Virtual Population Analysis

1
Virtual Population Analysis

• Goals
• Describe the methodology and underlying
  assumptions of VPA
• Compare and contrast VPA performed for
• Discrete Fisheries
• Continuous Fisheries
• Discuss the potential consequences on VPA
  estimates of
• poor terminal F assumptions
• incorrect M
• aging errors
• unit stock assumptions
• misreported catches

2
A little nomenclature
Cohort Analysis a.k.a. Virtual Population
Analysis a.k.a. Sequential Population Analysis

• Follows a single cohort
• estimates virtual or unseen population
• looks a sequential catch data
• terms often interchangeable
• based on same general principles

3
Mortality in Review
Nt1 Nt e-(FM)
F instantaneous fishing mortality rate M
instantaneous natural mortality rate
Based on exponential model ofcontinuous
mortality effects.
Numbers
Time
4
When catch-at-age data is availablefor all
fished age classes
Na1,t1 Na,t - Ca,t - Da,t
For time t Na,t - number of age a
(cohort) (unknown) Ca,t - number of age a
caught (fisheries data) Da,t - number dying of
natural causes (estimates or studies)
5
For any single cohort
Time Numbers R ? R1 NR2
CR1 DR1 R2 0 CR2 DR2 R3
all dead in 3 years

• Sum all cohorts for each time
• Virtual Population
• Remember, require
• catch-at-age data
• natural mortality estimates
• Note
• no parameter estimation yet...
• fish accounting

6
VPA In Discrete Fisheries

• Assume F and M occur separately
• brief interception fisheries
• herring, salmon, etc.
• Nt ? less D ? less C ? Nt1??

For each cohort
Nt Nt1 Ct Dt
Dt Nt (1-s)
survival
7
Population at beginning of year (after last
years fishing)
Population prior to fishing (less natural
mortality)
Nt Nt s
Harvest Rate
ht Ct / Nt
Instantaneous Fishing Mortality
Ft -ln(1 - ht)
8
The VPA Result

• provides dynamic
• population
• also harvest rates (by age)
• BUT incomplete cohorts
• not all caught yet
• current pops. not known
• BUT current of most interest!
• see H W p. 353 for herring example

9
Continuous Fisheries

• fishing and natural mortality occurring
  continuously throughout the year

Nt1 Nt e-(FM)
proportion of mortalitydue to fishing
We seek an expression of Nt interms of Nt1 ,
M(or s), and Ct asbefore, but ...
10
Pope (1972) derived approximation
Nt Nt1 eM Ct eM/2

• based on instant mid-year fishery
• Works well when (FM) lt 0.7
• error overestimates Nt
• errors accumulate

11
Exact VPA vs Popes Approx.
12
Dealing with Incomplete Cohorts Terminal F
Assumptions

• h, F or N cannot be known for years with
  incomplete cohorts
• N from other methods
• direct estimates (surveys)
• other statistical methods
• Assume current F values
• estimates of F from auxiliary data
• calculate F from
• nominal effort
• assumed q values (FqE)

Nt Ct (Ft M) (1 - e -Zt ) Ft
Remember Z F M
13
How good is our guess?? Iterated or Tuned VPA
Terminal F Values Converge
14
Caveats for VPA

• commonly used but difficult to refute (lack of
  alternatives)
• based on only THREE key assumptions
• all fish are dead before some age
• natural mortality is known
• no net em/immigration
• still systematic biases have occurred!!
• Terminal F assumptions
• Incorrect M/ Changing M
• Aging Errors
• Migrations
• Misreporting Fishing Mortality

15
Terminal F Assumptions

• using past F as the current F
• untuned or untested with auxiliary data
• catchability can increase as stock declines
• common in clupeoids
• unrecognized high q will make stock appear
  larger than it is
• actions
• select terminal Fs to reflect suspected
  variations in q
• sensitivity to a range of possible q values
• use updated VPAs to examine possible past
  biases and trends
• newly completed cohorts

16
Incorrect Natural Mortality

• Constant M
• if value used is too large
• estimated cohorts be too large
• assumed mortality not present
• NOTE will assume current cohorts too large!!!

• Changing M
• VPA assumes single, constant M
• time trends in M could generate corresponding,
  spurious time trends in estimated abundance
• dangerous if using VPA to evaluate past
  management actions

17
Aging Errors

• accurate catch-at-age data is the foundation
  of VPA
• incorrect aging biases cohort age estimates
• asymmetrical
• strong cohorts spill over
• 10 error
• age 2 10, age 3 1000
• estimate age 2 109
• estimate age 3 901
• aging errors mask recruitment variability
• hide relationships
• bias toward indifference to stock size in
  management

18
Unit Stock Assumption

• Immigration
• increase in local stock
• worked backward in VPA
• makes cohort appear too large at recruitment
• more serious with older fish

• Emigration
• proportional to stock density
• act like natural mortality
• random
• add noise to any trends

19
Misreporting of Fishing Mortality

• unrecorded landings
• discarding
• fishing-induced mortality
• not catch
• unaccounted for in VPA equations
• if constant, constant bias
• if variable, may mask trends and responses
• Correct VPA calculations with estimated
  misreporting