title: Quantifying functionals of age distributions in the wild by solving an operator equation.
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 residual 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 subjects 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 characterizes 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.
authors.affiliation: Department of Statistics, University of California, One Shields Avenue, Davis, CA, 95616, USA. haoji@ucdavis.edu.
authors.forename: Hao
authors.identifier: http://orcid.org/0000-0003-0887-6106
authors.initials: H
authors.lastname: Ji
authors.affiliation: Department of Statistics, University of California, One Shields Avenue, Davis, CA, 95616, USA.
authors.forename: Hans-Georg
authors.initials: HG
authors.lastname: Müller
authors.affiliation: Department of Agriculture, Crop Production and Rural Environment, University of Thessaly, Fytokou Street, N. Ionia, 384 46, Vólos, Greece.
authors.forename: Nikos T
authors.initials: NT
authors.lastname: Papadopoulos
authors.affiliation: Department of Entomology and Nematology, University of California, One Shields Avenue, Davis, CA, 95616, USA.
authors.forename: James R
authors.initials: JR
authors.lastname: Carey
mesh_terms: D017677:Age Distribution; D000818:Animals; D000835:Animals, Wild; D003198:Computer Simulation; D003465:Culex; D017753:Ecosystem; D016018:Least-Squares Analysis; D016014:Linear Models; D055641:Mathematical Concepts; D008954:Models, Biological; D015233:Models, Statistical; D012621:Seasons
keywords: Aging in the wild; Culex pipens; Existence of solution; Functional singular representation; Inverse problem; Operator equation; Residual demography