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 = aL b b > b < b =

Length-Weight Relationships Strong relationship between length and weight Iowa SMB R 2 = 0.99 P = Weight = (Length) 3.123

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 L b

Length-Weight Relationship

Iowa SMB r 2 = 0.99 P = log 10 (W) = log 10 (L)

Condition So…weight can be predicted from length

Condition

Indices of Condition Fulton condition factor Relative condition factor Relative weight

Fulton Condition Factor K = C = K TL, K SL C TL, C SL

Fulton Condition Factor K TL =

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 Iowa SMB r 2 = 0.99 P = log 10 (W’) = log 10 (L)

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/W s ) log 10 (W s ) = a’ + b log 10 (L) –Note: a’ = log 10 (a)

Relative Weight First equation was for LMB using data from Carlander (1977) –Compiled weights and a curve was fit to the 75 th - percentile weights to develop the Ws equation

Regression-Line-Percentile (RLP) Obtain length-weight data from populations across the distribution of the species Fit log 10 -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 75 th -percentile weight for each 1-cm length group Fit an equation to the 75 th -percentile weights

Regression-Line-Percentile (RLP)

n = 74

Regression-Line-Percentile (RLP) Obtain the 75 th -percentile weight for each 1-cm length group

Regression-Line-Percentile (RLP) log 10 (Ws) = log 10 (length) Minimum length = 130 mm

Relative Weight—SMB Example Minimum length = 150 mm

Relative Weight