J. Math. Biol. (2017) 75:973–984
Quantifying functionals of age distributions in the wild
by solving an operator equation
· Hans-Georg Müller
Nikos T. Papadopoulos
· James R. Carey
Received: 8 August 2015 / Revised: 19 January 2017 / Published online: 17 February 2017
© Springer-Verlag Berlin Heidelberg 2017
Abstract Residual demography is a recent concept that has proved to be a useful
tool to gain insights about the age distributions of wild populations, especially insects.
We develop an operator equation that permits the derivation of functionals of the age
distribution in wild populations, such as mean age, within the framework of resid-
ual demography. Our method combines information from an observed captive cohort,
which consists of subjects that are sampled from the wild with unknown ages and then
raised in the laboratory until death, and from a reference cohort that consists of sub-
jects raised in the laboratory since birth of the same population. Targeting functionals
such as the mean of the wild age distribution has the advantage of avoiding strong
assumptions such as stationarity and stability of the population that one would need
when targeting the entire survival distribution in the wild. Our main result character-
izes the existence of a solution of the operator equation that yields the functional of
interest. The proposed method also enjoys straightforward and easy implementation.
A data example is included illustrating an application, where one aims to attain the
mean age of mosquitoes in the wild, based on seasonal captive cohorts from Greece
and a simulated reference cohort, separately for various summer and fall months.
Hans-Georg Müller: Research supported by NSF Grants DMS-1104426 and DMS-1407852.
Department of Statistics, University of California, One Shields Avenue, Davis, CA 95616, USA
Department of Agriculture, Crop Production and Rural Environment, University of Thessaly,
Fytokou Street, N. Ionia, 384 46 Vólos, Greece
Department of Entomology and Nematology, University of California, One Shields Avenue, Davis,
CA 95616, USA