Length-weight relationships and condition indices

•      Lecture Outline

–   Length-weight relationships

–   Condition indices

•      Assignments

–    Study for the test!                    

Use of length and weight data

1)      Develop conversion factors

2)      Evaluate condition

a)      Somatic

b)      Gonad

3)      Must understand bivariate statistics

a)      y = mx + b

Mathematical description of weight-length relationship

1)      Slope and intercept

a)      Slope – rate of increasing weight with length

b)      Intercept – extrapolated weight at length = 0

2)      Power function

a)         Wt = aLnb

3)      Linear regression of logarithmically transformed data

a)      Log10(Wt) = a + bLog10(Ln)

Condition indices

1)      Should be easy to interpret

2)      Should not be biased across length classes or species

3)      Should indicate health or well being

4)      Standardized across time and space

a)      Take samples in same season and location in waterbody

Fulton Condition Factor

1)      C = Wgt/Ln3 x 10,000

2)      b is not exactly 3 because fishes have different body shapes

3)  Tends to increase with increased fish length

Relative Condition Factor

1)      Kn = (W/W’)

2)      W’ – predicted weight based on weight-length equation for a fish of its length in that population

a)      Power function or log transformed data

3)      Average fish should have a Kn value of 1.0

4)      Limited to within-population comparisons

Relative Weight

1)      Wr = (W/ Ws) x 100

2)      Ws =  length-specific standard weight predicted by a weight-length regression constructed to represent the species

3)      Log10 (Ws) = a’ + b[Log10(ln)]

4)      Where to get a’ and b?

a)      Fit curve to 75th percentile

b)      Table 15.1 in Fisheries Techniques

5)      Value of 100 represents a fish in optimal condition

6)      Widely accepted in the fisheries profession

7)      Has been shown to be related to:

Food availability

Size structure

Growth

Other health indices

 

Analysis of growth

1)      Analysis of covariance (ANCOVA)

a)      Statistical test to estimate probability the slope and intercept are different

b)      Comparisons are easily made for 2 (or few) populations

c)      Need to ensure you only look at lengths common to both populations

2)      Analysis of variance across using Wr

a)      First make sure there are no differences in Wr across length groups

b)      Then compare mean Wr across length groups and/or populations