*David J. Gibson*

- Published in print:
- 2014
- Published Online:
- January 2015
- ISBN:
- 9780199671465
- eISBN:
- 9780191792496
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199671465.003.0008
- Subject:
- Biology, Plant Sciences and Forestry

This chapter moves forward from Chapter 7 (planning, choosing, and using statistics) and introduces some more advanced statistical methods that are of particular importance to plant population ...
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This chapter moves forward from Chapter 7 (planning, choosing, and using statistics) and introduces some more advanced statistical methods that are of particular importance to plant population ecologists. The general goal of these methods is to quantify the spatiotemporal dynamics of plant populations. The basis for ecological modelling is described and advanced methods are described in four sections: first- and second-order spatial pattern analysis (including tessellation models); life table response experiments (LTREs), survivorship curves, and matrix models; cellular automata models, individual-based dynamic population models (e.g., SORTIE), and integral projection models (IPMs); and population viability analysis (PVA). Methods of spatial analysis are illustrated through use of a completely mapped plant dataset. Matrix models are illustrated through reanalysis of a published example. Recommended R packages for each method are provided.Less

This chapter moves forward from Chapter 7 (planning, choosing, and using statistics) and introduces some more advanced statistical methods that are of particular importance to plant population ecologists. The general goal of these methods is to quantify the spatiotemporal dynamics of plant populations. The basis for ecological modelling is described and advanced methods are described in four sections: first- and second-order spatial pattern analysis (including tessellation models); life table response experiments (LTREs), survivorship curves, and matrix models; cellular automata models, individual-based dynamic population models (e.g., SORTIE), and integral projection models (IPMs); and population viability analysis (PVA). Methods of spatial analysis are illustrated through use of a completely mapped plant dataset. Matrix models are illustrated through reanalysis of a published example. Recommended R packages for each method are provided.

*Louis W. Botsford, J. Wilson White, and Alan Hastings*

- Published in print:
- 2019
- Published Online:
- November 2019
- ISBN:
- 9780198758365
- eISBN:
- 9780191818301
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198758365.003.0005
- Subject:
- Biology, Biodiversity / Conservation Biology, Biomathematics / Statistics and Data Analysis / Complexity Studies

This chapter begins by revisiting the M’Kendrick/von Foerster model, but using size instead of age as the state variable. It then uses the lessons from that model to describe how individual growth ...
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This chapter begins by revisiting the M’Kendrick/von Foerster model, but using size instead of age as the state variable. It then uses the lessons from that model to describe how individual growth and mortality rates determine both stand distributions (a population of mixed ages) and cohort distributions (all one age). In particular, incorporating variability in growth trajectories is shown to be important in obtaining realistic results—though it is not without pitfalls. Ultimately, the numerical calculations required to model size-structured populations for future projections are more challenging than those needed for age structure, so the chapter closes by discussing some mathematical tools that have been developed to accomplish this. These include the integral projection model, a recent approach that is very useful because, while more complex, it has a lot in common with the age-structured models examined in Chapters 3 and 4.Less

This chapter begins by revisiting the M’Kendrick/von Foerster model, but using size instead of age as the state variable. It then uses the lessons from that model to describe how individual growth and mortality rates determine both stand distributions (a population of mixed ages) and cohort distributions (all one age). In particular, incorporating variability in growth trajectories is shown to be important in obtaining realistic results—though it is not without pitfalls. Ultimately, the numerical calculations required to model size-structured populations for future projections are more challenging than those needed for age structure, so the chapter closes by discussing some mathematical tools that have been developed to accomplish this. These include the integral projection model, a recent approach that is very useful because, while more complex, it has a lot in common with the age-structured models examined in Chapters 3 and 4.

*Tim Coulson and H. Charles J. Godfray*

- Published in print:
- 2007
- Published Online:
- November 2020
- ISBN:
- 9780199209989
- eISBN:
- 9780191917370
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780199209989.003.0006
- Subject:
- Environmental Science, Applied Ecology

What determines the densities of the different species of plants, animals, and micro-organisms with which we share the planet, why do their numbers fluctuate and ...
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What determines the densities of the different species of plants, animals, and micro-organisms with which we share the planet, why do their numbers fluctuate and extinctions occur, and how do different species interact to determine each other’s abundance? These are some of the questions addressed by the science of ecological population dynamics, the subject that underpins all the chapters in this book. In this chapter we introduce some of the basic principles of the subject by concentrating on the dynamics of singlespecies systems. These are species whose population biology can be studied without also explicitly including the dynamics of other species in the community. The chief justification for this brutal abstraction is that it allows many of the underlying processes to be described simply and more clearly. Moreover, arguments based on the analysis of single-species population dynamics are often surprisingly useful in understanding real populations, especially those in relatively simple environments such as agro-ecosystems. At the core of population dynamics is a simple truism: the density or numbers of individuals in a closed population is increased by births, and decreased by deaths. If the population is not closed then we need also to include immigration and emigration in our calculation. A population in which births exceed deaths will tend to increase and one where the reverse is true will tend to decrease. But more significant is the mode of change. If birth and death rates remain constant then the consequent increase or decrease in population numbers occurs exponentially—population dynamics occurs on a geometric rather than an arithmetic scale. In the first section of this chapter we describe the calculation of exponential growth rates for different types of population, and explore how such calculations, even though they are based on the simplistic assumption of constant demographic rates, can be very useful for a variety of problems in applied population biology. The fact that populations persist over appreciable periods of time inescapably means that demographic rates—births and deaths, immigration and emigration—do not remain constant. In fact, population persistence in the long term requires that as populations increase in density the death rate must rise relative to the birth rate and eventually exceed it.
Less

What determines the densities of the different species of plants, animals, and micro-organisms with which we share the planet, why do their numbers fluctuate and extinctions occur, and how do different species interact to determine each other’s abundance? These are some of the questions addressed by the science of ecological population dynamics, the subject that underpins all the chapters in this book. In this chapter we introduce some of the basic principles of the subject by concentrating on the dynamics of singlespecies systems. These are species whose population biology can be studied without also explicitly including the dynamics of other species in the community. The chief justification for this brutal abstraction is that it allows many of the underlying processes to be described simply and more clearly. Moreover, arguments based on the analysis of single-species population dynamics are often surprisingly useful in understanding real populations, especially those in relatively simple environments such as agro-ecosystems. At the core of population dynamics is a simple truism: the density or numbers of individuals in a closed population is increased by births, and decreased by deaths. If the population is not closed then we need also to include immigration and emigration in our calculation. A population in which births exceed deaths will tend to increase and one where the reverse is true will tend to decrease. But more significant is the mode of change. If birth and death rates remain constant then the consequent increase or decrease in population numbers occurs exponentially—population dynamics occurs on a geometric rather than an arithmetic scale. In the first section of this chapter we describe the calculation of exponential growth rates for different types of population, and explore how such calculations, even though they are based on the simplistic assumption of constant demographic rates, can be very useful for a variety of problems in applied population biology. The fact that populations persist over appreciable periods of time inescapably means that demographic rates—births and deaths, immigration and emigration—do not remain constant. In fact, population persistence in the long term requires that as populations increase in density the death rate must rise relative to the birth rate and eventually exceed it.