Lecture 1 review
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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.

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Lecture 1 review

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Lecture 1 review

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

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


Lecture 1 review

Slope=rt

Nt+1=Nt

Nt+1

Nt

What if you plot Nt+1 against Nt, ie if you assume one predictor of next year’s population is this year’s population?

What if your data indicate that the slope doesn’t change, i.e. r is constant or at least independent of Nt?


Lecture 1 review

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

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)


Lecture 1 review

Fitness-maximizing strategies for adjusting feeding activity lead to density-dependence in survival, growth rates


A point about average rates like sa and mean fecundity f

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


Lecture 1 review

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


An example bill pine s sra reconstruction of shad population change in hudson and other rivers

An example: Bill Pine’s SRA reconstruction of shad population change in Hudson and other rivers

There is a long

History of catch

Statistics (removal

Rates)

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


We can back calculate surplus production from catch and biomass change

We can back-calculate surplus production from catch and biomass change


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