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This chapter describes techniques for modeling forest dynamics. Topics covered include the equation of population flux, life tables, transition matrix models, population viability analysis, growth and yield models, and ecological models.

Orangutan populations are particularly susceptible to local extinction due to hunting, habitat loss, and fragmentation because they live at low population densities, grow slowly, and reproduce rarely. This chapter uses Population Viability Analysis (PVA) to consider the conservation implications of orangutan life history and population biology. First, a baseline model that incorporates the best available orangutan life-history data is presented. This model is then used to examine how plausible variation in model parameters, changes in the intensity of human-induced threats, and different conservation and management interventions would affect the probability of orangutan population persistence. The effects of existing threats on the extinction risk of specific orangutan populations on Borneo and Sumatra are also modelled. Finally, the conservation and management implications of this modeling exercise are considered.

In this chapter, Corey J. A. Bradshaw and Barry W. Brook, discuss measures of biodiversity patterns followed by an overview of experimental design and associated statistical paradigms. Conservation biology is a highly multidisciplinary science employing methods from ecology, Earth systems science, genetics, physiology, veterinary science, medicine, mathematics, climatology, anthropology, psychology, sociology, environmental policy, geography, political science, and resource management. Here we focus primarily on ecological methods and experimental design. It is impossible to census all species in an ecosystem, so many different measures exist to compare biodiversity: these include indices such as species richness, Simpson's diversity, Shannon's index and Brouillin's index. Many variants of these indices exist. The scale of biodiversity patterns is important to consider for biodiversity comparisons: α (local), β (between‐site), and γ (regional or continental) diversity. Often surrogate species ‐ the number, distribution or pattern of species in a particular taxon in a particular area thought to indicate a much wider array of taxa ‐ are required to simplify biodiversity assessments. Many similarity, dissimilarity, clustering, and multivariate techniques are available to compare biodiversity indices among sites. Conservation biology rarely uses completely manipulative experimental designs (although there are exceptions), with mensurative (based on existing environmental gradients) and observational studies dominating. Two main statistical paradigms exist for comparing biodiversity: null hypothesis testing and multiple working hypotheses – the latter paradigm is more consistent with the constraints typical of conservation data and so should be invoked when possible. Bayesian inferential methods generally provide more certainty when prior data exist. Large sample sizes, appropriate replication and randomization are cornerstone concepts in all conservation experiments. Simple relative abundance time series (sequential counts of individuals) can be used to infer more complex ecological mechanisms that permit the estimation of extinction risk, population trends, and intrinsic feedbacks. The risk of a species going extinct or becoming invasive can be predicted using cross‐taxonomic comparisons of life history traits. Population viability analyses are essential tools to estimate extinction risk over defined periods and under particular management interventions. Many methods exist to implement these, including count‐based, demographic, metapopulation, and genetic. Many tools exist to examine how genetics affects extinction risk, of which perhaps the measurement of inbreeding depression, gene flow among populations, and the loss of genetic diversity with habitat degradation are the most important.

The distribution and dynamics of populations reflect the interplay between dispersal and demography with landscape structure. Understanding how landscape structure affects populations is essential to effective habitat management and species conservation, especially within landscapes undergoing habitat loss and fragmentation as a result of human land-use activities. This chapter thus begins with an overview of the effects of habitat loss and fragmentation on populations, followed by a discussion of species distribution modeling. Then, because population assessment figures so prominently in evaluating a species’ extinction risk to landscape change, the chapter considers the different classes of population models used to estimate population growth rates and population viability, including the use of metapopulation and spatially explicit simulation models.

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.

This chapter describes how models can aid in managing populations to prevent extinction, given uncertainty about their state. From previous chapters, it is clear that avoiding extinction requires keeping both abundance and the replacement rate high. However, for both, the question remains, how high? The question of how high abundance should be to achieve a certain risk is addressed by existing population viability analyses (PVA). By contrast, the problem of maintaining high replacement has received little attention. This chapter describes how uncertainty in population parameters and the frequency spectrum of the environment both affect estimates of the probability of extinction, including examples of PVAs that pay greater attention to those complications. Additionally, an example is provided of tracking both abundance and replacement to avoid extinction for many different populations of a single taxon, Pacific salmon. Finally, the role of portfolio effects (diversity in variance among populations) is explored.

Most ecological populations exist in a randomly fluctuating environment, and these fluctuations influence vital rates, thus changing population dynamics. These changes are the focus of this chapter. The primary practical concern about environmental variability is the possibility that it could cause a population to go extinct, so the chapter describes several approaches to estimating the probability of extinction. The first is the small fluctuations approximation (SFA) to describe the growth of a population with a randomly varying Leslie matrix. The results reveal that randomly varying populations grow more slowly on average than the equivalent deterministic population. Further applications of the SFA examine how correlated variation in different vital rates affects the probability of extinction, when variability is too large to use the SFA, and how it has been applied to population time series. Finally, several other approaches to estimating extinction risk—also known as population viability analysis—are compared.