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Estimating Animal Numbers
• Uses
• Definitions
• Types of methods and analyses
Estimating Animal Numbers
• Populations vs. Experimental Units
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Estimating Animal Numbers
• Population
• Abundance or population size (N)
• Density
• Relative abundance/density
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
Estimating
Animal
Numbers
Indices
Censuses
Surveys
DISTANCE
METHODS
Estimating Animal Numbers
Censuses
• Aerial photography/counts
– Waterfowl
– Deer
– Large animals
Estimating Animal Numbers
Censuses
• Thermal IR
– Large homeotherms
Estimating Animal Numbers
Censuses
• Drive counts
– Large animals
Estimating Animal Numbers
Censuses
• Total mapping of territories
• Spot or Territory mapping
Estimating Animal Numbers
Censuses
• Radar
Estimating Animal Numbers
Censuses
• Point counts
Estimating Animal Numbers
Censuses
• Various total counts on plots
Estimating Animal Numbers
Surveys
• Mark-recapture
• Distance sampling
– Line transects & point counts
• Distance methods
• Removal methods
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
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
Estimating Animal Numbers
Mark-Recapture
• Sample Size & Precision
– # captures & capture probability
– # marked
– # sampling occasions
– Population size
– Survival rates
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
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•
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•
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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)
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.
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
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
Estimating Animal Numbers
Mark-Recapture
• Schumacher Method
– Model
N = Σ (CiMi2)
Σ RiMi
95% CI = …
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)
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
0
32
0
2
54
18
36
32
3
37
31
6
68
4
60
47
13
74
5
41
36
5
87
N = 93.1 frogs
95% CI = 81.7 – 108.1
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)
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).
Estimating Animal Numbers
Mark-Recapture
• Jolly-Seber Method
– Field voles sampled on 11 days
Time of capture
Time of last capture
1
1
2
3
4
5
6
7
8
9
10
11
15
1
0
0
0
0
0
0
0
0
15
0
1
0
0
0
0
0
0
37
2
0
0
0
0
0
0
61
4
1
1
0
0
0
75
3
2
0
0
0
77
4
0
0
0
69
0
0
0
8
1
0
14
0
2
3
4
5
6
m6
7
8
9
10
19
Total marked (mt)
0
15
16
37
64
79
81
76
8
15
19
Total unmarked (ut)
22
26
32
45
25
22
26
15
11
12
3
Total caught (nt)
22
41
48
82
89
101
107
91
19
27
22
Total released (st)
21
41
46
82
88
99
106
90
19
26
22
Estimating Animal Numbers
Mark-Recapture
• Jolly-Seber Method
Sample
Prop. marked
Size of
marked pop.
1
0
0
2
0.381
17.5
45.9
3
0.347
17.2
4
0.458
5
Prob. of Φ
95% CI of Φ
0.832
0.546-1.000
41.1-69.5
0.395
0.270-0.575
49.5
48.0-57.9
0.862
0.751-0.961
40.7
88.8
84.4-100.0
0.824
0.739-0.908
0.722
70.5
97.7
94.6-104.0
0.925
0.859-0.983
6
0.784
87.5
111.6
108.0-118.7
0.853
0.769-0.937
7
0.759
91.7
120.8
115.3-132.0
0.651
0.565-0.748
8
0.837
76.0
90.8
90.8-194.4
0.104
0.058-0.194
9
0.450
9.3
20.7
19.0-28.9
0.738
0.550-0.927
10
0.571
15.0
26.2
26.2-47.7
11
0.870
N
95% CI of N
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 traphappy)
– Unequal opportunity to be caught because of trap
position
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
4
3.2
5
4
0.5
6
0
0.1
7
0
0
Estimating Animal Numbers
Mark-Recapture
• Zero-Truncated Poisson Test of Equal Catchability
– Snowshoe hares captured during 7 days
Total individuals captured = 261
Mean # of captures per individual = 1.425
Estimated mean # of captures = 0.756
– 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
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
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)
Estimating Animal Numbers
Line Transects
• General methods
b
Θ
c
L
w
a
w
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
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) = 0.00021 quail/m2 = 2.1 quail/ha
95% CI or other estimate of variation ?
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
Estimating Animal Numbers
Line Transects
• Emlen’s Method
8
7
– Scaled quail data
# birds
6
5
4
3
2
1
0
Perpendicular distance from transect (m)
D = 40 birds/(2)(60m)(2500m) = 0.000133 birds/m2 = 1.33 birds/ha
Estimating Animal Numbers
Line Transects
• Hayne Density Estimate
– ≥2 of 3 needed
• Sighting distance
• Perpendicular distance
• Sighting angle
DH = …
95% CI = …
Estimating Animal Numbers
Point Counts
• Basic Density Estimate
r
D = n/πr2p
where:
D = animal density
n = number of animals counted
r = radius of plot
p = number of points/plots
• Emlen correction & detection probability
• (Relative) Abundance estimates (unlimited
radius)
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
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
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
9.3
4
16.2
12.6
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) = 0.004 tree/m2
95% CI = … = 0.003-0.005 tree/m2
Random dispersion pattern
where n = # samples/points
Tree example
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
Estimating Animal Numbers
Distance Methods
• Point-Quarter
N = 4(4n-1)/π Σ(rij2) = 193 tree/ha
Distance from point to tree (rij; m)
95% CI = … = 140-263 tree/m2
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
3.16
7.14
2.73
9
3.49
5.70
9.12
8.37
10
5.88
4.15
13.95
7.10
Where: n = # samples/points
r = distance from point I to
the nearest organism in
quadrant j
Tree example
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
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)
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
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
0
2
72
125
3
91
197
4
82
288
5
55
370
6
90
425
7
48
515
8
40
563
Estimating Animal Numbers
Removal Methods
• Leslie Method
Alternatively:
Abundance/density
estimated by knowing
catch and effort at
each occasion
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
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
Females
Males
Total
Preseason survey
550
167
717
Harvest
185
363
548
Post season survey
296
53
349
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)│= │(0.767 - 0.848)/(0.848 - 0.338)│ = 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)(1 - 0.338)/(1 - 0.767) = 0.45 or 45%
Preseason Population
= Harvest/Sex-specific mortality
Females:
Males:
185/0.07 = 2643 pheasants
363/0.45 = 807 pheasants
Total: 3450 pheasants
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