Matrix models and sensitivity analysis of populations classified by age and stage : a vec-permutation matrix approach

© The Author(s), 2011. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Theoretical Ecology 5 (2012): 403-417, doi:10.1007/s12080-011-0132-2.Matrix population models in which individuals are classified by both age and stage can be constructed using the vec-permutation matrix. The resulting age-stage models can be used to derive the age-specific consequences of a stage-specific life history or to describe populations in which the vital rates respond to both age and stage. I derive a general formula for the sensitivity of any output (scalar, vector, or matrix-valued) of the model, to any vector of parameters, using matrix calculus. The matrices describing age-stage dynamics are almost always reducible; I present results giving conditions under which population growth is ergodic from any initial condition. As an example, I analyze a published stage-specific model of Scotch broom (Cytisus scoparius), an invasive perennial shrub. Sensitivity analysis of the population growth rate finds that the selection gradients on adult survival do not always decrease with age but may increase over a range of ages. This may have implications for the evolution of senescence in stage-classified populations. I also derive and analyze the joint distribution of age and stage at death and present a sensitivity analysis of this distribution and of the marginal distribution of age at death.This research was supported by National Science Foundation Grant DEB-0816514 and by a Research Award from the Alexander von Humboldt Foundation

Empirical Models of Transitions between Coral Reef States: Effects of Region, Protection, and Environmental Change

There has been substantial recent change in coral reef communities. To date, most analyses have focussed on static patterns or changes in single variables such as coral cover. However, little is known about how community-level changes occur at large spatial scales. Here, we develop Markov models of annual changes in coral and macroalgal cover in the Caribbean and Great Barrier Reef (GBR) regions

Novel challenges and opportunities in the theory and practice of matrix population modelling: an editorial for the special feature: “Theory and Practice in Matrix Population Modelling” of Ecological Modelling

Demography is at the core of ecology, evolution, and conservation biology. The simple recognition that individuals in a given population contribute to its dynamics in different ways revolutionised the ways in which demographers approach data collection, analyses, and interpretation of their study populations, from bacteria to humans. Matrix population models, discrete-time, discrete-state (i.e. individuals are categorised into discrete categories based on traits such as age or stage), were first introduced to the scientific community by Patrick Leslie 75 years ago. Since then, the applications of matrix population models to ecology, evolution, and conservation biology have strongly been running strong and in parallel with its robust mathematical development. This special feature contains 14 novel contributions that represent some the cutting-edge mathematical formulations and applications of this powerful demographic tool. In addition to highlighting the key contributions of this manuscripts, we provide suggestions to some of the challenges that researchers using matrix population models must overcome in the coming decades to truly unlock the potential of this analytical demographic tool

Novel challenges and opportunities in the theory and practice of matrix population modelling: an editorial for the special feature: “Theory and Practice in Matrix Population Modelling” of Ecological Modelling

Demography is at the core of ecology, evolution, and conservation biology. The simple recognition that individuals in a given population contribute to its dynamics in different ways revolutionised the ways in which demographers approach data collection, analyses, and interpretation of their study populations, from bacteria to humans. Matrix population models, discrete-time, discrete-state (i.e. individuals are categorised into discrete categories based on traits such as age or stage), were first introduced to the scientific community by Patrick Leslie 75 years ago. Since then, the applications of matrix population models to ecology, evolution, and conservation biology have strongly been running strong and in parallel with its robust mathematical development. This special feature contains 14 novel contributions that represent some the cutting-edge mathematical formulations and applications of this powerful demographic tool. In addition to highlighting the key contributions of this manuscripts, we provide suggestions to some of the challenges that researchers using matrix population models must overcome in the coming decades to truly unlock the potential of this analytical demographic tool