# 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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