Size Structure

Learning Objectives

• Construct and interpret length-frequency distributions

• Describe, calculate, and interpret Swingle’s ratios• Describe the development and interpretation of

standardized length categories• Calculate and interpret PSS indices• Describe differences associated with using

traditional and incremental size-structure indices• Identify the dynamic rate functions and relations

with size structure indices

Size Structure

• Methods of measurement of fish population structure

• Calculation of indices• Interpretation of structural indices

Fish Length and Weight

Considerations

Indices

Homer Swingle

• Faculty member at Auburn University

• One of the first to use experimental ponds to obtain insight on management

• Interested in “balanced” fish populations in ponds

Balance

• “The interrelationships in fish populations are satisfactory if the populations yield, year after year, crops of harvestable fish that are satisfactory in amount when the basic fertilities of the bodies of water containing those populations are considered. Such populations are considered to be ‘balanced populations’ and the species within such a population are ‘in balance.’”

• “Balance then denotes a condition within a population such that if 100 pounds of fish are harvested one year the correct numbers of replacements will be provided from the population so that a satisfactory poundage of fish of desirable size may be harvested in succeeding years. If the population provides too many replacements, these fish will not reach a satisfactory size for harvesting; conversely, if too few replacements are provided, the capacity of the body of water to produce will not be fully utilized and the harvestable poundage will seriously decline.”

Swingle’s F/C Ratio

Swingle’s F/C Ratio

• F = • C =

Swingle’s F/C Ratio

Swingle’s F/C Ratio

Swingle’s Y/C Ratio

• Y = • C =

Swingle’s Y/C Ratio

Swingle’s Y/C Ratio

Swingle’s At

Swingle’s At

Species Minimum weightBLG, RESF, and similar sunfishes 0.1Crappies 0.26LMB 0.4Bullheads 0.3GZS 0.5CHCF 0.5Gar 1.0Buffalo 1.0Carp 1.0

Swingle’s At

Swingle’s At

Swingle’s At

Swingle’s At

Swingle’s E

• Swingle’s E =

• Lower bound of balanced with 1 “C” and 1 “F” species is 1.4:1 (BLG:LMB). Therefore, there is 1 pound of LMB for every 2.4 lbs of fish (100 × 1 / 2.4 = 41.6%)– LMB (balanced) =– LMB (desired)=

Other Swingle Indices

• A value =

• I value =

• S value =

Jenkins and Morais Metric

• AP/P ratio– AP = – P =

– Plotted on a log10 vs log10 scale

– Curve should be above the 1:1 line to have sufficient prey for predators

Jenkins and Morais Metric

Swingle Ratios and Similar Indices

• Potential problems and practicality???

Length-Frequency Histograms

Guidelines

• ROT…sample 100 fish > stock-length

Guidelines

• Y-axis

Guidelines

• X-axis are bins• “bin bias”

Bin Bias

Length (mm)

0 100 200 300 400

Rel

ativ

e fr

eque

ncy

(%)

0.00

0.05

0.10

0.15

0.20

0.25

0.30

Length (mm)

0 100 200 300 400

Rel

ativ

e fr

eque

ncy

(%)

0.00

0.02

0.04

0.06

0.08

Length (mm)

0 100 200 300 400

Rel

ativ

e fr

eque

ncy

(%)

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

Length-Frequency Indices

Length Categorization

Weithman and Anderson (1978) Gabelhouse (1984)

Length Categorization

• Stock length =

• Quality length =

• Preferred length =

• Memorable length =

• Trophy length =

Length Categorization

Proportional Stock Density (PSD)

• Proportion of stock-length fish that are quality length or greater

• PSD = 100 × (# of fish > minimum quality length / # of fish > minimum stock length)

• Round to nearest whole number!

PSD-WAE Example

PSD-WAE Example

Length (mm)

200 300 400 500 600 700 800

Rel

ativ

e fr

eque

ncy

(%)

0

2

4

6

8

10

12

14

16

18

PSD

200 300 400 500 600 700 800

Num

ber

0

2

4

6

8

Length (mm)

200 300 400 500 600 700 800

Num

ber

0

2

4

6

8

S Q

S = 29Q = 17

S = 29Q = 17

RSDs

• RSD = 100 × (# of fish > specified length / # of fish > stock length)

• Round to nearest whole number!• Specified length (e.g., RSD-35)• Standard length categories

RSD-WAE Example

Substock (< 250 mm) = 7Stock (250 mm) = 29Quality (380 mm) = 17Preferred (510 mm) = 10Memorable (630 mm) = 6Trophy (760 mm) = 0

200 300 400 500 600 700 800

Num

ber

0

2

4

6

8

Length (mm)

200 300 400 500 600 700 800

Num

ber

0

2

4

6

8

S Q

PSD = 59RSD-P = RSD-M = RSD-370 =

PSD = 59RSD-P = RSD-M = RSD-370 =

P M T

Traditional versus Incremental RSDs

• Traditional RSDs• Incremental

RSD-WAE Example

Length (mm)

200 300 400 500 600 700 800

Rel

ativ

e fr

eque

ncy

(%)

0

2

4

6

8

10

12

14

16

18

S Q P M T

RSD-WAE Example

SS =S-Q = Q-P =P-M =M-T =T =

RSD-WAE Example

Length (mm)

200 300 400 500 600 700 800

Rel

ativ

e fr

eque

ncy

(%)

0

2

4

6

8

10

12

14

16

18

S Q P M T

SQ QP PM MT TSS

Traditional versus Incremental RSDs

• Incremental RSDs

• Traditional RSDs

Proportional Size Structure (PSS)

• Confusion in terminology with Proportional Stock Density and Relative Stock Density

Proportional Size Structure

Current NewPSD PSSQ

RSD-Q PSSQ

RSD-P PSSP

RSD-M PSSM

RSD-T PSST

RSD S-Q PSSSQ

RSD Q-P PSSQP

RSD P-M PSSPM

RSD M-T PSSMT

Terminology

Size Structure

Size Structure

Size Structure

Biases

Biases

Biases

Balance

• Balanced populations have predictable PSD (or PSSQ)

• Examples– BLG – Crappie – LMB

Balance

AT, but with biomass

Additional insight

Size Structure Indices

Size Structure Indices

Size Structure Indices

“The Classic Story of BLG and LMB PSDs”

What about other species?

What about other species?