Condition
Learning Objectives• Describe condition and different methods for
measuring or indexing condition• Calculate and interpret length-weight relationships• Describe the advantages and disadvantages of
different methods for describing condition• Describe the RLP technique• Calculate and interpret different condition indices• Describe relations of condition to rate functions
Power Function
• W = aLb
• b >• b < • b =
Length (mm)
0 100 200 300 400 500 600
Wei
ght (
g)
0
500
1000
1500
2000
2500
3000
3500
Length-Weight Relationships• Strong relationship between length and
weightIowa SMBR 2 = 0.99P = 0.0001
Weight = 0.00000639 (Length)3.123
Logarithm Rules
Logarithm Rules
• Multiplication inside the log can be turned into addition outside the log, and vice versa
• Division inside the log turned into subtraction (denominator is subtracted) outside, and vice versa
• An exponent inside log moved out as a multiplier, and vice versa
Power Function
• So, if W = a Lb
Length-Weight Relationship
Length (mm)
0 100 200 300 400 500 600
Wei
ght (
g)
0
500
1000
1500
2000
2500
3000
3500
log10 length (mm)
1.8 2.0 2.2 2.4 2.6 2.8
log 1
0 w
eigh
t (g
)
0
1
2
3
4
log10 length (mm)
1.8 2.0 2.2 2.4 2.6 2.8
log 1
0 w
eigh
t (g
)
0
1
2
3
4
Length-Weight Relationship
Iowa SMBr 2 = 0.99P = 0.0001
log10 (W) = -5.033 + 3.057 log10 (L)
Condition
• So…weight can be predicted from length
Length (mm)
0 100 200 300 400 500 600
Wei
ght (
g)
0
500
1000
1500
2000
2500
3000
3500
Condition
Indices of Condition
• Fulton condition factor • Relative condition factor • Relative weight
Fulton Condition Factor
• K = • C =
• KTL, KSL
• CTL, CSL
Fulton Condition Factor
KTL =
Fulton Condition Factor
• Condition factors vary for the same fish depending on whether you estimate K or C
Relative Condition Factor
• Compensates for differences in body shape
• Kn =
Relative Condition Factor
log10 length (mm)
1.8 2.0 2.2 2.4 2.6 2.8
log 1
0 w
eigh
t (g
)
0
1
2
3
4Iowa SMBr 2 = 0.99P = 0.0001
log10 (W’) = -5.033 + 3.057 log10 (L)
Relative Condition Factor
Relative Condition Factor
• Average fish of all lengths and species have a value of 1.0 regardless of species of unit of measurement
• Limited by the equation used to estimate W’– Communication is hindered among agencies
• Also, tend to see systematic bias in condition with increasing length
• To help alleviate these problems and to improve utility of the condition indices, relative weight (Wr) was derived
Relative Weight
• Wr = 100 x (W/Ws)
• log10 (Ws) = a’ + b log10 (L)
– Note: a’ = log10 (a)
Relative Weight
• First equation was for LMB using data from Carlander (1977)– Compiled weights and a curve was fit to the
75th-percentile weights to develop the Ws equation
Regression-Line-Percentile (RLP)
• Obtain length-weight data from populations across the distribution of the species
• Fit log10-transformed length-weight equation to obtain estimates of a’ and b for each population
• Estimate weight of fish at 1-cm intervals (from minimum and maximum lengths in data set) for each population
• Obtain the 75th-percentile weight for each 1-cm length group
• Fit an equation to the 75th-percentile weights
Regression-Line-Percentile (RLP)
Regression-Line-Percentile (RLP)
Flathead catfishn = 4 populations
log10 length (mm)
1.8 2.0 2.2 2.4 2.6 2.8 3.0
log 1
0 w
eigh
t (g
)
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
Regression-Line-Percentile (RLP)
Regression-Line-Percentile (RLP)
n = 74
Regression-Line-Percentile (RLP)
• Obtain the 75th-percentile weight for each 1-cm length group
Regression-Line-Percentile (RLP)
log10 length (mm)
2.0 2.2 2.4 2.6 2.8 3.0 3.2
log 10
wei
ght
(g)
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0log10 (Ws) = -5.542 + 3.230 log10 (length)Minimum length = 130 mm
Relative Weight—SMB Example
Minimum length = 150 mm
Relative Weight
Relative Weight
Relative Weight
Relative Weight
Relative Weight
Relative Weight
Relative Weight
Relative Weight