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Fragile Dominion: Complexity and the Commons
By Simon A. Levin
This book explores the mechanisms sustaining biodiversity, the importance of biodiversity, and lessons from complexity theory for its management.
Published by Perseus Books, Reading, MA. 1999. |
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2005
Durrett, R. and S. A. Levin. 2005. Can stable social groups be maintained by homophilous imitation alone? Journal of Economic Behavior and Organization 57(3): 267-286.
A central problem in the biological and social sciences concerns the conditions required for emergence and maintenance of cooperation among unrelated individuals. Most models and experiments have been pursued in a game-theoretic context and involve reward or punishment. Here we show that such payoffs are unnecessary, and that stable social groups can sometimes be maintained provided simply that agents are more likely to imitate others who are like them (homophily). In contrast to other studies, to sustain multiple types we need not impose the restriction that agents also choose to make their opinions different from those in other groups. |
Couzin, I.D., J. Krause, N. R. Franks, and S. A. Levin. 2005. Effective leadership and decision-making in animal groups on the move. Nature 433: 513-516.
For animals that forage or move in groups, decision-making processes depend on social interactions among group members1,2. However, often relatively few individuals have pertinent information, such as knowledge about the location of a food source3,4, or of a migration route5-9. Using a simple model we show how information can be transmitted within groups in the absence of signalling mechanisms and when it is not possible for group members to establish who has and who has not got information. We reveal that the larger the group the smaller the proportion of informed individuals needed to guide the group and that only a very small proportion of informed individuals is required to achieve close to
maximal accuracy. Furthermore, our model provides new insights into the mechanisms of effective leadership in biological systems. We specify the optimal leadership strategy as a group-size dependent compromise between the tendency of
informed individuals to take the decisions of other group members into account and their own preferred direction of movement. |
Livnat, A., S. W. Pacala and S. A. Levin. 2005. The evolution of intergenerational discounting in offspring quality. The American Naturalist 165(3): 311-321.
Intergenerational effects occur when an individual's actions affect not only its own survivorship and reproduction but also those of its offspring and possibly later descendants. In the presence of intergenerational effects, short-term and long-term measures of success (such as the expected numbers of surviving offspring and of farther descendants, respectively) may be in conflict. When such conflicts occur, life-history theory normally takes long-term measures to predict the outcome of selection. This ignores the fact that, because traits change in timethrough mutation, sex, and recombinationlong-term relations disintegrate. We study this issue with numerical simulations and analytical models combining intergenerational effects and evolutionary change. In the models, the parental investment per offspring, as well as the total reproductive effort, stand for investments in future generations. The models show that the rate of evolutionary change determines the level of those investments. Higher rates of mutation and of sexual as opposed to parthenogenetic reproduction favor lower parental investment per offspring and lower total reproductive effort. It follows that the level of investment of ancestors in descendants responds to the genetic relatedness between the generations of the lineage, in a manner unaccounted for by preexisting theory. |
Smith, D. L., S. A. Levin and R. Laxminarayan. 2005. Strategic interactions in multi-institutional epidemics of antibiotic resistance. Proceedings of the National Academy of Sciences, USA 102(8): 3153-58.
The increasing frequency of antibiotic resistance in hospital-acquired infections is a major public health concern that has both biological and economic causes. Here we develop conceptual mathematical models that couple the economic incentives and population biology of hospital infection control (HIC). We show that the optimal investment by a hospital for HIC changes with the proportion of patients already colonized with antibiotic-resistant bacteria (ARB) at the time of admission. As that proportion increases, the optimal behavior of a hospital is to increase spending to control ARB with low transmissibility and decrease spending on those with high transmissibility. In some cases, the global optimum investment in HIC can shift discontinuously from one that contains transmission to a do-nothing policy once the proportion already colonized at the time of admission becomes too great. We also show that investments in HIC are determined by a strategic game when several hospitals share patients. Hospitals acting selfishly and rationally will free-ride on the investments of other hospitals, and the level of free-riding should increase with the number of other hospitals in the area. Thus, in areas with many hospitals, the rational strategy for each hospital is to spend less than in areas with few hospitals. Thus, we predict that transmission rates and the prevalence of ARB should be higher in urban hospitals, for instance, compared with rural hospitals. We conclude that regional coordination and planning for HIC is an essential element of public health planning for hospital-acquired infections. |
Webb, C. T. and S. A. Levin. 2005. Cross-system perspectives on the ecology and evolution of resilience. Pp. 151-172. In: (E. Jen, ed.), Robust Design: A Repertoire of Biological, Ecological, and Engineering Case Studies, SFI Lecture Note Series. Oxford University Press.
The notion of resilience or robustness for ecological systems applies most naturally to the ability of the system to maintain its macroscopic features, such as species diversity or nutrient cycling, rather than to a narrower and unattainable possibility of constancy. Indeed, it is the lack of constancy at lower levels of organization that conveys robustness on ecosystems in the large. The robustness of ecosystem processes, such as nutrient cycling, can be compared across different types of ecosystems; similarly, structure in ecosystems, which may be important for resilience, can be defined by the strength of interactions among species, allowing examination of structure-function relationships and their evolution. The resilience of the whole ecosystem may fundamentally lie at the level of species themselves, within modules of closely interacting species, or as an emergent property of the whole, complex ecosystem. Evidence from diverse ecosystems suggests that biodiversity is correlated with emergent ecosystem resilience. This may be because biodiversity itself, through functional redundancy, causes resilience, but there are also other causal mechanisms such as disturbance experience and historical constraint that can promote resilience and produce biodiversity as a by-product. Resilience can be emergent in another sense as well when local disturbance history selects for traits that are also important for surviving larger scale or novel perturbations. Because of differences in diversity and prior selection by tree fall, we use comparisons of the response of tropical and temperate forests to disturbance by hurricanes as an example. We discuss the role of biodiversity vs. alternative mechanisms in resilience and the importance of prior natural selection. |
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2004
Feng, Z, D.L. Smith, E. McKenzie and S. Levin. 2004. Coupling the population dynamics of malaria and population genetics of sickle-cell genetics across time scales. Mathematical Biosciences 189: 1-19
Malaria has long been a scourge to humans. The exceptionally high mortality in some regions has led to strong selection for resistance, even at the cost of increased risk of potentially fatal red blood cell deformities in some offspring. In particular, genes that confer resistance to malaria when they appear in heterozygous individuals are known to lead to sickle-cell anemia, or other blood diseases, when they appear in homozygous form. Thus, there is balancing selection against the evolution of resistance, with the strength of that selection dependent upon malaria prevalence. Over longer time scales, the increased frequency of resistance in a population might be expected to decrease the frequency of malaria and reduce selection for resistance. However, possession of the sickle-cell gene leads to longer-lasting parasitaemia in heterozygote individuals, and therefore the presence of resistance may actually increase infection prevalence.
In this paper, we explore the interplay among these processes, operating over very different time scales. In particular, we show that on the fast time scale of malarial dynamics, the disease level reaches an equilibrium; on the slower, evolutionary time scale, this equilibrium tracks gene frequency. We analyze the slow time scale dynamics to investigate the impact of malaria on the evolution of resistance. |
Heal, G., B. Walker, S. Levin , K. Arrow, P. Dasgupta, G. Daily, P. Ehrlich, K.-G. Maler, N. Kautsky, J. Lubchenco, S. Schneider, D. Starrett. 2004. Genetic diversity and interdependent crop choices in agriculture. Resource and Energy Economics 26(2): 175-184.
The extent of genetic diversity in food crops is important as it affects the risk of attack by pathogens. A drop in diversity increases this risk. Farmers may not take this into account when making crop choices, leading to what from a social perspective is an inadequate level of diversity. |
Klausmeier, C. A., E. Litchman, and S. A. Levin. 2004. Phytoplankton growth and stoichiometry under multiple nutrient limitation. Limnology and Oceanography 49: 1463-1470 .
Phytoplankton growth and stoichiometry depend on the availability of multiple nutrients. Here we use a mathematical model of phytoplankton with flexible stoichiometry to explain patterns of phytoplankton composition in chemostat experiments and nutrient drawdown dynamics in the field. Exponential growth and equilibrium represent two distinct phases, each amenable to mathematical analysis. In a chemostat at a fixed dilution (growth) rate, phytoplankton stoichiometry matches the nutrient supply stoichiometry over a wide range at low growth rates and over a narrow range at high growth rates. In a chemostat with a fixed nutrient supply stoichiometry, phytoplankton stoichiometry varies with dilution rate nonlinearly, between the supply stoichiometry at low dilution rates and a species-specific optimal ratio at high dilution rates. The flexible-stoichiometry model predicts low equilibrium concentrations of both nutrients over a wide range of supply ratios, contrary to the predictions of a traditional fixed-stoichiometry model. The model is in quantitative agreement with experimental data, except at extreme nutrient supply ratios, which require a negative feedback from quota to uptake to fit the data. Our analysis points to the importance of understanding the regulation of uptakerates in determining phytoplankton stoichiometry. |
Klausmeier, C. A., E. Litchman, T. Daufresne, and S. A. Levin. 2004. Optimal nitrogen-to-phosphorus stoichiometry of phytoplankton. Nature 429: 171-174.
Redfield noted the similarity between the average nitrogen-tophosphorus ratio in plankton (N:P 5 16 by atoms) and in deep oceanic waters (N:P 5 15; refs 1, 2). He argued that this was neither a coincidence, nor the result of the plankton adapting to the oceanic stoichiometry, but rather that phytoplankton adjust the N:P stoichiometry of the ocean to meet their requirements through nitrogen fixation, an idea supported by recent modelling studies3,4. But what determines the N:P requirements of phytoplankton? Here we use a stoichiometrically explicit model of phytoplankton physiology and resource competition to derive from first principles the optimal phytoplankton stoichiometry under diverse ecological scenarios. Competitive equilibrium favours greater allocation to P-poor resource-acquisition machinery and therefore a higher N:P ratio; exponential growth favours greater allocation to P-rich assembly machinery and therefore a lower N:P ratio. P-limited environments favour slightly less allocation to assembly than N-limited or lightlimited environments. The model predicts that optimal N:P ratios will vary from 8.2 to 45.0, depending on the ecological conditions. Our results show that the canonical Redfield N:P ratio of 16 is not a universal biochemical optimum, but instead represents an average of species-specific N:P ratios. |
Nakamaru, M. and S. A. Levin. 2004. Spread of two linked social norms on complex interaction networks. J. Theoretical Biology 230: 57-64.
In this paper, we study the spread of social norms, such as rules and customs that are components of human cultures. We consider the spread of two social norms, which are linked through individual behaviors. Spreading social norms depend not only on the social network structure, but also on the learning system. We consider four social network structures: (1) complete mixing, in which each individual interacts with the others at random, (2) lattice, in which each individual interacts with its neighbors with some probability and with the others at random (3) power-law network, in which a few influential people have more social contacts than the others, and (4) random graph network, in which the number of contacts follows a Poisson distribution. Using the lattice model, we also investigate the effect of the small-world phenomenon on the dynamics of social norms. In our models, each individual learns a social norm by trial and error (individual learning) and also imitates the other's social norm (social learning). We investigate how social network structure and learning systems affect the spread of two linked social norms.
Our main results are: (1) Social learning does not lead to coexistence of social norms. Individual learning produces coexistence, and the dynamics of coexistence depend on which social norms are learned individually. (2) Social norms spread fastest in the power-law network model, followed by the random graph model, the complete mixing model, the two-dimensional lattice model and the one-dimensional lattice. (3) We see a "small world effect" in the one-dimensional model, but not in two dimensions. |
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2003
Levin, S.A. 2003. Complex adaptive systems: Exploring the known, the unknown and the unknowable. Bulletin of the American Mathematical 40: 3-19.
The notion of complex adaptive systems has found expression in everything from cells to societies, in general with reference to the self-organization of complex entities, across scales of space, time and organizational complexity. Much of our understanding of complex adaptive systems comes from observations of Nature, or from simulations, and a daunting challenge is to summarize these observations mathematically. In essence, we need a statistical mechanics of heterogeneous populations, in which new types are continuously appearing through a variety of mechanisms, mostly unpredictable in their details.
Complexity comes in a variety of forms, and not all complex, self-organizing systems are adaptive systems in the sense that I will use the term in this paper. Soap bubbles, or the frost-heaving patterns in tundra soils, may arise from self-organization without benefit of any selection or design. Indeed, local variational principles may capture the essential features of such pattern formation mathematically, for example through the minimal surfaces equation, implying some sort of constrained optimization. However, the process by which this optimization takes place is quite different from what happens in biological evolution, in which multiple reproductive lines compete based on realized fitnesses.
In general, I will define complex adaptive systems by three properties (Levin 1999); (1) diversity and individuality of components (2) localized interactions among those component and (3) an autonomous process that uses the outcomes of those interactions to select a subset of those components for replication or enhancement. This is a fairly general and flexible definition, which allows the notion of "local" to be modified as the situation demands. In most cases, the notion of localization of interactions will involve a range of scales.
The prototypical model of a complex adaptive system is the evolving biosphere; hence, this will form the core of my discussion for the rest of this paper. However, all of the essential principles carry over to other complex adaptive systems, and I will point out appropriate parallels along the way.
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Kareiva, P. and S.A. Levin, eds. 2003. The Importance of Species: Perspectives on Expendability and Triage. Princeton University Press. Pp. 427. |
Levin, S.A., H.C. Muller-Landau, R. Nathan, J. Chave. 2003. The ecology and evolution of seed dispersal: a theoretical perspective. Annual Review of Ecology, Evolution, and Systematics 34: 575-604.
Models of seed dispersal—a key process in plant spatial dynamics—have played a fundamental role in representing dispersal patterns, investigating dispersal processes, elucidating the consequences of dispersal for populations and communities, and explaining dispersal evolution. Mechanistic models of seed dispersal have explained seed dispersion patterns expected under different conditions, and illuminated the circumstances that lead to long-distance dispersal in particular. Phenomenological models have allowed us to describe dispersal pattern, and can be incorporated into models of the implications of dispersal. Perhaps most notably, population and community models have shown that not only mean dispersal distances but also the entire distribution of dispersal distances are critical to range expansion rates, recruitment patterns, genetic structure, metapopulation dynamics, and ultimately community diversity at different scales. Here, we review these developments, and provide suggestions for further research. |
Levin, S. A. and S. W. Pacala. 2003. Ecosystem dynamics. Pp: 61-95. In: (K.-G. Mäler and J. R. Vincent, eds) Handbook of Environmental Economics, Volume 1. Elsevier Science B.V., North Holland, Amsterdam.
Ecological communities—the biotic essence of ecosystems—are comprised of many species, which are in turn made up of large numbers of individuals, each with their own separate ecological and evolutionary agendas. The dynamics of ecosystems emerge from the collective dynamics of huge numbers of individual parts, and in turn feed back to influence those parts. To understand how to preserve the services that ecosystems provide it is essential to understand how communities are organized, and which are the most relevant ways to measure biodiversity. Not all species were created equal as regards their role in maintaining functioning of ecosystems, or their resiliency in the face of stress. Thus it is essential to develop ways to relate processes at the level of individual organisms to the populations of which they are members, and to the communities and ecosystems in which they reside. We must learn to scale from the small to the large, from the individual to the collective to the community, from the leaf to the plant to the biosphere. We need, in effect, to build a statistical mechanics of ecological communities, founded upon a combination of observation, controlled experimentation and simulation, and mathematical theory.
The problems we face will be familiar to economists, who well recognize the need to integrate micro- and macro- perspectives, and to relate the dynamics of societies to the way individuals make decisions. They will also recognize the context dependence of decision-making, and that in consequence the dynamics of systems are highly nonlinear, hence constrained by the accidents of history. It is these issues, and how to deal with them, that will form the core of this paper. |
Lin, J., V. Andreasen, R. Casagrandi and S.A. Levin. 2003. Traveling waves solutions in a model of influenza A drift. J. Theoretical Biology 222: 437-445.
Between major pandemics, the influenza A virus changes its antigenic properties by accumulating point mutations (drift) mainly in the RNA genes that code for the surface proteins hemagglutinin (HA) and neuraminidase (NA). The successful strain (variant) that will cause the next epidemic is selected from a reduced number of progenies that possess relatively high transmissibility and the ability to escape from the immune surveillance of the host. In this paper, we analyse a one-dimensional model of influenza A drift (Z. Angew.Math.Mech.76 (2)(1996)421) that generalizes the classical SIR model by including mutation as a diffusion process in a phenotype space of variants. The model exhibits traveling wave solutions with an asymptotic wave speed that matches well those obtained from numerical simulations. As exact solutions for these waves are not available, asymptotic estimates for the amplitudes of infected and recovered classes are provided through an exponential approximation based on the smallness of the diffusion constant. Through this approximation, we find simple scaling properties to several parameters of relevance to the epidemiology of the disease. |
Muller-Landau, H. C., S. A. Levin and J. E. Keymer. 2003. Theoretical perspectives on the evolution of long-distance dispersal and the example of specialized pests. Ecology 84: 1957-67.
Long-distance dispersal (LDD)—dispersal beyond the bounds of the local patch or cluster of conspecifics—will be most advantageous in landscapes in which large areas of suitable habitat are consistently available at long distances from established populations. We review conditions under which LDD will be selected, and conclude that biotic interactions and in particular specialized natural enemies are likely to be one of the most important factors selecting for LDD in many species. We use simple spatially implicit and spatially explicit models to illustrate how such pests affect the evolutionarily stable strategy (ESS) for in-vestment in LDD. Patches currently occupied by parents are more likely to be infected than distant, potentially unoccupied, patches, thus advantaging dispersal. Patchy infestations also result in higher variance in reproductive success among patches, which alone selects for increased among-patch dispersal. Both these effects increase with the strength of the impact of infestation, and with the number of species competing for space in the community. We discuss the potential of different types of models and analytical tools to capture the impacts of pests on the evolution of LDD, and conclude that even simple models can illustrate the general relationship between pest pressure and LDD advantage, but only spatially explicit simulation models can fully elucidate the resulting ecological and evolutionary dynamics. In conclusion, we consider the potential role of selection for LDD in the spread of invasive species, and in long-term responses to habitat fragmentation and range shifts. |
Pacala, S. W., E. Bulte, J. A. List and S. A. Levin. 2003. False alarm over environmental false alarms. Science 301: 1187-1188.
A series of books, culminating most recently in B. Lomborg’s The Skeptical Environmentalist, conclude that environmental scientists issue too many warnings that subsequently turn out to
be exaggerated or false. We evaluate this claim in the framework of a cost-benefit analysis of evidentiary standards in the environmental sciences. Is the sensitivity of our environmental alarm set too high? We conclude that marginal benefits currently far outweigh marginal costs, indicating that evidentiary standards for reporting hazards are too conservative, not too liberal. |
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2002
Buttel, L., R. Durrett and S. A. Levin. 2002.
Competition and species packing in patchy environments. Theoretical Population
Biology 61: 265-276.
In models of competition in which space is treated
as a continuum, and population size as continuous, there are no limits
to the number of species that can coexist. For a finite number of sites,
N, the results are different. The answer will, of course, depend on the
model used to ask the question. In the Tilman-May-Nowak ordinary differential
equation model, the number of species is asymptotically C log N with most
species packed in at the upper end of the range of possible species. In
contrast, for metapopulation models with discrete individuals and stochastic
spatial systems with various competition neighborhoods, we find a traditional
species area relationship CN^a, with no species clumping along the phenotypic
gradient. The exponent a is larger by a factor of 2 for spatially explicit
models. In words, a spatial distribution of competitors allows for greater
diversity than a metapopulation model due to the effects of recruitment
limitation in their competition.
Chave, J., H. C. Muller-Landau and S. A. Levin.
2002. Comparing classical community models: Theoretical consequences for
patterns of diversity. American Naturalist 159: 1-23.
Mechanisms proposed to explain the maintenance
of species diversity within ecological communities of sessile organisms
include niche differentiation mediated by competitive trade-offs, frequency
dependence resulting from species-specific pests, recruitment limitation
due to local dispersal, and a speciation-extinction dynamic equilibrium
mediated by stochasticity (drift). While each of these processes, and
more, have been shown to act in particular communities, much remains to
be learned about their relative importance in shaping community-level
patterns. We used a spatially-explicit, individual-based model to assess
the effects of each of these processes on species richness, relative abundance,
and spatial patterns such as the species-area curve. Our model communities
had an order-of-magnitude more individuals than any previous such study,
and we also developed a finite-size scaling analysis to infer the large-scale
properties of these systems in order to establish the generality of our
conclusions across system sizes. As expected, each mechanism can promote
diversity. We found some qualitative in community patterns across communities
in which different combinations of these mechanisms operate. Species-area
curves follow a power law with short-range dispersal and a logarithmic
law with global dispersal. Relative-abundance distributions are more even
for systems with competitive differences and trade-offs than for those
in which all species are competitively equivalent, and they are most even
when frequency dependence (even if weak) is present. Overall, however,
communities in which different processes operated showed surprisingly
similar patterns, which suggests that the form of community-level patterns
cannot in general be used to distinguish among mechanisms maintaining
diversity there. Nevertheless, parameterization of models such as these
from field data on the strengths of the different mechanisms could yield
insight into their relative roles in diversity maintenance in any given
community.
Chave, J., K. Wiegand and S. Levin. 2002. Spatial
and biological aspects of reserve design. Environmental Modeling and Assessment
7 (2): 115-122.
The optimal spatial design of protected reserves
requires attention to the biological mechanisms underlying community organization,
and sustaining ecosystem services. Identifying the key mechanisms is especially
difficult in species-rich ecosystems. We investigate the example of the
tropical rainforest, a biome that is under threat of continuing fragmentation,
yet which shelters the majority of living species on Earth. Simple dynamic
and spatially explicit simulations, which model the dynamics of plant
communities, allow us to elucidate the interplay between patterns of fragmentation
and seed dispersal mechanisms in maintaining biodiversity.
Dushoff, J., L. Worden, J. Keymer and S. A. Levin.
2002. Scale invariance in aspect space and community assembly. Theoretical
Population Biology 62: 329-338.
A fundamental problem challenging natural scientists
is to understand how macroscopic patterns, such as population abundance
distributions and element ratios, emerge and are sustained in ecosystems,
given that evolution typically operates most strongly at the level of
individuals and their genomes. How do such patterns persist in the face
of evolutionary innovation? In this paper, we explore this issue through
dynamical models of community assembly and metapopulation dynamics in
dynamic landscapes, and discuss individual-based approaches to the control
of element cycles.
Earn, D. J. D., J. Dushoff and S. A. Levin. 2002.
Ecology and evolution of the flu. Trends in Ecology and Evolution 117(7):
334-340.
Influenza (flu) is an extremely common infectious
disease, but it is unusual in that the primary time scales for disease
dynamics (epidemics) and viral evolution (new variants) are roughly the
same. Recently, extraordinarily reliable phylogenetic reconstructions
of influenza virus evolution have been made using samples from both extant
and extinct strains. In addition, because of their public health importance,
flu epidemics have been monitored throughout the period over which the
phylogenetic trees extend. In parallel with this empirical work, theoretical
ecologists have developed mathematical and computational models that elucidate
many properties of multi-strain systems. In the future, to unravel and
interpret the complex interactions between ecological and evolutionary
forces on influenza dynamics, the documented evolution of the virus must
be related to the observed population dynamics of the disease. New theoretical
insights are also required to simplify model structures and facilitate
predictions that can be tested with accessible data. 2001
Okubo, A. and S.A. Levin, eds. 2001.
Diffusion
and Ecological Problems: Modern Perspectives, 2nd Edition. Interdisciplinary
Applied Mathematics, Vol 14. Springer, New York. Pp. 467.
This book surveys
a wide variety of mathematical models of diffusion in the ecological
context. It is written with the primary intent of providing scientists,
particularly physicists but also biologists, with some background in
the mathematics and physics of diffusion, and shows how they can be
applied to ecological problems. The secondary intent is to provide a
specialized textbook for graduate students who are interested in mathematical
ecology. The reader is assumed to have a basic knowledge of probability
and differential equations. Each chapter in this new edition has been
substantially updated by appropriate leading researchers in the field,
and contains much new material covering developments in the field in
the last 20 years. This book surveys a wide variety of mathematical
models of diffusion in the ecological context. It is written with the
primary intent of providing scientists, particularly physicists but
also biologists, with some background in the mathematics and physics
of diffusion, and shows how they can be applied to ecological problems.
The secondary intent is to provide a specialized textbook for graduate
students who are interested in mathematical ecology. The reader is assumed
to have a basic knowledge of probability and differential equations.
Each chapter in this new edition has been substantially updated by appropriate
leading researchers in the field, and contains much new material covering
developments in the field in the last 20 years.
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Levin,
S.A., ed. 2001. Encyclopedia
of Biodiversity, Five Volumes, Academic Press, San Diego, CA.
"The Encyclopedia of Biodiversity
brings together, for the first time, a study of the dimensions of
diversity. It examination of the services biodiversity provides,
and measures to protect it. Major themes of the work include the
evolution of biodiversity, systems for classifying and defining
biodiversity, ecological patterns and theories of biodiversity,
and an assessment of contemporary patterns and trends in biodiversity."
—Academic Press Book Catalog |
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