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Dynamic behavior of upper trophic level populations: age -structured models with density-dependent recruitment Louis W. Botsford Wildlife, Fish, and Conservation Biology. Fished populations have greater variability (e.g., Hsieh, et al 2006). Fished. Unfished.
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Dynamic behavior of upper trophic level populations: age-structured models with density-dependent recruitmentLouis W. BotsfordWildlife, Fish, and Conservation Biology
Fished populations have greater variability (e.g., Hsieh, et al 2006) Fished Unfished After removing the effects of age of maturation on the CV of abundance, fished species have greater CV than unfished species.
New view No longer: Environment Catch Salmon catch PDO t t Rather: Recruitment Catch Biomass Development Fecundity Survival Variable Environment Population
Population Model Age-structured model with density-dependent recruitment na,t=abundance at age a, time t na+1,t+1= sana,t1<a<A n1,t= Rt, recruitment, where Where = annual reproduction With fi= fecundity at age i
Mathematical Analysis (1) Equilibrium level + (2) Variability about equilibrium Slow change (decadal) Rapid change (inter-annual) Changes in sa, fa, development rate
(1) Equilibrium with fishing Fecundity, fa Survival, sa Lifetime Egg Production age Recruitment Slope=1/(Lifetime Egg Production) Egg Production (Sissenwine and Shepherd 1987)
Examples of Spawning Age Distributions, Age Truncation with fishing Fishing mortality, F Pacific Ocean Perch, POP Pacific Whiting, Hake Coho salmon Differences in effect of fishing
Example of effect of fishing (reduced adult survival, s) on equilibrium recruitment of cohosalmon Recruitment Egg production
(2) Variability (sensitivity) increases with slope of egg-recruit equilibrium
POP,Hake, Coho Differences in response to fishing Relative CV of Recruitment POP=.8 at 0 Hake=.8 at 0 Coho=.8 at 0 Relative CV of Egg Production POP=.13 at 0 Hake=.23 at 0 Coho=.71 at 0 Relative CV of Catch POP=.12 at 0 Hake=.26 at 0 Coho=.54 at 0 0 collapse Fishing
Frequency Dependence of Sensitivity 1. Populations sensitive to generational frequencies, and low frequencies (more sensitive with narrow spawning ages) 2. Age truncation increases this sensitivity Sensitivity = sout/sin
Truncation increases resonance because egg production is a weighted version of past recruitment
Fishing changes age structure, changing dynamics, i.e., equilibrium and cohort resonance. Unfished Cod fished Egg Production (a) = survival(a) xmaturity(a) x fecundity (a) heavily fished Unfished fished Salmon heavily fished Salmon FLEP= normalized LEP Cod Collapse value
Recruitment time series for salmon and cod examples, with white noise forcing early survival Unfished Fished Heavily fished Grey = cod Black= salmon
Variance spectra Generic cod Generic salmon Heavily fished Heavily fished Fished Fished Unfished Unfished
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 Example: changing spectrum of ENSO, 1870-1997 Torrence and Compo (1998)
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 THANKS! At The Ag School, UC Davis