MEPS 127:15-26 (1995)  -  doi:10.3354/meps127015

Population growth of northern anchovy and Pacific sardine using stage-specific matrix models

Lo NCH, Smith PE, Butler JL

We applied a stage-specific population matrix, the Lefkovitch matrix, to the northern anchovy Engraulismordax and the Pacific sardine Sardinopssagax to determine which vital rates in the life history have the most effect on population growth. Three vital rates considered are the daily stage-specific instantaneous mortality rate, stage duration and daily age-specific fecundity per female. The models incorporate variability in growth rates among individuals and link simpler stage-based and more complicated individual-based modeling approaches. The elasticity of population growth rate for anchovy (percentage change from a 1% change of a vital rate) was greatest for mortality in yolk-sac larvae, fecundity of 2 yr old fish (111 to 135 mm), and stage duration in late larvae (11 to 35 mm). For sardine, elasticity was greatest for mortality in life stages of egg and yolk-sac larvae, fecundity of 5 and 6 yr old fish (211 to 250 mm), and stage duration in the early larvae (5 to 10 mm). When stage duration was variable, elasticity was 1/10 as large as when stage duration was constant, indicating that sensitivity of populations to changes in vital rates is reduced by variation in growth rates. Population growth rates for both species increased with variance in individual growth rates. Thus, a population with individuals that grow at varying rates is more likely to increase. Our models indicate that growth rates are important determinants of population growth and recruitment and it is likely that growth and mortality rates are linked. We suggest, therefore, that inexpensive estimates of larval growth rates could be used to help forecast future recruitment.


Population matrix projection model . Sensitivity . Stage-specific vital rates . Pelagic fish . Stage duration


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