FMSP stock assessment tools Training Workshop

1. FMSP stock assessment tools Training Workshop LFDA Theory

2. LFDA Theory Session 1 – Contents • What does LFDA do? • Why use LFDA? • LFDA Data Requirements • Von Bertalanffy growth curves • Length based methods of estimation • Methods used in LFDA

3. What does LFDA do? It uses length frequency data to provide estimates of: • Von Bertalanffy growth parameters (both non-seasonal and seasonal); • Total mortality, Z (= F+M). These estimates can then be used in subsequent packages (eg Yield) to provide further information

4. The analytical stock assessment approach using LFDA and Yield Length frequency data Biological data, management controls (size limits, closed seasons etc) Data / inputs Assessment tools LFDA Yield Intermediate parameters L∞, K, t0 (growth) Indicators Z ( - M ) Fnow(Eq) Per recruit Fmax F0.1 F%SPR With SRR FMSY Ftransient Reference points Management advice Compare to make management advice on F e.g. if Fnow > FMSY, reduce F by management controls if Fnow < FMSY, OK Figure 4.1

5. Why use LFDA? • Many standard stock assessment methods use age composition data. • In tropical waters, good ageing materials (otoliths, scales etc) are not always available • Due to the minimal seasonal effects, making ageing unreliable • Getting large enough datasets can be rather expensive • Length composition data can often be converted into age composition data via a growth curve, and assessment methods can be modified to work with length data. • Length data are relatively cheap and easy to collect.

6. Data Requirements (1/3) • Sample sizes • Sufficient sample size to eliminate biases. • Ensure data are correctly raised for each sampling period. • Distributions (numbers and timing) • How should you organise your sampling to get the right numbers and timings? • Cost

7. Data Requirements (2/3) • LFDA datasets contain a number of length frequency distributions (LFDs). • LFDA requires that all distributions in a dataset have the same length class intervals and minimum length. • LFDA also needs to know at what time of year the catch that makes up each distribution was taken. This is known as the sample timing. • For LFDA, sample timings are expressed as a fraction of a year, e.g. 0.5, with separate years being separated by a full unit e.g. 1.5.

8. Data Requirements (3/3)

9. Data format Data can be imported from a spreadsheet, database or word processing file. Need: • length-classes as row headings; • sample timings as column headings.

10. Example data and plot

11. Von Bertalanffy Growth Curves (1/4) • Non-seasonal growth curves Simplest and common for tropical marine fisheries. Non-seasonal von Bertalanffy Growth Curve. • Seasonal growth curves More common for temperate, cold water or freshwater habitats. Sinusoidal – constant growth but periods where growth rate slows down. Hoenig and Choudary Hanumura (1982). Periods of zero growth – Growth stops for part of the year. Pauly et al. (1992)

12. Von Bertalanffy Growth Curves (2/4) • Mathematical equation to describe the length (L) of fish as a function of age (t) Lt = L∞ [ 1 – exp (- K (t – t0)) ] • Lt = Length at time t • L∞ = Asymptotic maximum length • K = Growth rate parameter • t = Time ( corresponding to the age of fish) • t0 =time at which the fish has zero length.

13. Von Bertalanffy Growth Curves (3/4) • Lethrinus mahsena • Sky emperor (Dame berri, Lascar) K = 0.194 L∞ = 30.8 cm T0 = -0.332 y Data from Seychelles 1998 (www.fishbase.org) L∞ = 30.8cm T0= -0.332

14. Von Bertalanffy Growth Curves (4/4) Seasonal growth with a period of zero growth starting in the middle of the year. Seasonal growth with a “slow-growth period” in the middle of the year.

15. Length Based Methods of Growth Parameter Estimation • Graphical Methods Gulland and Holt, Ford-Walford, Chapman, von Bertalanffy, Bhattacharya, Cassie • Modal Separation MacDonald and Pitcher, Fournier and Breen • Computer Based Methods Many different methods in computer packages such as LFDA, and the FAO’s packageFiSAT.

16. Go to practical presentation

17. LFDA Theory Session 2 • Estimating mortality rates • Methods used in LFDA

18. Mortality Rates Definition of a “cohort” “A cohort is a batch of fish all of approximately the same age and belonging to the same stock.” (FAO, 1992) Definitions of M, F and Z: • M is the “natural mortality rate”, i.e. the proportion of individuals that would die of natural causes without any other influence. • F is the “fishing mortality rate”, i.e. the proportion of individuals that would die due to fishing. • Z is the “total instantaneous mortality rate” i.e. the proportion of individuals in a cohort that will on average die in a particular time period.

19. Estimation Methods for Total Mortality –”Z” • There are a number of different methods for calculating mortality estimates from length frequency data. • Length Converted Catch Curve • Beverton-Holt • Powell Wetherall

20. Length Converted Catch Curve (LCCC) (1/3) • Where direct estimation of ages is possible, you can estimate the mortality rate based on the numbers surviving at each age class. • In tropical waters this is often not possible and alternative techniques have been developed using length data as a replacement for age based data. • One such method is called the “length converted catch curve” or the “linearised length converted catch curve”.

21. Length Converted Catch Curve (LCCC) (2/3) • The conversion of length data into ages is a fairly complicated mathematical process, changing lengths into ages using the average growth curve for the entire cohort. • The end result of the process is a simple plot of the log of the number of survivors of different length classes against age. The mortality rate is the negative slope of the line plotted between the length at which the first length class is fully exploited and the length at which age classes start to become converged.

22. Length Converted Catch Curve (LCCC) (3/3) Data not used as not under full exploitation Data not used as too close to L∞ Data used to calculate Z

23. Beverton-Holt • Beverton and Holt (1956) showed that there is a relationship between length (L) and total mortality (Z) and length at first capture (L’). • Need to have accurate estimates for both K and L∞ from the von Bertalanffy growth equation to use this method.

24. Powell-Wetherall (1/3) • Powell (1979) developed a method, extended by Wetherall et al. (1987), for estimating growth and mortality parameters using the idea that the shape of the right hand tail of a length frequency distribution was determined by the asymptotic length L and the ratio between the total mortality rate Z and the growth rate K. • This model has the same assumptions as the Beverton-Holt model in that we must have good estimates for K and L∞. • The results of this method provide estimates for each distribution of L∞ and the ratio of Z/K.

25. Powell-Wetherall (2/3) • By manipulating the Beverton-Holt equation given previously it can be shown that;

26. Powell-Wetherall (3/3) • Therefore taking all fish between L’ and the point of convergence towards L∞ as for the LCCC method, we can calculate estimates for L∞ and Z/K for each length frequency distribution in our dataset. • If we have already estimated L∞ and K from previous analyses we can therefore estimate Z.

27. LFDA Theory Session Summary • Von Bertalanffy Growth Curves • How we can use length frequency data. • History of evolution of estimation. • Estimation of growth parameters. • Theory of methods used in LFDA. • Estimation of mortality estimates. • Theory of methods used in LFDA.