Ho: equal catchability (rejected)
Observed Χ2 = 7.77
Critical Χ2 = 5.99
df = 2 (x - 2; x groups combined so all frequencies > 1)
α = 0.05
Total individuals captured = 261
Mean # of captures per individual = 1.425
Estimated mean # of captures = 0.756

30. Estimating Animal Numbers Line Transects & Point Counts
Sometimes referred to as Distance Sampling
If probability of detection incorporated
Used to estimate abundance and density for many species, particularly birds
Relatively easy to apply, but labor intensive
Involves observing (both sight and sound) individuals within an area of known or estimated size

31. Estimating Animal Numbers Line Transects
Assumptions
Animals on the line will never be missed
Animals do not move before detection
Animals are not counted twice
Position and distance to animals are correctly estimated (Hayne & Emlen)
Individual observations are independent events
Larger counts yield better estimates (>60)

32. Estimating Animal Numbers Line Transects
General methods w c b a L Θ
where:
D = animal density
L = transect length
2w = transect width
ai = position of observer
bi = sighting distance (distance between animali and observer)
ci = perpendicular distance between animali and transect line
Θi = sighting angle
n = number of individuals counted

33. Estimating Animal Numbers Line Transects
Basic Density Estimate
D = n/2Lw
Counts usually biased low due to missed individuals
Example: Five transects (500m each) were run and 53 scaled quail were counted within 50m of the transect line.
D = n/2Lw = 53/(2)(2500)(50) = quail/m2 = 2.1 quail/ha
95% CI or other estimate of variation ?

34. Estimating Animal Numbers Line Transects
Emlen’s Method
Assumes that all individuals within a threshold distance are observed. After determining the threshold distance only individuals within this distance are used in calculations
Detection probability
Models
Correction to transect & point estimators (also mark-recapture and other estimators)
Radio-telemetry

35. Estimating Animal Numbers Line Transects
Emlen’s Method
Scaled quail data
0-10
11-20
21-30
31-40
41-50
51-60
61-70
71-80
81-90
91-100
Perpendicular distance from transect (m) 1 2 3 4 5 6 7 8
# birds
D = 40 birds/(2)(60m)(2500m) = birds/m2 = 1.33 birds/ha

36. Estimating Animal Numbers Line Transects
Hayne Density Estimate
≥2 of 3 needed
Sighting distance
Perpendicular distance
Sighting angle
DH = …
95% CI = …

37. Estimating Animal Numbers Point Counts
Basic Density Estimate
Emlen correction & detection probability
(Relative) Abundance estimates (unlimited radius) r
D = n/πr2p
where: D = animal density
n = number of animals counted
r = radius of plot
p = number of points/plots

38. Estimating Animal Numbers Distance Methods
Called plotless sampling methods
Use distance measures
Typically, used on plants and sessile animals
Estimate abundance, density, and dispersion
All methods assume random dispersion (each has test for dispersion)
T-square
Point quarter
Byth & Ripley
Ordered distance
Variable area transect

39. Estimating Animal Numbers Distance Methods
T-square
Measure the distance (xi) from random point (O) to nearest organism (P); then measure the distance (zi) from the organism (P) to its nearest neighbor (Q) with the restriction that the angle OPQ (= the T-square) must be >90°
Sample size
Random location of points

40. Estimating Animal Numbers Distance Methods
T-square
Sample #
xi (m)
zi (m) 1
12.6
8.7 2
9.3
16.4 3
7.5 4
16.2 5
8.8
3.5 6
10.1
11.2 7
6.2
13.6 8
1.5
9.1 9
14.3
2.7 10
9.6
8.6 11
11.3
7.9 12
8.9
12.1 13
6.3
15.6 14
13.9
9.9 15
10.8
13.7 16
7.6
8.4
N = 2n/π Σ(zi2) = tree/m2
95% CI = … = tree/m2
Random dispersion pattern
where n = # samples/points
Tree example

41. Estimating Animal Numbers Distance Methods
Point Quarter
Locate random points; divide area around each point into 90° quadrants; measure the distance to the nearest individual in each quadrant
Points must be far enough apart so that the same individuals are not measured more than once

42. Estimating Animal Numbers Distance Methods
Point-Quarter
N = 4(4n-1)/π Σ(rij2) = 193 tree/ha
95% CI = … = tree/m2
Where: n = # samples/points
r = distance from point I to the nearest organism in quadrant j
Distance from point to tree (rij; m)
Point (i)
Quadrant 1 (j)
Quadrant 2 (j)
Quadrant 3 (j)
Quadrant 4 (j) 1
3.05
4.68
9.15
7.88 2
2.61
12.44
19.21
3.87 3
9.83
5.41
7.55
11.16 4
7.41
9.66
1.07
3.93 5
1.42
7.75
3.48
1.88 6
8.86
11.81
6.95
7.32 7
12.35
9.00
8.41
3.16 8
10.18
7.14
2.73 9
3.49
5.70
9.12
8.37 10
5.88
4.15
13.95
7.10
Tree example

43. Estimating Animal Numbers Removal Methods
In these methods, part of the population of interest is removed and the original population is estimated from the progressive decrease in size after subsequent removals.
Typically used to estimate density and survival of small mammal and harvested populations.
Advantages of removal methods are that they are relatively quick and inexpensive techniques to estimate wildlife populations. These techniques have the obvious disadvantage of significantly affecting the population.
Leslie
Change-in-ratio

44. Estimating Animal Numbers Removal Methods
Assumptions
the probability of being caught is constant for all animals on each harvest occasion
capture or removal of one individual does not interfere with capture of other individuals
no births, deaths, immigration, or emigration during the trapping period (closed population)

45. Estimating Animal Numbers Removal Methods
Leslie Method
This method, also known as the Regression Method, uses simple linear regression to estimate the population before any removals have taken place
For reliable estimates of population size, this method requires that a large proportion of the population be removed during each trapping period, and that enough sampling periods are obtained to fit a reliable regression line through the points

46. Estimating Animal Numbers Removal Methods
Leslie Method
Example: Snap traps were used to catch short-tailed shrews for 8 days.
Trap Day (n)
# Shrews Harvested (y)
Cumulative Harvested (x) 1
125 2 72 3 91
197 4 82
288 5 55
370 6 90
425 7 48
515 8 40
563

47. Estimating Animal Numbers Removal Methods
Leslie Method
Alternatively:
Abundance/density estimated by knowing catch and effort at each occasion

48. Estimating Animal Numbers Removal Methods
Change-in-ratio Method
Assumptions
The population has 2 types of organisms (e.g., males & females)
A differential change in the numbers of the 2 types of organisms occurs during the observation period

49. Estimating Animal Numbers Removal Methods
Change-in-ratio Method
Ring-necked pheasant data
where: P1 = proportion of group 1 before removal
R1 = proportion of group 1 after removal
K1 = proportion of group 1 in total kill
U = overall mortality rate
P1 = proportion of females prior to harvest = 550/717 = 0.767
R1 = proportion of females after harvest = 296/349 = 0.848
K1 = proportion of females in total harvest = 185/548 = 0.338
U = │(P1 - R1)/(R1 - K1)│= │( )/( )│ = 0.159
Sex-specific Mortality
Females: (U)(K1/P1) = (0.159)(0.338/0.767) = 0.07 or 7%
Males: (U)(1 - K1)/(1 - P1) = (0.159)( )/( ) = 0.45 or 45%
Preseason Population
= Harvest/Sex-specific mortality
Females: 185/0.07 = 2643 pheasants
Males: 363/0.45 = 807 pheasants
Total: 3450 pheasants
Females
Males
Total
Preseason survey
550
167
717
Harvest
185
363
548
Post season survey
296 53
349

50. Estimating Animal Numbers Indices
Types
Constant proportion*
Frequency
Track counts
Scat counts
Call counts
Scent-stations
Catch-per-unit effort
Flush counts
Questionnaires
Roadside counts
Spotlight counts
Aerial counts