USP. Estimating mortality

Transcription

1 USP Estimating mortality

2 Number of fish Catch (millions of fish) 2 Estimating Z: Catch curve analysis Data requirements: A reliable method to determine age or growth rate of stock of interest Relative or absolute numbers of fish by age/length group Age / time Temporarily snapshots: pseudocohort analysis Series of measurements through time: cohort analysis Length (cm)

3 Nt 3 Revision: The stock equation Z= t N t 1 N e t Z=.2 Z=.4 Z=.6 Z=.8 Z=M+F M t F t

4 4 Estimating total mortality (Z): Part 1 Lets pretend we have information on age of the fish. The stock equation for a cohort, over a short time interval is then: N N e a 1, y 1 a, y Z a, y Na+1,t+1: Abundance of age a+1 in the beginning of time t+1 Na,t: Abundance of age a in the beginning of time t Za,t: Total mortality of age a over the time period t to t+1 Taking a logarithm of an exponential function gives: ln a 1, y 1 a, y a, y a, y a, y a 1, y 1 ay, N ln N Z Z ln N ln N Z ln N N a ay, 1, y 1 If we have a relative measure of population size we can estimate Z

5 5 Estimating total mortality (Z): Part 2 The math: CPUE ay, Assume: E E and q q Z t C E ln ln ln ay ay y y 1 a a 1 N N t t C 1 ay y a a 1 y 1 a 1 ay, a 1, y 1 E q C E q C C If there has been no change in effort over time or in catchability by age (size) one can use the log ratio of the number of fish caught at each to estimate the total mortality. This derivation show that if we have some measurement of catches by age (or length) we can estimate Z. E: Effort q: Catchability

6 Catch (millions of fish) 6 The catch development of one cohort Catch per time unit Younger fish less available (qa changes with age) 3. Decline in older ages due to mortality if qa does not change with age Age / time Time

7 7 Estimating total mortality of older fish 1 Catch in numbers (Ca,y) Fjöldi fiskaí afla(milljónir) year class year Ár 9

8 8 Estimating total mortality of older fish 2 Logarithmic scale Catch in numbers (Ca,y) Fjöldi fiskaí afla(milljónir) year class year Ár

9 9 Estimating total mortality of older fish 3 Catch in numbers (Ca,y) Fjöldi fiskaí afla(milljónir) Z =.48 (38%) year Ár

10 1 Estimating total mortality of older fish 4 Catch in numbers (Ca,y) Fjöldi fiskaí afla(milljónir) year Ár

11 11 Cod: Estimates of total mortality (Z) Ln catch in numbers (ln Ca,y) Fjöldi í afla Year class Z = 1.41 (75%) year Ár 5 9 Year class 1989 Z =.54 (42%) Z = F + M

12 USP Catch curves from length data

13 Number of fish 13 How do we estimate mortality from length distributions? Catch per effort, not per time 25 Need to convert length to time and catch per length interval to catch per time interval Length (cm) Not time but length

14 Number of fish 14 How do we estimate mortality from length distributions? Mortality is a rate measure relative to time Since relationship between time and length is nonlinear we need to transform the length frequency distribution Lets first define the number of fish caught in length interval from L1 to L2 as: C L 1, L 2 We refer to this as catch from hereon C L 1, L Length

15 Time Length 15 The inverse VBGF: Converting length to time If one has estimates of K and L from the VBLF one can convert length intervals to time intervals by the following formula: t This is the time it takes a fish to grow from length L1 to L2 The relative age at length L can be calculated by: t L, L L L L ln K L L 1 ln K L L L L 2 L 1 t L 1, L t L 1, L 2 Time L 1 L Length (cm)

16 C C 16 Converting length to time The age at midlength of the interval L1 to L2 is: t.5 L L ln K L.5 L L L 1 2 C L 1, L Length This is used to convert length to age for a length frequency distribution C L 1, L Time (months)

17 C/t C 17 Normalising the length frequency distribution To take into account that a length distribution contains data where the time unit within each length interval is not constant we divide the catch with the time duration that it takes the fish to pass through the length interval C L, L t 1 2 L, L 1 2 We now have a plot which is equivalent to the age based data C L, L t 1 2 L, L Time (months) Time (months)

18 C/t C/t 18 Estimating Z To estimate Z we take the logarithm of the of the catches per time unit and estimate the slope The formula in full is: C L, L t 1 2 L, L ln C L, L 1 2.5( L1 L2) CL 1, L2 tl 1, L ln 2 tl, L Same assumption apply as for the age based catch curves: i.e. ql1 = ql2 a Zt Since there is gear selectivity at younger length we can only use the larger size ranges to estimate Z Time (months) - ql1<>ql Time (months) Z

19 Numbers Length based measurements Snapshots (pseudochorts) most common Length

20 2 Estimating Z from a pseudocohort When operating on pseudocohorts the additional assumption is that the recruitment has been constant for the cohorts that are in the snapshot sample. Ideally would take some length frequency samples over time and take some kind of an average value. Length based Z calculation are very sensitivity to the value of K and Linf used Best is to estimate K and Linf on the stock of interest If use value from literature, make sure they are appropriate for the stock in question

21 USP Mark recapture experiments (only the concept introduced here)

22 Number recaptured per month 22 Number of recapture since release Example: Dab Months since release

23 Number of recaptures per month 23 Number of recaptures since release Example: Dab x month Numbers recaptured = 6e R 2 =.61 1% decline in number of recapture per month Months from release

24 Numer of recapture per month 24 Number of recapture since release: Ln transformation Example: Dab 1 Slope = 1.3 per year Equivalent to 7% decline per year Month since release

25 Number of recapture per year 25 Number of recapture since release Example: Plaice s 196s 199s Years since release

26 Number recaptured per year 26 Number of recapture since release Example: Plaice % decline per year 195s 196s 199s % decline per year Years since release

27 USP Natural mortality

28 - 28 The nature of M Abiotic factors Fishing Egg/larvae Juveniles Recruitment Adults M is a function of the following factors: Growth and therefore indirectly to K and Linf Figure 14. Factors influencing mortality at various life stages of fish. Size/weight, which is partly a function of longevity Age at maturation, partly a function of longevity Reproductive effort (relative energy distribution into gonad vs somatic tissues) Temperature, which determines metabolic rate and thus growth Intrinsic population growth rate (r) Estimation of natural mortality is very difficult. Any measure will be mostly be a rough gestimate The our interest in knowing natural mortality relates to the fact that F = Z M We can estimate Z from catch curve analysis but without an estimate of M we can not estimate F Inviable Starvation Predation Diseases Parasitism m Senescence

29 29 Z = M + q Effort Since fishing mortality is a function of effort we can derive the following: Need a range of effort levels Is limited to estimating M of adults Z M F Z M q Effort Smooth-tailed trevally Z Icelandic cod M=2 M=.2 Effort

30 3 Empirical derivations Pauly 198 Ln(M) = ln(linf) ln(k) ln(t) There are others: Rikhter and Efanov: M = f(age of maturity) Gunderson and Dygert 1988: M = f(gonad somatic index) Hoening 1984: M = (longevity) Pope: