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: N t+1 =SA t N t +SJ t f t Nt - 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: N t+1 =(SA t +SJ t f t )N t = r t N t where r t =SA t +SJ t f t

What if you plot N t+1 against N t, ie if you assume one predictor of next year’s population is this year’s population? NtNt N t+1 N t+1 =N t Slope=r t What if your data indicate that the slope doesn’t change, i.e. r is constant or at least independent of N t ?

As you saw in the last tutorial, complete independence of r t from N t 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

A point about average rates like SA and mean fecundity f When we say that a proportion SA t of N t survives, do we mean that every fish that is a member of N t has the same probability SA t of survival? NO! N t 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 N t =N 1 +N 2 +N 3 +… and if survival rates by age are SA 1, SA 2, SA 3,… then (Survivors)=N 1 SA 1 +N 2 SA 2 +N 3 SA 3 +… =Nt(P 1 SA 1 +P 2 SA 2 +P 3 SA 3 +…) where P a is proportion of age a fish in N t So the population SA t is a weighted average of the age- specific rates SA a, with each age rate weighted by P a

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 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