Age-Grouping, Time-Specific Life-Tables, and Predictive Population Models

This chapter describes techniques to create life-tables for animals whose generations overlap widely. Age-grouping is a prerequisite for these methods, which have been most widely applied to vertebrate populations. Age cannot be inferred from the developmental stage without reference to the environment. The speed of development may be temperature-dependent or influenced by factors such as oxygen and food availability. The methods for ageing animal groups, including invertebrates, fish, reptiles, amphibians, birds, and mammals, are reviewed. Time-specific life-tables, population modelling, and Leslie matrices are described. R code to analyze Leslie matrix dynamics is presented.

A Note on NIEP for Leslie and Doubly Leslie Matrices

The nonnegative inverse eigenvalue problem (NIEP) consists of finding necessary and sufficient conditions for the existence of a nonnegative matrix with a given list of complex numbers as its spectrum. If the matrix is required to be Leslie (doubly Leslie), the problem is called the Leslie (doubly Leslie) nonnegative eigenvalue inverse problem. In this paper, necessary and/or sufficient conditions for the existence and construction of Leslie and doubly Leslie matrices with a given spectrum are considered.

The inverse eigenvalue problem for Leslie matrices

The Nonnegative Inverse Eigenvalue Problem (NIEP) is the problem of determining necessary and sufficient conditions for a list of $n$ complex numbers to be the spectrum of an entry--wise nonnegative matrix of dimension $n$. This is a very difficult and long standing problem and has been solved only for $n\leq 4$. In this paper, the NIEP for a particular class of nonnegative matrices, namely Leslie matrices, is considered. Leslie matrices are nonnegative matrices, with a special zero--pattern, arising in the Leslie model, one of the best known and widely used models to describe the growth of populations. The lists of nonzero complex numbers that are subsets of the spectra of Leslie matrices are fully characterized. Moreover, the minimal dimension of a Leslie matrix having a given list of three numbers among its spectrum is provided. This result is partially extended to the case of lists of $n > 2$ real numbers.

strandCet: R package for estimating natural and non-natural mortality-at-age of cetaceans from age-structured strandings

Mortality is one of the most important parameters for the study of population dynamics. One of the main sources of information to calculate the mortality of cetaceans arises from the observed age-structure of stranded animals. A method based on an adaptation of a Heligman-Pollard model is proposed. A freely accessible package of functions (strandCet) has been created to apply this method in the statistical software R. Total, natural, and anthropogenic mortality-at-age is estimated using only data of stranded cetaceans whose age is known. Bayesian melding estimation with Incremental Mixture Importance Sampling is used for fitting this model. This characteristic, which accounts for uncertainty, further eases the estimation of credible intervals. The package also includes functions to perform life tables, Siler mortality models to calculate total mortality-at-age and Leslie matrices to derive population projections. Estimated mortalities can be tested under different scenarios. Population parameters as population growth, net production or generation time can be derived from population projections. The strandCet R package provides a new analytical framework to assess mortality in cetacean populations and to explore the consequences of management decisions using only stranding-derived data.

Demographic variability and heterogeneity among individuals within and among clonal bacteria strains

Identifying what drives individual heterogeneity has been of long interest to ecologists, evolutionary biologists and biodemographers, because only such identification provides deeper understanding of ecological and evolutionary population dynamics. In natural populations one is challenged to accurately decompose the drivers of heterogeneity among individuals as genetically fixed or selectively neutral. Rather than working on wild populations we present here data from a simple bacterial system in the lab, Escherichia coli. Our system, based on cutting-edge microfluidic techniques, provides high control over the genotype and the environment. It therefore allows to unambiguously decompose and quantify fixed genetic variability and dynamic stochastic variability among individuals. We show that within clonal individual variability (dynamic heterogeneity) in lifespan and lifetime reproduction is dominating at about 82-88%, over the 12-18% genetically (adaptive fixed) driven differences. The genetic differences among the clonal strains still lead to substantial variability in population growth rates (fitness), but, as well understood based on foundational work in population genetics, the within strain neutral variability slows adaptive change, by enhancing genetic drift, and lowering overall population growth. We also revealed a surprising diversity in senescence patterns among the clonal strains, which indicates diverse underlying cell-intrinsic processes that shape these demographic patterns. Such diversity is surprising since all cells belong to the same bacteria species, E. coli, and still exhibit patterns such as classical senescence, non-senescence, or negative senescence. We end by discussing whether similar levels of non-genetic variability might be detected in other systems and close by stating the open questions how such heterogeneity is maintained, how it has evolved, and whether it is adaptive.Data depositionThe processed image analysis data, R code, as well as the Leslie matrices will be archived at Dryad.org.