Lecture 1 topics.ppt by tongxiamy

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									         Lecture 1 review
• Why managers cannot avoid making
  predictions
• Approaches to prediction
• Components of population change
• What is a “population”?
• How natural populations behave
The ecological basis of sustainable
     production and harvest
• Population change can always be represented
  as
  (New N)=(Survivors)+(Surviving recruits)
• Or in shorthand:
  Nt+1=SAtNt+SJtftNt
  - SA =survival rate of 1+ year old fish
  - SJ =survival rate from egg to age 1
  - f =eggs per age 1+ year old fish
• Note the balance relationship can be written as:
  Nt+1=(SAt+SJt ft)Nt = rtNt where rt=SAt+SJt ft
   What if you plot Nt+1 against Nt, ie if you
assume one predictor of next year’s population
          is this year’s population?
Slope=rt
                                              Nt+1=Nt
        Nt+1




                        Nt
What if your data indicate that the slope doesn’t
change, i.e. r is constant or at least independent of Nt?
   As you saw in the last tutorial, complete
 independence of rt from Nt always leads to
    predictions of exponential increase or
       decline, never to sustainable N
• So the ecological basis of sustainable
  production is change in r with N
• Which component(s) of r change with N in
  some way so as to compensate for
  harvest effects?
  – SA? Goes down as harvest rate increases
  – SJ? Goes up, often dramatically!
  – f? Often goes down as harvest rate increases
    (smaller, less fecund fish)
  What happens when a population is
           fished down?
• There can be ecosystem-scale response
  – Reduced predator abundance (SA,SJ)
  – Increased prey abundance (f, growth and SJ)
• But more commonly there is increase in fine-
  scale (foraging arena) food availability
  – Reduced foraging time for same growth (SJ)
  – Increased growth rate (SJ especially overwinter, f)
• And sometimes other resources are in short
  supply
  – Hiding places for juveniles (SJ)
  – Higher quality foraging sites (SJ, f) (most fish show
    strong dominance hierarchies)
  Fitness-maximizing strategies for adjusting
feeding activity lead to density-dependence in
            survival, growth rates

                            Survival-growth tradeoff in stocked
                                  rainbow trout, optimizes
                              fitness=growth x survival rate
                      0.4
                                Natural
                      0.3       densities are
      Survival rate




                                mostly high,                    Low stocking
                                little growth                   Rates (low
                      0.2                                       densities)
                                change

                      0.1
                                                High stocking
                                                Rates
                       0
                            0             0.5        1            1.5          2
                                                Growth rate
A point about average rates like SA
       and mean fecundity f
• When we say that a proportion SAt of Nt survives, do we
  mean that every fish that is a member of Nt has the
  same probability SAt of survival? NO!
• Nt typically consists of a heterogeneous collection of
  individuals that we can classify by attributes like age.
  Natural survival rate typically increases with age
  (M=k/length; Lorenzen, McGurk)
• If Nt=N1+N2+N3+… and if survival rates by age are SA1,
  SA2, SA3,… then
        (Survivors)=N1SA1+N2SA2+N3SA3+…
                   =Nt(P1SA1+P2SA2+P3SA3+…)
     where Pa is proportion of age a fish in Nt
• So the population SAt is a weighted average of the age-
  specific rates SAa, with each age rate weighted by Pa
Age-structured models warn us to expect big
  drops in mean fecundity and production
  during both periods of heavy fishing and
       periods of population recovery
                                             mean fecundity
                             0.1             Vulnerable biomass                15                              A simulated population




                                                                                               Stock biomass
 Mean fecundity




                            0.08
                            0.06                                               10                              decline and recovery,
                            0.04                                               5                               based on yellowfin
                            0.02                                                                               tuna parameters
                               0                                           0
                               1950   1970     1990         2010        2030
                                                Year
                                                                                                                Associated changes in
                            3                                       1                                           surplus production and
  Surplus Production (SP)




                                                     SP
                                                                          Production/Biomass




                                                     SP/B                                                       production/biomass
                            2
                                                                               Surplus




                                                                    0.5
                            1                                                                                  Biomass next year = Biomass this year +
                                                                                                               Production – Catch
                            0                                       0                                          which implies: Production=Biomass next
                                0     5           10           15
                                                                                                               year-Biomass this year +Catch
                                       Biomass (B)
An example: Bill Pine’s SRA reconstruction
of shad population change in Hudson and
               other rivers
  20.0
  18.0                                         Vulnerable
                                               biomass                                                                             There is a long
  16.0
  14.0
                                               Catch (10^6 kg)                                                                     History of
  12.0                                                                                                                             catch
  10.0                                                                                                                             Statistics
   8.0                                                                                                                             (removal
   6.0                                                                                                                             Rates)
   4.0
   2.0
   0.0
   70
         80
              90
                   00
                        10
                             20
                                  30
                                       40
                                            50
                                                 60
                                                            70
                                                                      80
                                                                                    90
                                                                                              00
                                                                                                            10
                                                                                                                       20
  18
       18
            18
                 19
                      19
                           19
                                19
                                     19
                                          19
                                               19
                                                    19
                                                               19
                                                                             19
                                                                                           20
                                                                                                     20
                                                                                                                      20
                                                      2.5




                                                                                                                           But only a short,
                                                                                                     Obs C P U E
                                                       2
                                                                                                     P r ed C P U E




                                                      1.5

                                                                                                                           history of noisy
                                                       1

                                                                                                                           data on trends in
                                                      0.5
                                                                                                                           stock size
                                                       0
                                                        1975   1980   1985   1990   1995   2000   2005   2010
                            We can back-calculate surplus production
                                from catch and biomass change

                                 surplus production (Delta B+Catch)

                     3.0

                     2.5
Surplus production




                                                                                                                  surplus production/biomass
                     2.0
                                                                                                      0.6
                     1.5
                                                                                                      0.5




                                                                                 Production/biomass
                     1.0
                                                                                                      0.4
                     0.5                                                                              0.3

                     0.0                                                                              0.2
                           0.0         5.0          10.0           15.0   20.0
                                                                                                      0.1
                                       Stock size (vulnerable biomass)
                                                                                                       0
                                                                                                            0.0     5.0           10.0           15.0   20.0
                                                                                                                     Stock Size (vulnerable biomass)

								
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