Assessing Fishery Condition: Population Estimation

Transcription

1 Assessing Fishery Condition: Population Estimation Chapter 11 Thought for Today: "In God we trust, all others bring data." William Edward Deming ( ).

2 Why?

3 Needs / Requirements Objectives Info about animals Literature review Statistician MONEY

4 Terms and Definitions Population Density vs. biomass Census vs. sample vs. index Statistic (estimate) Parameter

5 Terms and Definitions Inferential Statistics Bias / Accuracy / Precision Sampling error A C Which is accurate but imprecise? B D

6 Direct Estimates / Census Direct counts Difficult, but easy to interpret Video monitoring

7 Indirect Census Hydro acoustics? Species?

8 Sample Counts Sample and extrapolate Random sampling

9 Sample Counts Terms Random sampling Independence Extrapolation and inference Assumptions No change in pop parameters B I D E

10 Stratified Random Sampling Habitat % Available Sampling Effort % of Pop

11 Sample Counts Ratio Methods Mark-Recapture Techniques

12 Lincoln Peterson Method Popular for small mammals and fish A mark recapture technique Sample, mark, release, resample

13 Mark Recapture Single Lincoln-Peterson Method Let s derive it (i.e., make a formula) by thinking about how marking fish then resampling would help us estimate the population size Hint: think proportions

14 N =? Survey 1: Survey 2: M = 12 n = 15 m = 4 Proportion marked in 2 nd sample ought to be related to proportion of total population marked

15 Lincoln Peterson N/M = n/m N = Mn m Confidence interval

16 Assumptions Mark Recapture

17 Lincoln Peterson Method Consequences of violation Trap Happy Trap Shy Tag loss, death (dilution) N = Mn m

18 What happens if you loose your marks (fish die or tags falls off or emigration)? 1. Underestimate 2. Overestimate 3. No effect

19 What happens if fish are trap happy? 1. Underestimate 2. Overestimate 3. No effect

20 In general, under-representation of marks leads to? 1. Underestimate 2. Overestimate 3. No effect

21 Rates of Exploitation / Harvest Mortality Mark fish Tally creel, note marked fish Exploitation rate = E = harvest / pop size Or m/m Cautions!

22 Improvements

23 Lincoln Peterson Method Bailey Modification N = M n + 1 m + 1 V = M2 n + 1 n m m (m + 2) N ˆ 1.96 V ( N ˆ )

24 Lincoln Peterson Method (Chapman modification) N = (M+1) n+1 m+1-1 V = (M + 1) n + 1 (M m) n m m (m + 2) N ˆ 1.96 V ( N ˆ ) CI means what?

25 Schnabel Multiple Mark Recapture Technique Continue to mark individuals M * n N 1 m M = total marked before capture m = # recaptured

26 Schnabel Data Day # Capt (n) # recapt (m) T Marked (M) Sum (m) Sum M * n M * n N 1 m handout Total Marked before capture

27 Schnabel Estimate M * n N 1 m V ( 1 N ) m ( Mn) % C.I N V ( N )

28 Regression (Depletion or Removal) Estimators Graphical and regression approach Rationale

29 Depletion Estimators Pass Catch Effort (min) Sum Catch CPUE (#/time) Effort = minutes fishing, # trap-hours, volume sieved with seine, etc.

30 CPUE (#/min) Catch must decline as numbers are depleted Use that trend to estimate what the population should be Sum of Catch (# individuals)

31 CPUE = Sum Catch R 2 = CPUE (#/min) Sum of Catch (# individuals)

32 160 CPUE (#/min) CPUE = Sum Catch R 2 = Solve the equation: What is X when Y is 0? Population Size = 478 Population Size = Sum of Catch (# individuals)

33 CPUE (# per min) % CI Sum of Catch (# Individuals)

34 Regression Estimators Assumptions Caveats

35 What happens when catchability decreases? 1. Overestimate 2. Underestimate 3. Not sure

36 Don t forget CPUE Measure of effort Index of abundance Disadvantages numerous

37 Direct Trend or Relativity Estimates CPUE

38 General Cautions on Population Estimates Difficult Reliable? Do you need it? Would an index be ok? C/f trends New methods available

39 Information theoretic approaches Program MARK (free) Very advanced