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Lecture 1 review

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- Why managers cannot avoid making predictions
- Approaches to prediction
- Components of population change
- What is a “population”?
- How natural populations behave

- 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

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)

- 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)

- 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

A simulated population decline and recovery, based on yellowfin tuna parameters

Associated changes in surplus production and production/biomass

Biomass next year = Biomass this year + Production – Catch

which implies: Production=Biomass next year-Biomass this year +Catch

There is a long

History of catch

Statistics (removal

Rates)

But only a short, history of noisy data on trends in stock size