Assessing Fishery Condition: Population Estimation Chapter 11 Thought for Today: "In God we trust, all others bring data." William Edward Deming (1900-1993).
Why?
Needs / Requirements Objectives Info about animals Literature review Statistician MONEY
Terms and Definitions Population Density vs. biomass Census vs. sample vs. index Statistic (estimate) Parameter
Terms and Definitions Inferential Statistics Bias / Accuracy / Precision Sampling error A C Which is accurate but imprecise? B D
Direct Estimates / Census Direct counts Difficult, but easy to interpret Video monitoring
Indirect Census Hydro acoustics? Species?
Sample Counts Sample and extrapolate Random sampling
Sample Counts Terms Random sampling Independence Extrapolation and inference Assumptions No change in pop parameters B I D E
Stratified Random Sampling Habitat % Available Sampling Effort % of Pop 1 70 70 2 10 10 3 5 5 4 10 10 5 5 5
Sample Counts Ratio Methods Mark-Recapture Techniques
Lincoln Peterson Method Popular for small mammals and fish A mark recapture technique Sample, mark, release, resample
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
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
Lincoln Peterson N/M = n/m N = Mn m Confidence interval
Assumptions Mark Recapture
Lincoln Peterson Method Consequences of violation Trap Happy Trap Shy Tag loss, death (dilution) N = Mn m
What happens if you loose your marks (fish die or tags falls off or emigration)? 1. Underestimate 2. Overestimate 3. No effect
What happens if fish are trap happy? 1. Underestimate 2. Overestimate 3. No effect
In general, under-representation of marks leads to? 1. Underestimate 2. Overestimate 3. No effect
Rates of Exploitation / Harvest Mortality Mark fish Tally creel, note marked fish Exploitation rate = E = harvest / pop size Or m/m Cautions!
Improvements
Lincoln Peterson Method Bailey Modification N = M n + 1 m + 1 V = M2 n + 1 n m m + 1 2 (m + 2) N ˆ 1.96 V ( N ˆ )
Lincoln Peterson Method (Chapman modification) N = (M+1) n+1 m+1-1 V = (M + 1) n + 1 (M m) n m m + 1 2 (m + 2) N ˆ 1.96 V ( N ˆ ) CI means what?
Schnabel Multiple Mark Recapture Technique Continue to mark individuals M * n N 1 m M = total marked before capture m = # recaptured
Schnabel Data Day # Capt (n) # recapt (m) T Marked (M) Sum (m) Sum M * n 1 50 2 3 4 M * n N 1 m handout Total Marked before capture
Schnabel Estimate M * n N 1 m V ( 1 N ) m ( Mn) 2 1 95% C.I. 1 1.96 N V ( N )
Regression (Depletion or Removal) Estimators Graphical and regression approach Rationale
Depletion Estimators Pass Catch Effort (min) Sum Catch CPUE (#/time) 1 100 10 2 40 8 3 41 12 Effort = minutes fishing, # trap-hours, volume sieved with seine, etc.
CPUE (#/min) 160 140 120 100 80 Catch must decline as numbers are depleted Use that trend to estimate what the population should be 60 40 140 190 240 290 340 390 Sum of Catch (# individuals)
160 140 120 CPUE = -0.4417 Sum Catch + 210.93 R 2 = 0.9582 CPUE (#/min) 100 80 60 40 20 0 140 190 240 290 340 390 440 490 Sum of Catch (# individuals)
160 CPUE (#/min) 140 120 100 80 60 40 20 CPUE = -0.4417 Sum Catch + 210.93 R 2 = 0.9582 Solve the equation: What is X when Y is 0? Population Size = 478 Population Size = 478 0 140 190 240 290 340 390 440 490 Sum of Catch (# individuals)
1400 1200 1000 CPUE (# per min) 800 600 400 200 95% CI 0-200 -400 100 200 300 400 500 600 Sum of Catch (# Individuals)
Regression Estimators Assumptions Caveats
What happens when catchability decreases? 1. Overestimate 2. Underestimate 3. Not sure
Don t forget CPUE Measure of effort Index of abundance Disadvantages numerous
Direct Trend or Relativity Estimates CPUE
General Cautions on Population Estimates Difficult Reliable? Do you need it? Would an index be ok? C/f trends New methods available
Information theoretic approaches Program MARK (free) Very advanced