V

Where subscripts i and j refer to species i and j, ri is the intrinsic rate of increase of species i, K is its carrying capacity (the equilibrium number of individuals for the species in the absence of interspecific competition), aj is the competition coefficient specifying how many individuals of species i are displaced by the presence of each individual of species j, and n is the number of competing species. In this model, an increase or decrease in the abundance of one species causes...

Resource competition

All plants require the same suite of essential resources to survive and reproduce, including water, light, and biologically available forms of nitrogen, phosphorus, carbon, potassium, calcium, magnesium, sulphur, and about 15 additional elements. Resource-addition field experiments have shown that between one and four of these resources may limit growth in a given habitat. At higher trophic levels, each plant may function as several relatively independent resources for herbivores (leaves,...

Other SRA distributions

Sugihara (1980) has also suggested a biological mechanism that will, among other things, produce the observed SRA patterns. The multidimensional 'niche space' of the community is imagined as being like a hypervolume, which is sequentially broken up by the component species, such that each of the S fragments denotes the relative abundance of a species. This sequential broken stick model is biologically and mathematically very different from MacArthur's broken stick model in which a stick is...

Modelling density dependence in annual plants

Ricker Curve

The simplest way of combining the three density-dependent processes that affect annual plant populations is to construct a Ricker curve N(t +1) N(t) f(N(t)) (see Chapter 3 in this volume). This shows next year's population N(t +1) (on the y axis) as a function of this year's population N(t) (on the x axis). A straight line through the origin at a slope of 45 is called the replacement line (where next year's population is equal to this year's population). Because the population must pass the...

Info

Which can be written more succinctly n(t +1) A n(t). Note that the numbers in the youngest age class are given by the numbers in each age class the season before multiplied by their fecundity, while the probabilities of surviving until the new season form the lower subdiagonal. The matrix A is an example of a population-projection matrix, and this particular form, where the population is structured by age, is called a Leslie matrix (Leslie, 1945). The simplest way to explore the growth rate of...

History of stability

To present an abbreviated history of the changing definitions of stability, I will discuss theoretical and empirical studies side by side. The empirical 1 Throughout this chapter, I use diversity in a broad sense, capturing many of the properties that have been used in the literature to characterize community complexity. Thus, I am using diversity and complexity synonymously. studies generally represent case studies in which stability is assessed in a way that is most meaningful and or...

Population dynamics of diatoms with a single limiting resource

Populations of single-celled algae are amenable to controlled experimentation, and the processes that drive their population dynamics are analytically tractable. Because they have such short generation times (days to weeks) it is appropriate to frame our models as differential equations in continuous time. In the single-species case, there are N individual plankton per unit volume of water, and we model their dynamics by considering the rates of gain and loss of individuals. The change in...

Systematic reserve design

The problem of selecting sites within regions addresses the central issue of efficiency in conservation planning select the set of sites that protects the greatest number of conservation elements (e.g. species, habitat types) for the lowest cost. Early approaches tackled this problem with stepwise algorithms (Kirkpatrick, 1983 Margules et al., 1988). Later workers framed the question as an optimization problem (Cocks and Baird, 1989 Camm et al., 1996). In its simplest form, the problem is one...

Building a reserve network

Faced with limited resources, numerous species in need of assistance, and ongoing habitat loss, several methodologies have been developed to help determine global conservation priorities. Given that not all conservation organizations have precisely the same mission and objectives, it comes as no surprise that strategies for global prioritization differ (Redford et al., 2003). Conservation International, for example, focuses on both hotspots regions that harbor large numbers of endemic species...

Herbivores and plant population dynamics

Every aspect of plant performance can be influenced by herbivorous animals and plant pathogens (germination, growth, seedling survival, flowering, seed-set, and seed mortality both pre- and post-dispersal Crawley, 1983,1997, 2000). This does not mean, however, that herbivore feeding has any impact on plant population dynamics under field conditions. For instance, plants may be able to compensate for herbivore feeding, there may be density dependence in mortality or fecundity, recruitment may...

Seasonal forcing and sustained epidemic oscillations

The above question parallels a long-standing population-dynamic debate about the cause of sustained host-natural enemy cycles of small mammals, game birds, and forest insects (Bjornstad and Grenfell, 2001). The key issue in ecology is generally to explain the rarity of such cycles in practice compared with basic theory here, the issue is reversed how do we explain the violent cycles of measles and other childhood diseases, given the long-term stability of very plausible simple models As with...

T3

100 -, 90 -80 -70 -60 -50 -40 -30 -20 -10 0 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 Figure 12.7 The global area of genetically modified crops, 1996-2005 James, 2005 . The potentials for genetic engineering are almost endless. But alongside the benefits are risks some real, some imagined. An impassioned debate in Europe is raising genuine concerns about ethics, environment, and the potential impact on human health Royal Society, 1998 Nuffield Council on Bioethics, 2003 . The developed...

Chapter

How populations cohere five rules for cooperation Subsequent chapters in this volume deal with populations as dynamic entities in time and space. Populations are, of course, made up of individuals, and the parameters which characterize aggregate behavior population growth rate and so on ultimately derive from the behavioral ecology and life-history strategies of these constituent individuals. In evolutionary terms, the properties of populations can only be understood in terms of individuals,...