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Department of Ecology & Evolutionary Biology
Levin Lab Mailing Address: 106A Guyot Hall
Princeton, NJ 08544-1003
Phone: (609) 258-6879. Fax (609) 258-6819

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Games cover
Detail from the cover of Levin, S.A., ed. Games, Groups and the Global Good (Springer, 2009).
Note: For a complete list of Simon A. Levin's publications, click here.
Arrow, K., Ehrlich, P., and S.A. Levin. 2014. Some perspectives on linked ecosystems and socio-economic systems. In Environment and Development Economics: Essays in Honor of Sir Partha Dasgupta, ed. S. Barrett et al., 95-116. Springer-Verlag.

This chapter explains that social and ecological systems are intertwined, complex adaptive systems. They are complex adaptive systems because, in each case, behavior by individuals affects the whole, and changes at the aggregate level in turn affect how individual behave. They are intertwined because the human economy has profoundly affected the sustainability of critical ecological systems, while the changes wrought to these systems will affect the welfare attainable by human societies, both today and in the future. Consideration of this perspective emphasizes unpredictability, and the need for policies that support resilience and robustness.

Levin, S.A. 2014. Public goods in relation to competition, cooperation, and spite. PNAS 111 (suppl 3): 10838-10845.

Public goods and common-pool resources are fundamental features of biological and social systems, and pose core challenges in achieving sustainability; for such situations, the immediate interests of individuals and the societies in which they are embedded are in potential conflict, involving game-theoretic considerations whose resolution need not serve the collective good. Evolution has often confronted such dilemmase.g., in bacterial biofilmsin the challenges of cancer, in nitrogen fixation and chelation, in the production of antiobiotics, and in the collective action problems across animal groups; there is much to learn from the Darwinian resolution of these situations for how to address problems our societies face today. Addressing these problems involves understanding the emergence of cooperative agreements, from reciprocal altruism and insurance arrangements to the social norms and more formal institutions that maintain societies. At the core are these issues of how individuals and societies discount the future and the interests of others, and the degree that individual decisions are influenced by regard for others. Ultimately, as Garrett Hardin suggested, the solution to problems of the commons is in "mutual coercion, mutually agreed upon," and hence in how groups of individuals form and how they arrive at decisions that ultimately benefit all.

Van Boeckel, T.P. et al. (including S.A. Levin). 2014. Global antiobiotic consumption 2000-2010: An analysis of national pharmaceutical sales data. Lancet Infectious Diseases: DOI: 10.1016/S1473-3099(14)70780-7.

Antibiotic drug consumption is a major driver of antibiotic resistance. Variations in antibiotic resistance across countries are attributable, in part, to different volumes and patterns for antibiotic consumption. We aimed to assess variations in consumption to assist monitoring of the rise of resistance and development of rational-use policies and to provide a baseline for future assessment.

Vasconcelos, V.T. et al. (including S.A. Levin). 2014. Climate policies under wealth inequality. PNAS: DOI/10.1073/pnas.132347911.

Taming the planet's climate requires cooperation. Previous failures to reach consensus in climate summits have been attributed, among other factors, to conflicting policies between rich and poor counties, which disagree on the implementation of mitigation measures. Here we implement wealth inequality in a threshold public goods dilemma of cooperation in which players also face the risk of potential future losses. We consider a population exhibiting an asymmetric distribution of rich and poor players that reflects the present-day status of nations and study the behavioral interplay between rich and poor in time, regarding their willingness to cooperate. Individuals are also allowed to exhibit a variable degree of homophily, which acts to limit those that constitute one's sphere of influence. Under the premises of our model, and in the absence of homophily, comparison between scenarios with wealth inequaltiy and without wealth inequality shows that the former leads to more global cooperation than the latter. Furthermore, we find that the rich generally contribute more than the poor and will often compensate for the lower contribution of the latter. Contributions from the poor, which are crucial to overcome the climate change dilemma, are shown to be very sensitive to homophily, which, if prevalent, can lead to a collapse of their overall contribution. In such cases, however, we also find that obstinate cooperative behavior by a few poor may largely compensate for homophilic behavior.
Bonachela, J.A., S.D. Allison, S.D. Martiny, and S.A. Levin. 2013. A model for variable phytoplankton stoichiometry based on cell protein regulation. BioGeoSciences 10: 3241-3279.

The elemental ratios of marine phytoplankton emerge from complex interactions between the biotic and abiotic components of the ocean, and reflect the plastic response of individuals to changes in their environment. The stoichiometry of phytoplankton is, thus, dynamic and dependent on the physiological state of the cell. We present a theoretical model for the dynamics of the carbon, nitrogen and phosphorus contents of a phytoplankton population.  By representing the regulatory processes controlling nutrient uptake, and focusing on the relation between nutrient content and protein synthesis, our model qualitatively replicates existing experimental observations for nutrient content and ratios. The population described by our model takes up nutrients in proportions that match the input ratios for a broad range of growth conditions. In addition, there are two zones of single-nutrient limitation separated by a wide zone of colimitation.  Within the co-limitation zone, a single point can be identified where nutrients are supplied in an optimal ratio.  When different species compete, the existence of a wide co-limitation zone implies a more complex pattern of coexistence and exclusion compared to previous model predictions.  However, additional comprehensive laboratory experiments are needed to test our predictions. Our model contributes to the understanding of the global cycles of oceanic nitrogen and phosphorus, as well as the elemental ratios of these nutrients in phytoplankton populations.

Farrior, C.E. et al. (including S.A. Levin). 2013. Resource limitation in a competitive context determines complex plant responses to experimental resource additions. Ecology 94(11): 2505-2517.

Almost all models of plant resource limitation are grounded in either one or both of two simple conceptual models: Liebig's Minimum Hypothesis (LMH), the idea that plants are limited by the resource in shortest supply, and the Multiple Limitation Hypothesis (MLH), the idea that plants should adjust to their environment so that all essential resources are equally limiting. Despite the differences in their predictions, experiments have so far failed to discriminate between them. In a simple factorial nitrogen and water addition experiment in a Minnesota grassland, we observed shifts in allocation that, as in previous studies, are not all explained by a single theory. We found that leaf biomass responded positively to nitrogen additions but did not respond to water additions. We found that fine-root biomass increased in response to water additions, but only at low nitrogen levels, and that fine-root biomass decreased in response to nitrogen additions, but only at high water levels.
To understand these responses we built a physiologically based model of plant competition for water, nitrogen, and space to predict plant allocation to fine roots and leaves. Critically, we include in our model the inherent variability of soil moisture and treat light, water, and nitrogen as resources with distinct mechanistic roles. Experimental results showed that plants were nitrogen and water limited. The model explains the experimental results, under conditions of co-limitation, as follows. Foliage increases with nitrogen additions but not water additions because leaf construction is constrained by nitrogen uptake. When water is added, plants spend a larger fraction of the growing season limited by light (and effectively nitrogen) than by water. Thus, water additions cause fine-root biomass to increase because of the increased importance of nitrogen limitation. The response of fine-foot biomass to water additions decreases with nitrogen additions because these additions reduce nitrogen limitation. In general, our results are explained by sequential resource limitation. The rate of carbon assimilation may be limited by a single resource at any one moment, but the identity of the limiting resource(s) changes throughout the growing season.

Levin, S.A. et al. 2013. Social-ecological systems as complex adaptive systems: Modeling and policy implications. Environment and Development Economics 18(2): 111-132.

Systems linking people and nature, known as social-ecological systems, are increasingly understood as complex adaptive systems. Essential features of these complex adaptive systemsuch as nonlinear feedbacks, strategic interactions, individual and spatial heterogeneity, and varying time scalespose substantial challenges for modeling. However, ignoring these characteristics can distort our picture of how these systems work, causing policies to be less effective or even counterproductive.  In this paper we present recent developments in modeling social-ecological systems, illustrate some of these challenges with examples related to coral reefs and grasslands, and identify the implications for economic and policy analysis.

Martiny, A. et al. (including S.A. Levin). 2013. Strong latitudinal patterns in the elemental ratios of marine plankton and organic matter. Nature Geoscience 6: 279-283.

Nearly 75 years ago, Alfred C. Redfield observed a similarity between the elemental composition of marine plankton in the surface ocean and dissolved nutrients in the ocean interior. This stoichiometry, referred to as the Redfield ratio, continues to be a central tenet in ocean biogeochemistry, and is used to infer a variety of ecosystem processes, such as phytoplankton productivity and rates of nitrogen fixation and loss. Model, field and laboratory studies have shown that different mechanisms can explain both constant and variable ratios of carbon to nitrogen and phosphorus among ocean plankton communities. The range of C/N/P ratios in the ocean, and their predictability, are the subject of much active research. Here we assess global patterns in the elemental composition of phytoplankton and particulate organic matter in the upper ocean, using published and unpublished observations of particulate phosphorus, nitrogen and carbon from a broad latitudinal range, supplemented with elemental data for surface plankton populations. We show that the elemental ratios of marine organic matter exhibit large spatial variations, with a global average that differs substantially from the canonical Redfield ratio. However, elemental ratios exhibit a clear latitudinal trend. Specifically, we observed a ratio of 195:28:1 in the warm, nutient-depleted low-latitude gyres, 137-18-1 in warm, nutrient-rich upwelling zones, and 78:13:1 in cold, nutrient-rich high-latitude regions. We suggest that the coupling between oceanic carbon, nitrogen and phosphorus cycles may vary systematically by ecosystem.

Pinsky, M.L. et al. (including S.A. Levin). 2013. Marine taxa track local climate velocities. Science 341(6151): 1239-1243.

Organisms are expected to adapt or move in response to climate change, but observed distribution shifts span a wide range of directions and rates. Explanations often emphasize biological distinctions among species, but general mechanisms have been elusive. We tested an alternative hypothesis: that differences in climate velocitythe rate and direction that climate shifts across the landscapecan explain observed species shifts. We compiled a database of coastal surveys around North America from 1968-2011, sampling 128 million individuals across 360 marine taxa. Climate velocity explained the magnitude and direction of shifts in latitude and depth much more effectively than did species characteristics. Our results demonstrate that marine species shift at different rates and directions because they closely track the complex mosaic of local climate velocities.
Akcay, E. et al. (including S.A. Levin). 2012. Evolution of cooperation and skew under imperfect information. PNAS 109(37): 14936-14941.

The evolution of cooperation in nature and human societies depends crucially on how the benefits from cooperation are divided and whether individuals have complete information about their payoffs.  We tackle these questions by adopting a methodology from economics called mechanism design. Focusing on reproductive skew as a case study, we show that full cooperation may not be achievable due to private information over individuals’ outside options, regardless of the details of the specific biological or social interaction.  Further, we consider how the structure of the interaction can evolve to promote the maximum amount of cooperation in the face of the informational constraints. Our results point to a distinct avenue for investigating how cooperation can evolve when the division of benefits is flexible and individuals have private information.

Dixit, A.K., S.A. Levin, and D.I. Rubenstein. 2012. Reciprocal insurance among Kenyan pastoralists. Theoretical Ecology 6: 173-187.

In large areas of low and locally variable rainfall in East Africa, pastoralism is the only viable activity, and cattle are at risk of reduced milk output and even death in dry periods. The herders were nomadic, but following the Kenyan government’s scheme of giving titles to group ranches, they are evolving reciprocity arrangements where a group suffering a dry period can send some of its cattle to graze on lands of another group that has better weather. We model such institutions using a repeated game framework. As these contracts are informal, we characterize schemes that are optimal subject to a self-enforcement dynamic incentive compatibility condition. Where the actual arrangements differ from the predicted optima, we discuss possible reasons for the discrepancy and suggest avenues for further research.

Shaw, A.K. and S.A. Levin. 2012. The evolution of intermittent breeding. Journal of Mathematical Biology 66(4-5): 685-703.

A central issue in life history theory is how organisms trade off current and future reproduction.  Avariety of organisms exhibit intermittent breeding, meaning sexually mature adults will skip breeding opportunities between reproduction attempts.  It’s thought that intermittent breeding occurs when reproduction incurs an extra cost in terms of survival, energy, or recovery time.  We have developed a matrix population model for intermittent breeding, and use adaptive dynamics to determine under what conditions individuals should breed at every opportunity, and under what conditions they should skip some breeding opportunities (and if so, how many). We also examine the effect of environmental stochasticity on breeding behavior. We find that the evolutionarily stable strategy (ESS) for breeding behavior depends on an individual’s expected growth and mortality, and that the conditions for skipped breeding depend on the type of reproductive cost incurred (survival, energy, recovery time). In constant environments there is always a pure ESS, however environmental stochasticity and deterministic population fluctuations can both select for a mixed ESS. Finally, we compare our model results to patterns of intermittent breeding in species from a range of taxonomic groups.

Staver, A.C. and S.A. Levin. 2012. Integrating theroetical rainfall and fire effects on savanna and forest stability dynamics. American Naturalist 180(2): 211-224.

The role of fire and climate in determining savanna and forest distributions requires comprehensive theoretical reevaluation.  Empirical studies show that climate constrains maximum tree cover and that fire feedbacks can reduce tree cover substantially, but neither the stability nor the dynamics of these systems are well understood.  A theoretical integration of rainfall effects with fire processes in particular is lacking. We use simple, well-supported assumptions about the percolation dynamics of fire spread and the demographic effects of climate and fire on trees to build a dynamic model examining the stability of tree cover in savannas and forests. Fire results in the potential for one or possibly two stable equilibria, while the effects of increasing rainfall on tree demography result in (discontinuous) increases in tree cover and in forest tree dominance. As rainfall increases, the system moves from (1) stable low tree cover to (2) bistability of low and high tree cover to (3) stable high tree cover.  Thus, theory suggests that tree cover uniquely determined by climate at low and high rainfall but determined by fire feedbacks at intermediate rainfall—as empirical studies suggest—may be a universal feature of systems where fire has strong effects on tree demography.

Tavoni, A., M. Schlueter, S.A. Levin. 2012. The survival of the conformist: Social pressure and renewable resource management. Journal of Theoretical Biology 299: 152-161.

This paper examines the role of other-regarding behavior as a mechanism for the establishment and maintenance of cooperation in resource use under variable social and environmental conditions. By coupling resource stock dynamics with social dynamics concerning compliance to a social norm prescribing non-excessive resource extraction in a common 10 pool resource, we show that when reputational considerations matter and a sufficient level of social stigma affects the violators of a norm, sustainable outcomes are achieved. We find large parameter regions where norm-observing and norm-violating types coexist, and analyze to what extent such coexistence depends on the environment.

Ziv, G. et al. (including S.A. Levin). 2012. Trading-off fish diversity, food security, and hydropower in the Mekong River Basin. PNAS 109(15): 5609-5614.

The Mekong River Basin, site of the biggest inland fishery in the world, is undergoing massive hydropower development. Planned dams will block critical fish migration routes between the river’s downstream floodplains and upstream tributaries. Here we estimate fish biomass and biodiversity losses in numerous damming scenarios using a simple ecological model of fish migration.  Our framework allows detailing trade-offs between dam locations, power production, and impacts on fish resources. We find that the completion of 78 dams on tributaries, which have not previously been subject to strategic analysis, would have catastrophic impacts on fish productivity and biodiversity. Our results argue for reassessment of several dams planned, and call for a new regional agreement on tributary development of the Mekong River Basin.
Ballantyne, F. IV., O.M.E. Schofield, and S.A. Levin. 2011. The emergence of regularity and variability in marine ecosystems: The combined role of physics, chemistry and biology. Scientia Marina 75(4): 719-731.

Marine ecosystems play an integral role in the functioning of life on earth. To predict how they will respond to global changes, and to manage and maintain effectively services upon which humans rely, we must understand how biological processes at the cellular level generate macroscopic patterns in the oceans. Here, we discuss how physics and biogeochemistry influence and constrain marine ecosystem structure and function, and outline key regularities and patterns of variability that models should aim to reproduce. We identify unanswered questions regarding how size-dependent physiological and ecological processes are linked to turbulent mixing. Specifically, how is size structure related to mixing over a range of spatial scales and how is it linked to the fate of primary production in the sea?

Couzin, I.D. et al (including S.A. Levin). 2011. Uninformed individuals promote democratic consensus in animal groups. Science 334: 1578-1580.

Conflicting interests among group members are common when making collective decisions, yet failure to achieve consensus can be costly. Under these circumstances individuals may be susceptible to manipulation by a strongly opinionated, or extremist, minority. It has previously been argued, for humans and animals, that social groups containing individuals who are uninformed, or exhibit weak preferences, are particularly vulnerable to such manipulative agents. Here, we use theory and experiment to demonstrate that, for a wide range of conditions, a strongly opinionated minority can dictate group choice, but the presence of uninformed individuals spontaneously inhibits this process, returning control to the numerical majority. Our results emphasize the role of uninformed individuals in achieving democratic consensus amid internal group conflict and informational constraints.

Levin, S.A. 2011. Building Bridges between ecology and economics. In Bringing Ecologists and Economists Together; The Askö Meetings and Papers, ed. T. Soderqvist, A. Sundbaum, C. Folk, and K-G. Mäler, 31-34. Dordrecht, Heidelberg, London, New York: Springer.

"The Askö meetings are an annual forum where leading economists and ecologists come together to discuss the myriad issues and challenges surrounding sustainable development. Organized by the Beijer Institute of Ecological Economics and held on the Island of Askö in the Stockholm Archipelago, Sweden, the meetings facilitate a dialogue in which various players with differing perspectives can arrive at common conclusions and solutions that benefit us all. Bringing Ecologists and Economists Together showcases ten papers chosen from Askö meetings held from 1993 to 2002. Most of them were written for a wide audience and published in well-renowned journals, and each one is introduced by an ecologist and an economist who place the papers in a contemporary context. Lucid and accessible, these papers are important reading for students and researchers in ecology, economics and environmental sciences as well as anyone else interested in how ecologists and economists can agree upon crucial sustainability issues." — Springer

Levin, S.A. 2011. Evolution at the ecosystem level: On the evolution of ecosystem patterns (Margarlef Prize in Ecology Lecture 2010). Contributions to Science 7(1): 11-16.

As environmental problems like overpopulation, overfishing, pollution and acid rain commanded greater public attention, much focus shifted to biogeochemical linkages, and to holistic studies of whole ecosystems. Ramon Margalef recognized as forcefully as anyone the remarkable intellectual leverage one could gain by transferring the unique perspectives and advances from one field to another. In this article I discuss the nascent unification of population biology and ecosystems science. Sustainable management requires that we relate the macroscopic features of communities and ecosystems to the microscopic details of individuals and populations. I argue that the distinctions that have prevented this synthesis are artificial, and that we need to overcome them to build a science that allows us to deal with the loss of the benefits we derive from ecosystems.

Staver, A.C., S. Archibald, and S. Levin. 2011. Tree cover in sub-Saharan Africa: Rainfall and fire constrain forest and savanna as alternative stable states. Ecology 92(5): 1063-1072.

Savannas are known as ecosystems with tree cover below climate-defined equilibrium values. However, a predictive framework for understanding constraints on tree cover is lacking. We present (a) a spatially extensive analysis of tree cover and fire distribution in sub-Saharan Africa, and (b) a model, based on empirical results, demonstrating that savanna and forest may be alternative stable states in parts of Africa, with implications for understanding savanna distributions.

Tree cover does not increase continuously with rainfall, but rather is constrained to low (.50%, "savanna") or high tree cover (.75%, "forest"). Intermediate tree cover rarely occurs. Fire, which prevents trees from establishing, differentiates high and low tree cover, especially in areas with rainfall between 1000 mm and 2000 mm. Fire is less important at low rainfall (.1000 mm), where rainfall limits tree cover, and at high rainfall (.2000 mm), where fire is rare. This pattern suggests that complex interactions between climate and disturbance produce emergent alternative states in tree cover.

The relationship between tree cover and fire was incorporated into a dynamic model including grass, savanna tree saplings, and savanna trees. Only recruitment from sapling to adult tree varied depending on the amount of grass in the system. Based on our empirical analysis and previous work, fires spread only at tree cover of 40% or less, producing a
sigmoidal fire probability distribution as a function of grass cover and therefore a sigmoidal sapling to tree recruitment function. This model demonstrates that, given relatively conservative and empirically supported assumptions about the establishment of trees in savannas, alternative stable states for the same set of environmental conditions (i.e., model
parameters) are possible via a fire feedback mechanism.
Integrating alternative stable state dynamics into models of biome distributions could improve our ability to predict changes in biome distributions and in carbon storage under climate and global change scenarios.
Bartumeus, F., L. Giuggiolli, M. Louzao, V. Bretagnolle, D. Oro, and S.A. Levin. 2010. Fishery activities distort seabird foraging. Current Biology 20:1-6.

Human fishing activities are negatively altering marine ecosystems in many ways, but scavenging animals such as seabirds are taking advantage of such activities by exploiting fishery discards. Despite the well-known impact of fisheries on seabird population dynamics, little is known about how discard availability affects seabird movement patterns. Using scenarios with and without trawling activity, we present evidence that fisheries modify the natural way in which two Mediterranean seabirds explore the seascape to look for resources during the breeding season. Based on satellite tracking data and a mathematical framework to quantify anomalous diffusion phenomena, we show how the interplay between traveling distances and pause periods contributes to the spatial spreading of the seabirds at regional scales (i.e., 10–250 km). When trawlers operate, seabirds show exponentially distributed traveling distances and a strong site fidelity to certain foraging areas, the whole foraging process being subdiffusive. In the absence of trawling activity, the site fidelity increases, but the whole movement pattern appears dominated by rare but very large traveling distances, making foraging a superdiffusive process.  Our results demonstrate human involvement on landscape-level behavioral ecology and provide a new ecosystemic approach in the study of fishery-seabird interactions.

Levin, S. 2010. Crossing scales, crossing disciplines: Collective motion and collective action in the Global Commons. Special Issue of the Philosophical Transactions of the Royal Society B (Royal Society's 350th Anniversary) 365(1537): 13-17.

Two conflicting tendencies can be seen throughout the biological world: individuality and collective behaviour. Natural selection operates on differences among individuals, rewarding those who perform better. Nonetheless, even within this milieu, cooperation arises, and the repeated emergence of multicellularity is the most striking example. The same tendencies are played out at higher levels, as individuals cooperate in groups, which compete with other such groups. Many of our environmental and other global problems can be traced to such conflicts, and to the unwillingness of individual agents to take account of the greater good. One of the great challenges in achieving sustainability will be in understanding the basis of cooperation, and in taking multicellularity to yet a higher level, finding the pathways to the level of cooperation that is the only hope for the preservation of the planet.

Levin, S.A. 2010. The evolution of ecology. Chronicle of Higher Education (August 13): B9-B11.

The scientific discipline of ecology is dynamic, steeped in historical tradition but adapting to its changing environment and building its own ecological network of interactions with other disciplines. What is ecology, what have some of its high points been, and, most important, where is it going? All of us on planet earth today, not just scientists, need to know the answers. Society has become increasingly aware that we are losing crucial parts of our ecosystem, and that the activities of human beings are threatening the sustainability of the biosphere as a life-support system for humanity. As I have written elsewhere, “Ecology, the unifying science in integrating knowledge of life on our planet, has become the essential science in learning how to preserve it.”

Nara, P.L. et al (including S.A. Levin). 2010. How can vaccines against influenza and other viral diseases be made more effective. PLoS Biology 8(12): e1000571.

A large fraction of the world’s most widespread and problematic pathogens, such as the influenza virus, seem to persist in nature by evading host immune responses by inducing immunity to genetically and phenotypically plastic epitopes (aka antigenic variation). The more recent re-emergence of pandemic influenza A/H1N1 and avian H5N1 viruses has called
attention to the urgent need for more effective influenza vaccines. Developing such vaccines will require more than just moving from an egg-based to a tissue-culture-based manufacturing process. It will also require a new conceptual understanding of pathogen-host interactions, as well as new approaches and technologies to circumvent immune evasion by pathogens capable of more genetic variation. Here, we discuss these challenges, focusing on some potentially fruitful directions for future research.

Torney, C.J., S.A. Levin, and I.D. Couzin. 2010. Spcialization and evolutionary branching within migratory populations. PNAS 107(47): 20394-9.

Understanding the mechanisms that drive specialization and speciation within initially homogeneous populations is a fundamental challenge for evolutionary theory. It is an issue of relevance for significant open questions in biology concerning the generation and maintenance of biodiversity, the origins of reciprocal cooperation, and the efficient division of labor in social or colonial organisms. Several mathematical frameworks have been developed to address this question and models based on evolutionary game theory or the adaptive dynamics of phenotypic mutation have demonstrated the emergence of polymorphic, specialized populations. Here we focus on a ubiquitous biological phenomenon, migration. Individuals in our model may evolve the capacity to detect and follow an environmental cue that indicates a preferred migration route. The strategy space is defined by the level of investment in acquiring personal information about this route or the alternative tendency to follow the direction choice of others. The result is a relation between the migratory process and a game theoretic dynamic that is generally applicable to situations where information may be considered a public good. Through the use of an approximation of social interactions, we demonstrate the emergence of a stable, polymorphic population consisting of an uninformed subpopulation that is dependent upon a specialized group of leaders. The branching process is classified using the techniques of adaptive dynamics.

Arrow, K. and S.A. Levin. 2009. Intergenerational resource transfers with random offspring. PNAS 106(33): 13702-13706.

A problem common to biology and economics is the transfer of resources from parents to children. We consider the issue under the assumption that the number of offspring is unknown and can be represented as a random variable. There are 3 basic assumptions. The first assumption is that a given body of resources can be divided into consumption (yielding satisfaction) and transfer to children. The second assumption is that the parents' welfare includes a concern for the welfare of their children; this is recursive in the sense that the children's welfares include concern for their children and so forth. However, the welfare of a child from a given consumption is counted somewhat differently (generally less) than that of the parent (the welfare of a child is “discounted”). The third assumption is that resources transferred may grow (or decline). In economic language, investment, including that in education or nutrition, is productive. Under suitable restrictions, precise formulas for the resulting allocation of resources are found, demonstrating that, depending on the shape of the utility curve, uncertainty regarding the number of offspring may or may not favor increased consumption. The results imply that wealth (stock of resources) will ultimately have a log-normal distribution.

Levin, S.A., ed. 2009. Games, Groups, and the Global Good. Berlin; London: Springer.

"How do groups form, how do institutions come into being, and when do moral norms and practices emerge? This volume explores how game-theoretic approaches can be extended to consider broader questions that cross scales of organization, from individuals to cooperatives to societies. Game theory' strategic formulation of central problems in the analysis of social interactions is used to develop multi-level theories that examine the interplay between individuals and the collectives they form. The concept of cooperation is examined at a higher level than that usually addressed by game theory, especially focusing on the formation of groups and the role of social norms in maintaining their integrity, with positive and negative implications. The authors suggest that conventional analyses need to be broadened to explain how heuristics, like concepts of fairness, arise and become formalized into the ethical principles embraced by a society." — Springer

Levin, S.A. 2009. "Games, Groups, Norms, and Societies." In Games, Groups, and the Global Good, ed. S.A. Levin, 143-153. Berlin; London: Springer.

The origin and evolution of social norms, social institutions (including religions), and moral systems involve an interplay among processes played out on diverse scales of space, time, and complexity. Such norms, social institutions, and systems (collectively referred to here as institutions) emerge from the collective actions of individuals and feed back to influence those behaviors, but on much faster time scales than the institutions themselves change. In evolutionary biology, this is an example of what Janzen (1980) termed "diffuse coevolution," in which an evolutionary response is not to a single agent (tight coevolution), but rather is a diffuse reponse to a collection of agents (or species). Dealing with such multiple dimensions requires a new level of game theory, not only multi-player but also multi-dimensional in other ways. Group formation and the resultant collective actions may lead to diffuse benefits for group members, but are sustained by individual decisions regarding costs and benefits within a social context. To sustain individual behaviors in the collective good, groups and societies develop explicit and implicit reward and punishment schemes, including moral systems. Understanding the interplay among these various players, operating on diverse scales, will require extension of game theoretical concepts to address dynamics on multiple scales, including analysis of meta-games, in which evolved strategies are diffuse responses to collections of situations.

Levin, S.A., ed. 2009. The Princeton Guide to Ecology. Princeton, NJ: Princeton University Press.

"The Princeton Guide to Ecology is a concise, authoritative one-volume reference to the field's major subjects and key concepts. Edited by eminent ecologist Simon Levin, with contributions from an international team of leading ecologists, the book contains more than ninety clear, accurate, and up-to-date articles on the most important topics within seven major areas: autecology, population ecology, communities and ecosystems, landscapes and the biosphere, conservation biology, ecosystem services, and biosphere management. Complete with more than 200 illustrations (including sixteen pages in color), a glossary of key terms, a chronology of milestones in the field, suggestions for further reading on each topic, and an index, this is an essential volume for undergraduate and graduate students, research ecologists, scientists in related fields, policymakers, and anyone else with a serious interest in ecology." —Princeton University Press

Ndifon, W., N.S. Wingreen, and S.A. Levin. 2009. Differential neutralization efficiency of hemagglutinin epitopes, antibody interference, and the design of influenza vaccines. PNAS 106(21): 8701-8706.

It is generally assumed that amino acid mutations in the surface protein, hemagglutinin (HA), of influenza viruses allow these viruses to circumvent neutralization by antibodies induced during infection. However, empirical data on circulating influenza viruses show that certain amino acid changes to HA actually increase the efficiency of neutralization of the mutated virus by antibodies raised against the parent virus. Here, we suggest that this surprising increase in neutralization efficiency after HA mutation could reflect steric interference between antibodies. Specifically, if there is a steric competition for binding to HA by antibodies with different neutralization efficiencies, then a mutation that reduces the binding of antibodies with low neutralization efficiencies could increase overall viral neutralization. We use a mathematical model of virus–antibody interaction to elucidate the conditions under which amino acid mutations to HA could lead to an increase in viral neutralization. Using insights gained from the model, together with genetic and structural data, we predict that amino acid mutations to epitopes C and E of the HA of influenza A/H3N2 viruses could lead on average to an increase in the neutralization of the mutated viruses. We present data supporting this prediction and discuss the implications for the design of more effective vaccines against influenza viruses and other pathogens.

Klausmeier, C.A., E. Litchman, T. Daufresne, and S.A. Levin. 2008. Phytoplankton stoichiometry. Ecological Research 23: 479-485.

Because phytoplankton live at the interface between the abiotic and the biotic compartments of ecosystems, they play an important role in coupling multiple nutrient cycles. The quantitative details of how these multiple nutrient cycles intersect is determined by phytoplankton stoichiometry. Here we review some classic work and recent advances on the determinants of phytoplankton stoichiometry and their role in determining ecosystem stoichiometry. First, we use a model of growth with flexible stoichiometry to reexamine Rhee and Goldman's classic chemostat data. We also discuss a recent data compilation by Hall and colleagues that illustrates some limits to phytoplankton flexibility and a model of physiological adaptation that can account for these results. Second, we use a model of resource allocation to determine the how the optimal nitrogen-to-phosphorus stoichiometry depends on the ecological conditions under which species grow and compete. Third, we discuss Redfield’s mechanism for the homeostasis of the oceans’ nitrogen-tophosphorus stoichiometry and show its robustness to additional factors such as iron-limitation and temporal fluctuations. Finally, we suggest areas for future research.

Levin, S.A. and J. Lubchenco. 2008. Resilience, robustness, and marine ecosystem-based management. Bioscience 58(1): 27-32.

Marine ecosystems provide essential services to humans, yet these services have been diminished, and their future sustainability endangered, by human patterns of exploitation that threaten system robustness and resilience. Marine ecosystems are complex adaptive systems composed of individual agents that interact with one another to produce collective effects, integrating scales from individual behaviors to the dynamics of whole systems. In such systems, small changes can be magnified through nonlinear interactions, facilitating regime shifts and collapses. Protection of the services these ecosystems provide must therefore maintain the adaptive capacities of these systems by preserving a balance among heterogeneity, modularity, and redundancy, tightening feedback loops to provide incentives for sound stewardship. The challenge for management is to increase incentives to individuals, and tighten reward loops, in ways that will strengthen the robustness and resilience of these systems and preserve their ability to provide ecosystem services for generations to come.

May, R.M., S.A. Levin, and G. Sugihara. 2008. Ecology for bankers. Nature 451: 893-895.

There is common ground in analysing financial systems and ecosystems, especially in the need to identify conditions that dispose a system to be knocked from seeming stability into another, less happy state.

Scanlon,T., K. Caylor, S.A. Levin, and I. Rodriguez-Inturbe. 2007. Positive feedbacks promote power-law clustering of Kalahari vegetation. Nature 449: 209-212.

The concept of local-scale interactions driving large-scale pattern formation has been supported by numerical simulations, which have demonstrated that simple rules of interaction are capable of reproducing patterns observed in nature.  These models of self-organization suggest that characteristic patterns should exist across a broad range of environmental conditions provided that local interactions do indeed dominate the development of community structure. Readily available observations that could be used to support these theoretical expectations, however, have lacked sufficient spatial extent or the necessary diversity of environmental conditions to confirm the model predictions. We use high-resolution satellite imagery to document the prevalence of self-organized vegetation patterns across a regional rainfall gradient in southern Africa, where percent tree cover ranges from 65% to 4%.  Through the application of a cellular automata model, we find that the observed power-law distributions of tree canopy cluster sizes can arise from the interacting effects of global-scale resource constraints (that is, water availability) and local-scale facilitation. Positive local feedbacks result in power-law distributions without entailing threshold behaviour commonly associated with criticality. Our observations provide a framework for integrating a diverse suite of previous studies that have addressed either mean wet season rainfall or landscape-scale soil moisture variability as controls on the structural dynamics of arid and semiarid ecosystems.


Buchman, T.G., J. Dushoff, P.R. Ehrlich, M. Feldman, S. Fitzpatrick, B. Levin, S.A. Levin, D.T. Miller, V.L. Patel, and P. Rozin. 2006. Battling bad behavior: how do you convince people to do what's in their best interest? The Scientist 20 (2): 51-57.

Many of society’s most vexing problems - the rise of antibiotic resistance, the current epidemic of obesity, armed conflicts that leave both sides worse off - have their roots in the suboptimal and often puzzling actions of individuals. At times conflicting self-interests power such behavior; the best solutions from a collective perspective fail due to the nature of individual payoffs. In other situations, however, people simply fail to do what is best even for themselves, in the face of good, freely available information. Despite stern warnings and mountains of strong evidence, some people continue to take up smoking. They overeat, overindulge in alcohol, and refuse to wear seatbelts or bicycle helmets. Informed by their doctors that antibiotics will do nothing for a viral infection, people demand them anyway, and knowing the larger dangers involved, physicians still prescribe them. Why do human beings often behave in such counterproductive and potentially self-destructive ways? What factors determine how information spreads and whether or not it will guide behavior? Answering these questions and understanding the factors that determine when and how information drives behavioral change is critical to advancing societal interests. From improving human health to reducing our footprint on the global environment, academic research has practical implications.

Levin, S.A. 2006. Learning to live in a Global Commons: socioeconomic challenges for a sustainable environment. Ecological Research, Special Feature 21(3): 328-333.

Ecologists, economists and other social scientists have much incentive for interaction.  First of all, ecological systems and socioeconomic systems are linked in their dynamics, and these linkages are key to coupling environmental protection and economic growth. Beyond this, however, are the obvious similarities in how ecological systems and socioeconomic systems function, and the common theoretical challenges in understanding their dynamics. This should not be surprising. Socioeconomic systems are in fact ecological systems, in which the familiar ecological phenomena of exploitation, cooperation and parasitism all can be identified as key features. Or, viewed from the opposite perspective, ecological systems are economic systems, in which competition for resources is key, and in which an evolutionary process shapes the individual agents to a distribution of specialization of function that leads to the emergence of flows and functionalities at higher levels of organization. Most fundamentally, ecological and socioeconomic systems alike are complex adaptive systems, in which patterns at the macroscopic level emerge from interactions and selection mechanisms mediated at many levels of organization, from individual agents to collectives to whole systems and even above. In such complex adaptive systems, robustness must be understood as emergent from selection processes operating at these many different levels, and the inherent nonlinearities can trigger sudden shifts in regimes that, in the case of the biosphere, can have major consequences for humanity. This lecture will explore the complex adaptive nature of ecosystems, and the implications for the robustness of ecosystem services on which we depend, and in particular examine the conditions under which cooperative behavior emerges. It will then turn attention to the socioeconomic systems in which environmental management is based, and ask what lessons can be learned from our examination of natural systems, and how we can modify social norms to achieve global cooperation in managing our common future. Of special interest will be issues of intragenerational and intergenerational equity, and the importance of various forms of discounting.

Levin, S.A. 2006. Unity from division: in search of a collective Kokoro. Commemorative Lecture II, Kyoto University, International Culture Forum, Kyoto, Japan, 29 October 2006.

Two conflicting tendencies can be seen throughout the biological world: individuality and collective behavior.  Natural selection operates on differences among individuals, rewarding those who perform better.  Nonetheless, even within this milieu, cooperation arises, and the repeated emergence of multicellularity is the most striking example.  The same tendencies are played out at higher levels, as individuals cooperate in groups, which compete with other such groups.  Most of our environmental and other challenges can be traced to such conflict, and to the unwillingness of individual agents to take account of the greater good.  We need to take multicellularity to yet a higher level, and find the collective Kokoro that is the only hope for the preservation of the planet.

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.

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.  

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.

Kareiva, P. and S.A. Levin, eds. 2003. The Importance of Species: Perspectives on Expendability and Triage. Princeton, NJ: Princeton University Press.

"A great many species are threatened by the expanding human population. Though the public generally favors environmental protection, conservation does not come without sacrifice and cost. Many decision makers wonder if every species is worth the trouble. Of what consequence would the extinction of, say, spotted owls or snail darters be? Are some species expendable? Given the reality of limited money for conservation efforts, there is a compelling need for scientists to help conservation practitioners set priorities and identify species most in need of urgent attention. Ecology should be capable of providing guidance that goes beyond the obvious impulse to protect economically valuable species (salmon) or aesthetically appealing ones (snow leopards). Although some recent books have considered the ecosystem services provided by biodiversity as an aggregate property, this is the first to focus on the value of particular species. It provides the scientific approaches and analyses available for asking what we can expect from losing (or gaining) species. The contributors are outstanding ecologists, theoreticians, and evolutionary biologists who gathered for a symposium honoring Robert T. Paine, the community ecologist who experimentally demonstrated that a single predator species can act as a keystone species whose removal dramatically alters entire ecosystem communities." —Princeton University Press

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.
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.

Okubo, A. and S.A. Levin, eds. 2001. Diffusion and Ecological Problems: Modern Perspectives, 2nd Edition. Interdisciplinary Applied Mathematics, Vol 14. New York: Springer.

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.
Levin, S.A., ed.  2001. Encyclopedia of Biodiversity, Five Volumes. San Diego, CA: Academic Press.

"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 Catalogue.

Levin, S.A. 1999. Fragile Dominion: Complexity and the Commons. Reading, MA: Perseus Books.

This book explores the mechanisms sustaining biodiversity, the importance of biodiversity, and lessons from complexity theory for its management.


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