Dynamic behavior of upper trophic level populations: age-structured models

with density-dependent recruitment

Louis W. BotsfordWildlife, Fish, and Conservation Biology

Fished populations have greater variability (e.g., Hsieh, et al 2006)

After removing the effects of age of maturation on the CV of abundance, fished species have greater CV than unfished species.

Fished

Unfished

New view

No longer:

Environment Catch

Rather:

VariableEnvironment

DevelopmentFecunditySurvival

Recruitment

Catch

Biomass

Population

t t

PDO Salmon catch

Population ModelAge-structured model with density-dependent recruitment

n1,t= Rt, recruitment, where

na,t=abundance at age a, time t

na+1,t+1= sa na,t 1<a<A

Where

With fi= fecundity at age i

= annual reproduction

Mathematical Analysis

(1) Equilibrium level + (2) Variability about equilibrium

Slow change (decadal) Rapid change (inter-annual)

Changes in sa, fa, development rate

Fecundity, fa

age

Survival, sa

Egg Production

Rec

ruitm

ent

Slope=1/(Lifetime Egg Production)

(1) Equilibrium with fishing

Lifetime

Egg

Production

(Sissenwine and Shepherd 1987)

Examples of Spawning Age Distributions, Age Truncation

with fishingPacific Ocean Perch, POP

Pacific Whiting, Hake

Coho salmon

Fishing mortality, F

Differences in effect of fishing

Example of effect of fishing (reduced adult survival, s) on equilibrium recruitment of coho salmon

Egg production

Recr

uitm

ent

(2) Variability (sensitivity) increases with slope of egg-recruit equilibrium

Differences in response to fishing

Relative CV of Egg Production

0 collapse Fishing

Relative CV of Recruitment

Relative CV of Catch

POP, Hake, Coho

POP=.8 at 0Hake=.8 at 0Coho=.8 at 0

POP=.13 at 0Hake=.23 at 0Coho=.71 at 0

POP=.12 at 0Hake=.26 at 0Coho=.54 at 0

1. Populations sensitive to generational frequencies, and low frequencies (more sensitive with narrow spawning ages)2. Age truncation increases this sensitivity

Sensitivity =sout/sin

Frequency Dependence of Sensitivity

Truncation increases resonance because egg production is a weighted version of past recruitment

Review: Another example with generic cod and generic salmon

Fishing changes age structure, changing dynamics, i.e., equilibrium and cohort resonance.

Unfished

Unfished

fished

fished

heavily fished

heavily fished

Salmon

Cod

Egg

Prod

uctio

n (a

) =

surv

ival

(a) x

mat

urity

(a) x

fecu

ndity

(a)

Salm

onCo

d

FLEP=normalized LEP

Collapse value

Recruitment time series for salmon and cod examples, with white noise forcing early survival

Unfished

Fished

Heavily fished

Grey = codBlack= salmon

Variance spectra

Generic codGeneric salmon

Unfished

Unfished

FishedFished

Heavily fishedHeavily fished

What do these results mean for climate change?

• If the frequencies of environmental forcing change (e.g., more frequent ENSOs), that could change variability.

• Slow change with climate will be confounded with greater sensitivity to low frequencies.

Population dynamic view of the changing climate: time scales or frequencies of ocean conditions

Torrence and Compo (1998)

Example: changing spectrum of ENSO, 1870-1997

How can EcoFor make use of these results?

• In most UTL populations, environmental variability will be affecting recruitment survival

• This tells us what frequencies recruitment will be sensitive to, but also the effects on other observations: egg production (e.g., CalCOFI surveys, Hsieh, et al. 2007), catch.

• It can be used as the “integration” due to UTL population dynamics (as in Di Lorenzo and Ohman)

Marine

Ecology

At

The Ag School,

UC Davis

THANKS!