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This chapter summarizes the methods available for estimating the population parameters that may be needed to assess biological sustainability, including population abundance, population and individual growth rates, rates of survival and productivity, and patterns of movement and distribution in space. The emphasis is on the need to sample populations effectively, and on understanding the strengths and weaknesses of a wide range of available survey methods. This provides a basis for selecting the most appropriate methods in a given situation, and for assessing how much effort will be required to get useable data. Extensive links are provided to detailed information on analytical methods, including software and online resources.

Once an exotic species has successfully established a self-sustaining population, it may spread beyond its initial point of introduction and establish meaningful interactions with species native to this location. This chapter reviews the relatively large literature on models of geographic range expansion (spread) in invasive species. In particular, it notes the tremendous bias towards a few, very successful and widespread exotic bird species, on our understanding of exotic species range expansion. For the same reasons that exotic birds have already contributed to understanding invasions (i.e., there is detailed information on their numbers and locations), it is argued that with the right research effort they can also help us gain a clear picture of why some exotic species do not expand their ranges once established, or only do so after a long lag period.

This chapter considers the influence of species-level traits in the establishment success of exotic birds. Previous treatments of such traits have failed to find consistent associations between species traits and establishment success. However, framing the issue in terms of the small population problem again provides useful insights into the role of species-level traits, and allows some general conclusions to be drawn about the roles of population growth rates, the predisposition to Allee effects, and the ability to cope with novelty in aiding establishment. This approach to sorting through the influence of species' traits on establishment success should provide a suitable framework for similar explorations within other exotic taxa. The more widespread confusion over the importance of species' traits to establishment success may be a by-product of failing to view the influence of these traits within the context of the small population paradigm.

The number of reproductive units is expected to grow exponentially in the absence of regulating feedbacks. The lack of feedbacks is a definitive assumption of any model predicting exponential growth, be it individual- or population-based, discrete or continuous, deterministic or stochastic. The exponential growth of a population can be characterised by its long-term per capita rate of increase (population growth rate, pgr) in any actual representation. Exponential growth with a constant pgr will occur whenever the stochastic changes in the environmental conditions—including modifying and regulating ones—affecting births and deaths are stationary in the long run. Case studies indicate that temporary periods of exponential population increase or decline must be regular in nature, and pgrs may show remarkable temporal and spatial invariance.

This chapter contains a discussion of the ecological and the genetic causes of variation in population growth rate in the flour beetle, Tribolium, especially as they are affected by variation in founder number and competition with other species. By relaxing group selection for three years, the author and his colleagues discovered correlated responses of population traits to group selection. These included outbreaks, density cycles, demographic variations, changes in competitive ability and a tendency toward local extinctions.

Descriptions and consequences of the environmental dependence of long-term population growth rates, i.e., of fitness, are in the focus of this chapter. The ecological tolerances of species (or other reproductive units) are represented by multivariate response functions. These describe the dependence of the long-term growth rate of unregulated populations on the regulating and modifying environmental variables affecting them. Some particular environmental variables, like climatic ones, are routinely used in ecology and population genetics for predicting the geographic distribution of species or ecotypes, while crucial regulating variables are often overlooked. In a reversed logic, response functions can be deduced from the actual geographic distributions of the reproductive units, but this area of research is heavily burdened by several practical problems. Comparative studies of adaptations represent another approach to determining tolerance functions through studying the joint effects of environmental and genetic variation on fitness.

This chapter focuses on the role that changes in mortality rates play in determining population growth rates in a variety of small rodent species, and discusses the four components of mortality in small mammals: prenatal mortality, nestling mortality, juvenile mortality, and adult mortality.

This chapter provides a comparative population dynamics of rodents and other mammals. Its main objective is to identify the factors that affect population growth rates, and it begins by discussing the evolution of intrinsic processes which regulate population. The chapter then examines the population control of large herbivorous mammals, in which human hunting or poaching is the main cause of population change. A multiple-factor explanation for population changes in small herbivorous mammals is also discussed.

The attempt to work out population estimates of the Mughal empire and, then, of India is based on two separate sets of assumptions. In the first set it is assumed that (a) the total area of cultivation in 1601 was 50 to 55 per cent of what it was in 1901, (b) the ratio of urban to rural population was 15:85, and (c) the average agricultural holding was 10 per cent larger in 1601 than in 1901. Whence population range for India, 1601: 136–50 million. The second set of assumptions is the following: (a) yield per unit of area was the same in 1601 and 1891, (b) area of land cultivated per capita also remained the same, and (c) crop-distribution also remained largely the same. These assumptions yield a population of 149.07 million for India in 1601. Putting the two estimates side by side, the chapter considers 145 million a reliable estimate of population for 1601, yielding a rate of growth of 0.21 per cent over the period 1601–1801.

Methods for constructing a life-table and budget for a species are described, and the various methods for the analysis of stage-frequency data reviewed. Stage-frequency data comprise counts of the individuals in different development stages in samples taken from a population over a period of time. The analysis of stage-frequency data to estimate the durations of the stages, the numbers entering stages, and survival rates is described. Examples of survivorship curves are presented, and the calculation of population growth rate described. Analysis of life-table data and demographic methods, including key-factor analysis, are described.

This chapter reviews the basic principles of predation, addresses whether predation is both necessary and sufficient to determine population growth rates in small rodents, and analyzes some empirical studies of predation in small rodents. These include a study on predator impact on the high brown lemming population in Barrow, Alaska; experimental predator reduction experiments in western Finland; and a weasel removal experiment in Scotland.