While lognormal distributions have been proposed as useful descriptors
of recruitment variability,
the very nature of the recruitment distributions is still debated.
To account quantitatively for recruitment distributions,
I here propose a Weibull exponential model;
it derives from a simple and natural hypothesis for uncorrelated
recruitment processes of spawning, hatching, growth and survival
through the early life stages to the point of vulnerability to the
fishery.
The quantification of Weibull exponentials is particularly important
with regards to extrapolations to low recruits that have not yet been
observed.
To test the Weibull exponential null-hypothesis, I examine annual
time-series of recruitment in major aquatic stocks.
The Weibull exponential quite describes the bulk (95%) of the
recruitment distributions of widely differing stocks,
while the remaining 5% of the largest recruits are occurring with a
much larger rate than predicted by the Weibull exponential.
Further, I study the inter-event times between unusually high numbers
in recruitment time-series data
and find that intermittent pulses of strong recruitment follow
non-Poisson statistics, which arises from year-to-year persistence of
the magnitude of recruitment:
large (or small) recruits are more likely to be followed by large (or
small) recruits.
This recruitment clustering effect is confirmed by the rescaled range
analysis method.
The empirical results imply that individual survivals on recruitment
levels are independent of initial cohort sizes but year-to-year
recruiting events exhibit long-term correlations.