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7 - Specific Models
- Patsy Haccou, Rijksuniversiteit Leiden, The Netherlands, Peter Jagers, Chalmers University of Technology, Gothenberg, Vladimir A. Vatutin, Steklov Institute of Mathematics, Moscow
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- Branching Processes
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- 04 May 2010
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- 19 May 2005, pp 200-277
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Summary
Coalescent Processes: Reversed Branching
Coalescence
Branching viewed backward is coalescence, the process of merging or clumping. It arises naturally in the structuring or formation of dispersed matter of various kinds and in various scales, from that of molecule aggregates in colloids (so-called micelles) to galaxies. It has been studied by physicists through computer simulation (e.g., Nilsson et al. 2000) and in a series of interesting mathematical articles by Aldous (1999).
Evolution can be viewed as a grand multi-type branching process, with new species that arise through mutation (see Jagers 1991; Jagers et al. 1992; Taib 1992). The study of the origin of species is then time-reversed branching (i.e., coalescence). In genetics, the latter is also used to trace the roots of the genetic composition of populations and its development. It was within this area that the first pure coalescence model, the Kingman coalescent (1982a), was formulated as a reverse counterpart to the diffusion approximation of the renowned Wright–Fisher model (Fisher 1930; Wright 1931; see also Ewens 1979).
The object of genetic models is thus population composition rather than size. Indeed, most population genetics even assumes that population size is completely constant over generations. As we show later, the Wright–Fisher model can be obtained as Galton–Watson branching with Poisson reproduction, conditioned at a constant population size. In the same vein, most population genetics simplifies the flow of time into generation counting. Instead, it is lineage that counts. What are the relations among n individuals sampled …
1 - Introduction
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- By Ulf Dieckmann, Laxenburg, Johan A.J. Metz, Leiden University, Michael Doebeli, University of British, Diethard Tautz, Universität zu Köln
- Edited by Ulf Dieckmann, International Institute for Applied Systems Analysis, Austria, Michael Doebeli, University of British Columbia, Vancouver, Johan A. J. Metz, Rijksuniversiteit Leiden, The Netherlands, Diethard Tautz, Universität zu Köln
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- Adaptive Speciation
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- 05 July 2014
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- 02 September 2004, pp 1-16
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Summary
A Shift in Focus
Millions of species currently exist on earth, and to secure an understanding of how all this magnificent variety arose is no small task. Biologists have long accepted Darwinian selection as the central explanation of adaptation and evolutionary change; yet, to date, no similar agreement has emerged about evolutionary processes that can create two species out of one. Almost 150 years after Darwin's seminal work On the Origin of Species (1859), conditions for and mechanisms of biological speciation are still debated vigorously.
The traditional “standard model” of speciation rests on the assumption of geographic isolation. After a population has become subdivided by external causes – like fragmentation through environmental change or colonization of a new, disconnected habitat – and after the resultant subpopulations have remained separated for sufficiently long, genetic drift and pleiotropic effects of local adaptation are supposed to lead to partial reproductive incompatibility. When the two incipient species come into secondary contact, individuals from one species cannot mate with those of the other – even if they try – or, if mating is still possible, their hybrid off spring are inferior. Further evolution of premating isolation (like assortative mate choice or seasonal isolation) and/or postmating isolation (like gametic incompatibility) eventually ensures that the two species continue to steer separate evolutionary courses.
The trigger for speciation in this standard model is geographic isolation. It is for this reason that the distinction between allopatric speciation (occurring under geographic isolation) and sympatric speciation (without geographic isolation) has taken center stage in the speciation debate.
19 - Epilogue
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- By Ulf Dieckmann, Laxenburg, Diethard Tautz, Universität zu Köln, Michael Doebeli, University Boulevard, Johan A.J. Metz, Leiden University
- Edited by Ulf Dieckmann, International Institute for Applied Systems Analysis, Austria, Michael Doebeli, University of British Columbia, Vancouver, Johan A. J. Metz, Rijksuniversiteit Leiden, The Netherlands, Diethard Tautz, Universität zu Köln
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- Adaptive Speciation
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- 05 July 2014
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- 02 September 2004, pp 380-394
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When Terry Erwin from the Smithsonian National Museum of Natural History examined the diversity of beetles that lived on a single species of tropical trees, he found 682 different beetle species, 163 of which he classified as specialist species that lived exclusively on the particular tree species used in his study. Since there are around 50000 tropical trees species, Erwin extrapolated that there must be on the order of 7 million specialist beetle species (Erwin 1982). Using similar extrapolations, Erwin (1982) also estimated the total number of tropical arthropod species as about 30000000. While these estimates may be too high (Schilthuizen 2000; Ødegaard 2000; Novotny et al. 2002), they are mind-boggling nevertheless and serve as an illustration of the incredible amount of species diversity that exists on our planet: estimates for the total number of extant species of plants and animals range from 10 million to 100 million (May 1990; Schilthuizen 2000). It is also estimated that the number of extant species represents only about 1% of the total number of species that ever existed during the history of life on earth. Together with the common phylogenetic ancestry usually inferred for the tree of life for higher organisms, this implies that speciation must have been truly rampant during the creation and evolution of our biosphere.
4 - Adaptive Dynamics of Speciation: Ecological Underpinnings
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- By Stefan A.H. Geritz, University of Turku, Éva Kisdi, University of Turku, Géza Meszéna, Eötvös University, Johan A.J. Metz, Leiden University
- Edited by Ulf Dieckmann, International Institute for Applied Systems Analysis, Austria, Michael Doebeli, University of British Columbia, Vancouver, Johan A. J. Metz, Rijksuniversiteit Leiden, The Netherlands, Diethard Tautz, Universität zu Köln
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- Adaptive Speciation
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- 05 July 2014
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- 02 September 2004, pp 54-75
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Introduction
Speciation occurs when a population splits into ecologically differentiated and reproductively isolated lineages. In this chapter, we focus on the ecological side of nonallopatric speciation: Under what ecological conditions is speciation promoted by natural selection? What are the appropriate tools to identify speciation-prone ecological systems?
For speciation to occur, a population must have the potential to become polymorphic (i.e., it must harbor heritable variation). Moreover, this variation must be under disruptive selection that favors extreme phenotypes at the cost of intermediate ones. With disruptive selection, a genetic polymorphism can be stable only if selection is frequency dependent (Pimm 1979; see Chapter 3). Some appropriate form of frequency dependence is thus an ecological prerequisite for nonallopatric speciation.
Frequency-dependent selection is ubiquitous in nature. It occurs, among many other examples, in the context of resource competition (Christiansen and Loeschcke 1980; see Box 4.1), predator-prey systems (Marrow et al. 1992), multiple habitats (Levene 1953), stochastic environments (Kisdi and Meszéna 1993; Chesson 1994), asymmetric competition (Maynard Smith and Brown 1986), mutualistic interactions (Law and Dieckmann 1998), and behavioral conflicts (Maynard Smith and Price 1973; Hofbauer and Sigmund 1990).
The theory of adaptive dynamics is a framework devised to model the evolution of continuous traits driven by frequency-dependent selection. It can be applied to various ecological settings and is particularly suitable for incorporating ecological complexity.
4 - Spatial Dimensions of Population Viability
- Edited by Régis Ferrière, Ecole Normale Supérieure, Paris, Ulf Dieckmann, International Institute for Applied Systems Analysis, Austria, Denis Couvet, Muséum National d'Histoire Naturelle, Paris
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- Book:
- Evolutionary Conservation Biology
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- 15 August 2009
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- 10 June 2004, pp 59-80
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Introduction
In most parts of the world, habitat loss is the number one threat to endangered species. For instance, in Finland the primary cause of threat is some form of habitat loss or alteration in 73% of the red-listed species (Rassi et al. 2001). Typically, a reduced total area of habitat is accompanied by habitat fragmentation, such that the remaining habitat occurs in smaller fragments with reduced connectivity. Many landscapes for many species have become highly fragmented (the habitat fragments are small or relatively small and physically completely isolated), while other landscapes have always been highly fragmented naturally. Species that live in such landscapes necessarily have fragmented populations, which more or less closely approach the metapopulation structure originally envisioned by Levins (1969). Levins' metapopulation is a system of local populations that inhabit individual habitat patches connected, to some extent, by migration. The classic metapopulation concept assumes that local populations may go extinct, and so leave the respective habitat patch temporarily unoccupied, while the metapopulation as a whole may persist in a balance between extinctions and colonizations (Levins 1969; Hanski and Gilpin 1997; Hanski 1999). In a broader sense, any assemblage of local populations connected by migration can be called a metapopulation, regardless of the occurrence of local extinctions (Hanski and Gilpin 1997). What is important is the spatially localized interactions of individuals, which may significantly change the dynamics of the metapopulation as a whole in comparison with a single panmictic population (Hanski 1999).
1 - Introduction
- Edited by Ulf Dieckmann, International Institute for Applied Systems Analysis, Austria, Johan A. J. Metz, Universiteit Leiden, Maurice W. Sabelis, Universiteit van Amsterdam, Karl Sigmund, Universität Wien, Austria
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- Adaptive Dynamics of Infectious Diseases
- Published online:
- 15 January 2010
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- 11 April 2002, pp 1-6
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Toward the end of the 1960s, by dint of science and collective efforts, humankind had managed to eradicate smallpox and to land on the moon. Accordingly, some of the best-informed experts felt that the time had come to close the book on infectious diseases, and that the colonization of interplanetary space was about to begin. Today, these predictions seem as quaint as the notion – also quite widespread at the time – that the Age of Aquarius was about to begin.
The subsequent decades have taught us to be less sanguine about the future. In 2001 we do not send out manned spacecraft to meet with extraterrestrials, but instead are shutting down obsolete space accommodation. And far from closing the book on infectious diseases, we find that books on infectious diseases still have to be written. Few experts believe, nowadays, that we are witnessing the beginning of the end of our age-old battle against germs. In 1999, for instance, the World Health Organization (WHO) launched an ambitious program, “Roll Back Malaria” – a battle cry that seems tellingly defensive. In the 1960s, optimists still entertained hopes that malaria could be wiped out altogether. And why not? It had worked for smallpox, after all.
Aside from the disappointments with malaria and other infectious diseases – alarming outbreaks of cholera or foot-and-mouth epidemics, for instance – we had to learn to come to terms with other baffling setbacks.
27 - Taking Stock: Relating Theory to Experiment
- Edited by Ulf Dieckmann, International Institute for Applied Systems Analysis, Austria, Johan A. J. Metz, Universiteit Leiden, Maurice W. Sabelis, Universiteit van Amsterdam, Karl Sigmund, Universität Wien, Austria
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- Book:
- Adaptive Dynamics of Infectious Diseases
- Published online:
- 15 January 2010
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- 11 April 2002, pp 379-398
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Introduction
This book is concerned with the way natural selection affects the virulence of disease agents, here loosely defined as damage to the host, and with how we can use this knowledge to design strategies for managing virulence. These questions are rooted in Darwinian thinking about evolution (Poulin 1998; Stearns 1999). If it were possible to resolve these questions at the level of evolutionary storytelling only, this book would not exist. The impetus behind this book came from recent advances in mathematical evolutionary theory, in particular the ongoing merger of the theories of population dynamics and natural selection. This merger enables quantitative, and therefore testable, predictions of the outcome of selection for a given ecological setting. As so often, applied problems form an ideal testbed for the new tools.
Since disease agents have short generation times and usually harbor considerable genetic variation, natural selection can potentially cause rapid changes in the genetic make-up of pathogen or parasite populations. Therefore, the evolution of parasite virulence is an obvious area to test new evolutionary theories. Another matter is whether such tests promise immediate applications. The theory of evolutionary dynamics is not at a stage that can produce lists of management strategies to solve any particular problem with certainty; to be fair, is any theory able to? However, any measure, even the considered absence of action, is guided by some theory in whatever verbal or mathematical form.
33 - Epilogue
- Edited by Ulf Dieckmann, International Institute for Applied Systems Analysis, Austria, Johan A. J. Metz, Universiteit Leiden, Maurice W. Sabelis, Universiteit van Amsterdam, Karl Sigmund, Universität Wien, Austria
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- Adaptive Dynamics of Infectious Diseases
- Published online:
- 15 January 2010
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- 11 April 2002, pp 460-464
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Far from conquering infectious diseases through good sanitation, vaccines, and antimicrobial agents, populations of humans – as well as those of other animals and plants – continue to be harassed by an onslaught of pathogens. Complex processes of host–pathogen adaptation are responsible for the perennial persistence of this threat.
To develop sustainable control strategies, it is important to ask which new selective pressures on virulence will thus be created, and how resistance against control measures can be slowed, prevented, or even reversed. On the one hand, population growth, increased mobility, and climate change create new opportunities for diseases, while on the other hand adaptations allow disease agents to overcome the current transmission barriers.
Can epidemiological changes be steered in the desired directions and can they be prevented from veering off course in detrimental ways? That is what this book is about. Its aims are
To show how evolutionary epidemiology as a science can profit from modeling techniques that take both population dynamics and natural selection into account;
To explore the design of strategies for virulence management based on models of the evolutionary dynamics of pathogen–host systems;
To highlight important unresolved research questions that need to be addressed before evolutionary predictions and management options are to be trusted; and
To foster the dialogue between theorists and empiricists in the field of evolutionary epidemiology.
What are the general predictions regarding the evolution of virulence traits, as they have emerged throughout this book?
24 - Epilogue
- Edited by Ulf Dieckmann, International Institute for Applied Systems Analysis, Austria, Richard Law, University of York, Johan A. J. Metz, Rijksuniversiteit Leiden, The Netherlands
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- Book:
- The Geometry of Ecological Interactions
- Published online:
- 14 January 2010
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- 04 May 2000, pp 513-516
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We would like to close this volume with a look at the future of mechanistic modeling in spatial ecology. We hope that at least some of the optimistic views sketched below come true. No doubt others, hopefully fewer, will turn out to be mirages.
Just as theory is at its best when it is demonstrably applicable to real ecological systems, field research is most important when it addresses questions that clearly transcend a particular study system. Few researchers, however, have sufficient command of both theory and experiment to actively participate at the two research fronts. It is therefore essential to extend chains of collaboration between empiricists and theorists. These chains should not become too long lest they break or the message passed along becomes too garbled. If such collaborative chains are to work effectively, each partner must have a good understanding of the others' vocabulary, basic concepts, and techniques.
One of this book's objectives is to foster dialogue between those researchers with empirical competence and those with theoretical skills in the field of spatial ecology. In practice, there is still an appreciable distance between the detailed investigations of plant interactions reported in Part A of this volume and the mathematical methods advanced in Part D. However, ecological theory is making great strides toward integrating more ecological realism into manageable models. Theorists and empiricists alike are searching for new kinds of models that are better able to account for the complex implications of spatial heterogeneity.
23 - The Dynamics of Invasion Waves
- Edited by Ulf Dieckmann, International Institute for Applied Systems Analysis, Austria, Richard Law, University of York, Johan A. J. Metz, Rijksuniversiteit Leiden, The Netherlands
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- Book:
- The Geometry of Ecological Interactions
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- 14 January 2010
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- 04 May 2000, pp 482-512
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Introduction
In this chapter we concentrate on certain macroscopic patterns in the transient behavior of spatially extended ecological systems. Chapters 17 and 22 on reaction–diffusion equations also deal with the macroscopic perspective, but from a different angle. Those chapters forego realistic movement and life-history detail in order to concentrate on interactions between individuals. In this chapter, we restrict ourselves to phenomena that are, in general, only weakly dependent on those interactions to arrive at robust and simple quantitative population-level predictions based on measurements of behavioral characteristics of individuals. Luckily, as Chapter 16 makes clear, such phenomena are not confined to the realm of mathematics, but commonly occur in real ecological systems as well.
Transient behavior is usually viewed as an effect of a temporary external perturbation of an otherwise stationary situation. From a biological perspective there are two principal types of perturbations. The first type are abiotic perturbations, such as an unusually severe drought; these usually affect large regions, leaving the spatial distributions of species macroscopically homogeneous. The other type of perturbation is the introduction of a new species or the occurrence of an advantageous mutation in an already established species. Such perturbations originate locally and from the initial inoculum spread over space in a wavelike manner. It is the second type of transient behavior that we consider here.
An invasion generally starts with the arrival of a small number of individuals of a new species or a mutation in a single individual. Thus the initial phase of an invasion is dominated by demographic stochasticity.
1 - Introduction
- Edited by Ulf Dieckmann, International Institute for Applied Systems Analysis, Austria, Richard Law, University of York, Johan A. J. Metz, Rijksuniversiteit Leiden, The Netherlands
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- Book:
- The Geometry of Ecological Interactions
- Published online:
- 14 January 2010
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- 04 May 2000, pp 1-6
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Species form different kinds of patches; these patches form a mosaic and together constitute the community. Recognition of the patch is fundamental to an understanding of structure. Patches are dynamically related to each other. But there are also departures from this inherent tendency to orderliness. At any given time, therefore, structure is the resultant of causes which make for order, and those that tend to upset it. Both sets of causes must be appreciated.
Abbreviated from Watt (1947, p. 2) Pattern and process in the plant communityA sea change has come over theoretical ecology in the past 10 years. The era of the simple general model that tries to capture the elusive essence of an ecological community is rapidly fading from sight. This is the age of the individual-based, spatially explicit, computer-based model (Huston et al 1988; DeAngelis and Gross 1992; Judson 1994).
Why has this transformation taken place? First there is the simple matter of practicality: desktop computing power has reached a level at which it is quite feasible to simulate individuals as they move across a landscape, interact, reproduce, and die. Second is the issue of language: for many ecologists, rules encoded in computer algorithms are much more accessible than the formal mathematical language of dynamical systems. Third is the appreciation that important ecological intricacies, such as the mechanisms by which organisms interact in communities, often cannot be incorporated sufficiently faithfully into simple models. Fourth is an awareness that the simple models traditionally used in ecology have not always proved very successful in accounting for phenomena observed in natural systems.