Condition

1. Condition

2. 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

3. Power Function • W = aLb • b > • b < • b =

4. Length-Weight Relationships • Strong relationship between length and weight Iowa SMB R 2 = 0.99 P = 0.0001 Weight = 0.00000639 (Length)3.123

5. Logarithm Rules

6. 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

7. Power Function • So, if W = a Lb

8. Length-Weight Relationship

9. Length-Weight Relationship Iowa SMB r 2 = 0.99 P = 0.0001 log10 (W) = -5.033 + 3.057 log10 (L)

10. Condition • So…weight can be predicted from length

11. Condition

12. Indices of Condition • Fulton condition factor • Relative condition factor • Relative weight

13. Fulton Condition Factor • K = • C = • KTL, KSL • CTL, CSL

14. Fulton Condition Factor KTL =

15. Fulton Condition Factor • Condition factors vary for the same fish depending on whether you estimate K or C

16. Relative Condition Factor • Compensates for differences in body shape • Kn =

17. Relative Condition Factor Iowa SMB r 2 = 0.99 P = 0.0001 log10 (W’) = -5.033 + 3.057 log10 (L)

18. Relative Condition Factor

19. 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

20. Relative Weight • Wr = 100 x (W/Ws) • log10 (Ws) = a’ + b log10 (L) • Note: a’ = log10 (a)

21. 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

22. 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

23. Regression-Line-Percentile (RLP)

24. Regression-Line-Percentile (RLP)

25. Regression-Line-Percentile (RLP)

26. Regression-Line-Percentile (RLP) n = 74

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

28. Regression-Line-Percentile (RLP) log10 (Ws) = -5.542 + 3.230 log10 (length) Minimum length = 130 mm

29. Relative Weight—SMB Example Minimum length = 150 mm

30. Relative Weight

31. Relative Weight

32. Relative Weight

33. Relative Weight

34. Relative Weight

35. Relative Weight

36. Relative Weight

37. Relative Weight