fish population assessment how many fish do we have?

Fish Population Assessment


How many fish do we have?How many fish do we have?



Estimating population size

Estimating population size

1) Plot method 2) Mark and recapture

(Peterson method) 3) Mark and recapture

(Schnabel method) 4) Change in ratio or

dichotomy method 5) Removal sampling

(Zippin method)

1) Plot method 2) Mark and recapture

(Peterson method) 3) Mark and recapture

(Schnabel method) 4) Change in ratio or

dichotomy method 5) Removal sampling

(Zippin method)

Plot MethodPlot Method

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ˆ N =A

a× n

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A =

a =

n =

ˆ N =

Total population area

Size of the plot

Average number of fish per plot

Population estimate

Plot Method - Estimated Variance

Plot Method - Estimated Variance

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V ( ˆ N ) =A2

a×

V (n)

s×

A − (sa)

A

V (n) =(ni − n )2

s −1∑

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ni =

s =

Number of fish counted in ith plot

Number of plots used

Plot Method - 95% confidence interval

Plot Method - 95% confidence interval

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ˆ N ± t V ( ˆ N )

t for s-1 df, p=0.05

Plot Method -Example

Plot Method -Example

Pond area = 100 m2

Size of plot = 1 m2

Average number of fish per plot = 1.5

Pond area = 100 m2

Size of plot = 1 m2

Average number of fish per plot = 1.5

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100m2

1m2 ×1.5 =150

Mark and Recapture - Peterson Method (single)

Mark and Recapture - Peterson Method (single)

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ˆ N =M(C +1)

(R +1)

M =

C =

R =

Number of fish initially marked & released

Number of fish collected/examined in 2nd period

Number of recaptures found in C

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R

C=

M

N

N =MC

RBailey modification

Mark and Recapture - Variance

Mark and Recapture - Variance

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V ( ˆ N ) =M 2(C +1)(C − R)

(R +1)2(R + 2)

Mark and Recapture - 95% confidence intervalMark and Recapture -

95% confidence interval

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ˆ N ±1.96 V ( ˆ N )

Mark and Recapture - Example


M = 550 C = 500 R = 157

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ˆ N =550(500 +1)

(157 +1)=1,744

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V ( ˆ N ) =5502(501)(500 −157)

(157 +1)=13,096



M = 550 C = 500 R = 157

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ˆ N ±1.96 13,096 =1,744 ± 224

P(1,520 ≤ ˆ N ≤1,968) = 0.95

Mark and Recapture - Schnabel Method

Mark and Recapture - Schnabel Method

Multiple episodes of mark and recapture

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ˆ N =CM∑R∑

CM = total captures X marked fish available for recapture

R = recaptures of marked fish

Schnabel Method - Variance & 95% C.I.Schnabel Method - Variance & 95% C.I.

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V (1ˆ N

) =R∑

( CM)2∑

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1ˆ N

±1.96 V (1ˆ N

) Then invert for 95% C.I. for N

Schnabel Method - example p. 137 (2nd ed.)


Period R Unmarked

TotalC

M CM

1 0 150 150 0 0

2 22 203 225 150 33,750

3 26 86 112 353 39,536

…. …. …. …. 439 ….

Total 254 457,208



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ˆ N =CM∑R∑

=457,208

254=1,800

95% C.I. = 1,602 - 2,049

Change in Ratio orDichotomy MethodChange in Ratio orDichotomy Method

Requirements:

1) two recognizable classes Species SexesAdults vs. juvenilesAge classes

2) different rates of exploitation

Requirements:

1) two recognizable classes Species SexesAdults vs. juvenilesAge classes

2) different rates of exploitation


Two assumptions must be met:

1) All population change is due to harvestNo mortality, recruitment, migration

2) Figures for harvest must be reliable (need for GOOD data)

Two assumptions must be met:

1) All population change is due to harvestNo mortality, recruitment, migration

2) Figures for harvest must be reliable (need for GOOD data)


Two classes, X & YTwo classes, X & Y

X/Y

0Total harvest

Zero X harvested per Y

Conducted by sport orcommercial fisheries orartificial manipulation(selective removal)


1. Total harvest C (CX , CY)

2. Sample size before harvest n1 (X1 ,Y1)

3. Sample size after harvest n2 (X2 ,Y2)

1. Total harvest C (CX , CY)

2. Sample size before harvest n1 (X1 ,Y1)

3. Sample size after harvest n2 (X2 ,Y2)


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P1 =X1

n1

P2 =X2

n2

ˆ N X =P1(CX − P2C)

P1 − P2

Proportion of X in first sample

Proportion of X in second sample

Population estimate for X


Population estimate for X + Y

Population estimate for Y

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ˆ N X +Y =ˆ N XP1

ˆ N Y = ˆ N X +Y − ˆ N X

Change in Ratio orDichotomy Method -

Example


Example Trout (T) and suckers (S) Sample before harvest:

n1=90, T1=30, S1=60

Sample after harvest: n2=58, T2=14, S2=44

Harvest between samples: 160 trout, 160 suckers

Trout (T) and suckers (S) Sample before harvest:

n1=90, T1=30, S1=60

Sample after harvest: n2=58, T2=14, S2=44

Harvest between samples: 160 trout, 160 suckers


Example


Example

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P1 =30

90= 0.333

P2 =14

58= 0.2414

Proportions of trout in two samples


Example


Example

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ˆ N T =0.333(160 − (0.2414 × 320))

0.333 − 0.2414= 300

ˆ N T +S =300

0.333= 900

ˆ N S = 600 Sucker estimate

Trout estimate

Trout and suckers combined

Removal Sampling -Zippin Method


3-pass removal U1=number of fish removed on 1st pass

U2=number of fish removed on 2nd pass

U3=number of fish removed on 3rd pass

M=sum of all removals (U1+U2+U3) t=number of removal passes (3) C=weighted sum = (1 X U1)+(2 X U2)+(3

X U3)

3-pass removal U1=number of fish removed on 1st pass

U2=number of fish removed on 2nd pass

U3=number of fish removed on 3rd pass

M=sum of all removals (U1+U2+U3) t=number of removal passes (3) C=weighted sum = (1 X U1)+(2 X U2)+(3

X U3)



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ˆ p =

ˆ p = 0.996784 + (−0.924031)R + (0.319563)R2 + (−0.390202)R3

R =C − M

M

Capture probability



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ˆ N =M

1− (1− ˆ p )t

SE( ˆ N ) =ˆ N ( ˆ N − M)M

M 2 −[ ˆ N ( ˆ N − M)(tˆ p )2 /(1 − ˆ p )]

95%C.I. = ˆ N ± 2SE( ˆ N )

Population estimate

Removal Sampling -Zippin Method - example


Slimy sculpin in Garvin Brookt = 3U1 = 250U2 = 125U3 = 65M = 440

C = (1) 250 + (2) 125 + (3) 65 = 695

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R =C − M

M=

695 − 440

440= 0.5795

ˆ p = 0.996784 + (−0.924031)0.5795 + (0.319563)0.57952 + (−0.390202)0.57953

= 0.4927



Slimy sculpin in Garvin Brook

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ˆ N =M

1 − (1 − ˆ p )t =440

1 − (1 − 0.4927)3 = 506

SE( ˆ N ) = 8.71≅ 9

95%CI = 506 ±18



Slimy Sculpin Removal Sampling

y = -0.4943x + 249.64

R2 = 0.9999

0

50

100

150

200

250

300

0 100 200 300 400 500 600

Fish removed in all previous passes

U

fish population assessment how many fish do we have?

Documents

x slide

y slide

dichotomy method population

recapture schnabel method

recapture variance slide

recapture peterson method

plot population

x y population