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-Weight Relationships
• Strong relationship between length and weight
3500
Iowa SMB
R 2 = 0.99
P = 0.0001
3000
Weight (g)
2500
Weight = 0.00000639 (Length)3.123
2000
1500
1000
500
0
0
100
200
300
Length (mm)
400
500
600
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
4
3500
3000
3
log10 weight (g)
Weight (g)
2500
2000
1500
1000
2
1
500
0
0
0
100
200
300
Length (mm)
400
500
600
1.8
2.0
2.2
2.4
log10 length (mm)
2.6
2.8
Length-Weight Relationship
4
Iowa SMB
r 2 = 0.99
P = 0.0001
log10 weight (g)
3
2
1
log10 (W) = -5.033 + 3.057 log10 (L)
0
1.8
2.0
2.2
2.4
log10 length (mm)
2.6
2.8
Condition
• So…weight can be predicted from length
Condition
3500
3000
Weight (g)
2500
2000
1500
1000
500
0
0
100
200
300
Length (mm)
400
500
600
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
4
Iowa SMB
r 2 = 0.99
P = 0.0001
log10 weight (g)
3
2
1
log10 (W’) = -5.033 + 3.057 log10 (L)
0
1.8
2.0
2.2
2.4
log10 length (mm)
2.6
2.8
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 75thpercentile 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)
4.5
log10 weight (g)
4.0
3.5
Flathead catfish
n = 4 populations
3.0
2.5
2.0
1.5
1.0
0.5
1.8
2.0
2.2
2.4
2.6
log10 length (mm)
2.8
3.0
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)
5.0
log10 (Ws) = -5.542 + 3.230 log10 (length)
Minimum length = 130 mm
log10 weight (g)
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
2.0
2.2
2.4
2.6
2.8
log10 length (mm)
3.0
3.2
Relative Weight—SMB Example
Minimum length = 150 mm
Relative Weight
Relative Weight
Relative Weight
Relative Weight
Relative Weight
Relative Weight
Relative Weight
Relative Weight