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It can be cognitively demanding to understand how a system or organization made up of many very different interconnected elements actually works. But the fact that such systems or organizations are difficult to understand doesn’t make them inherently bad. In addition to its more obvious costs, complexity confers critical benefits, especially in dynamic and uncertain environments. The authors draw on their experience and perspectives in business, biology, and physics to offer some reflections on the nature, benefits, and costs of complexity and provide some guidance on managing it. Their recommendations: In growing your organization, make sure that it remains modular in structure and that all components and connections conform to a small number of simple operating principles. Embed a bias for change, avoid imposing too many controls on your people, and let the market judge which changes work. Finally, always optimize your organization globally and keep fixing, repairing, and pruning. INSET: AN INTERVIEW WITH CARSTEN RASMUSSEN, COO OF LEGO. [ABSTRACT FROM AUTHOR]

Anthropogenic CO2emissions must soon approach net zero to stabilize the global mean temperature. Although several international agreements have advocated for coordinated climate actions, their implementation has remained below expectations. One of the main challenges of international cooperation is the different degrees of socio-political acceptance of decarbonization. Here, we interrogate a minimalistic model of the coupled human-natural system representing the impact of such socio-political acceptance on investments in clean energy infrastructure and the path to net-zero emissions. Despite its simplicity, the model can reproduce complex interactions between human and natural systems, and it can disentangle the effects of climate policies from those of socio-political acceptance on the path to net zero. Although perfect coordination remains unlikely, because clean energy investments are limited by myopic economic strategies and policy systems that promote free-riding, more realistic decentralized cooperation with partial efforts from each actor could still lead to significant cuts in emissions.

The authors present the use of market interest rate loans as a relatively simple inter-family estate planning alternative which provides income tax benefits and possible transfer tax benefits. Older family members provide younger family members with market rate interest promissory notes in exchange for assets.

Are the oceans turning into deserts? Rising temperature, increasing surface stratification, and decreasing vertical inputs of nutrients are expected to cause an expansion of warm, nutrient deplete ecosystems. Such an expansion is predicted to negatively affect a trio of key ocean biogeochemical features: phytoplankton biomass, primary productivity, and carbon export. However, phytoplankton communities are complex adaptive systems with immense diversity that could render them at least partially resilient to global changes. This can be illustrated by the biology of the Prochlorococcus“collective.” Adaptations to counter stress, use of alternative nutrient sources, and frugal resource allocation can allow Prochlorococcusto buffer climate‐driven changes in nutrient availability. In contrast, cell physiology is more sensitive to temperature changes. Here, we argue that biogeochemical models need to consider the adaptive potential of diverse phytoplankton communities. However, a full understanding of phytoplankton resilience to future ocean changes is hampered by a lack of global biogeographic observations to test theories. We propose that the resilience may in fact be greater in oligotrophic waters than currently considered with implications for future predictions of phytoplankton biomass, primary productivity, and carbon export.

The Ten Steps to Responsible Inland Fisheries are global recommendations to address the subordinate position of inland fisheries in sustainability dialogues. Regional and local perspectives are essential for implementing global initiatives. Hence, we surveyed state fisheries agency administrators and American Fisheries Society Governing Board members about the importance, funding, and achievability of the Steps. Respondents rated Science, Communication, and Assessment as highly important, well funded, and achievable steps, unlike Aquaculture and a global Action Plan. Nutrition was rated the most inadequately supported yet achievable step, highlighting an opportunity to promote nutritional contributions of inland fisheries. Opinions were similar between administrators and Governing Board members across U.S. regions, suggesting a foundation for incorporating underemphasized steps into management programs by building multi‐organizational partnerships and applying lessons from better integrated steps (e.g., Science, Assessment). Overall, the Steps can advance freshwater science and management in the United States while increasing the visibility of inland fisheries that are rarely prioritized globally.

U.S. public companies are dying at faster and faster rates; in fact, they have a one in three chance of being delisted in the next five years. Why? They are failing to adapt to the growing complexity of their environments, the authors argue—misreading those environments, selecting the wrong approaches to strategy, or failing to support a viable approach with the right behaviors and capabilities. Drawing on their research at the intersection of business strategy, biology, and complex systems, BCG’s Martin Reeves and Daichi Ueda, along with Princeton biologist Simon Levin, describe six principles that confer robustness in what’s known as complex adaptive systems—principles that are directly applicable to business. Firms should: • maintain heterogeneity of people, ideas, and endeavors • sustain a modular structure of loosely connected components • preserve redundancy among components • expect surprise, but reduce uncertainty • create feedback loops and adaptive mechanisms to ensure the variation, selection, and propagation of innovations • foster trust and reciprocity in their business ecosystems Rising corporate mortality is an increasing threat, and the forces driving it are likely to remain strong for the foreseeable future. Understanding and implementing the principles that create robustness in complex adaptive systems can mean the difference between survival and extinction. INSET: An Increasingly Complex Environment.. [ABSTRACT FROM AUTHOR]

This variation on the normal CRUT has two noncharitable income interests before the remainder passes to the charitable beneficiary, and thus allows more wealth to be kept within the donor's family at a low tax cost. Further, unless the value of the trust's assets decline, the charity should receive assets at least equal to the value of the initial contribution to the trust. Although significant problems may arise on the premature death of either the donor or the noncharitable beneficiary, there are ways to mitigate these risks.

The near-zero charitable remainder unitrust (CRUT) can be distinguished from conventional CRUTs and net income make-up CRUTs by the fact that the primary purpose of a near-zero CRUT is to pass wealth with minimal transfer taxes. Other CRUTs are used to reduce estate taxes, provide retirement income and make charitable contributions. Under a near-zero CRUT, income is paid to the donor for a term and then to a beneficiary, with the remainder going to the charity. The tax advantage to the donor result from current deductions for the charitable contribution and discounted valuation for gift tax purposes.

Phytoplankton stoichiometry modulates the interaction between carbon, nitrogen and phosphorus cycles. Environmentally driven variations in phytoplankton C:N:P can alter biogeochemical cycling compared to expectations under fixed ratios. In fact, the assumption of fixed C:N:P has been linked to Earth System Model (ESM) biases and potential misrepresentation of responses to future change. Here we integrate key elements of the Adaptive Trait Optimization Model (ATOM) for phytoplankton stoichiometry with the Carbon, Ocean Biogeochemistry and Lower Trophics (COBALT) ocean biogeochemical model. Within a series of global ocean‐ice‐ecosystem retrospective simulations, ATOM‐COBALT reproduced observations of phytoplankton N:P, and compared to static ratios, exhibited reduced phytoplankton P‐limitation, enhanced N‐fixation, and increased low‐latitude export, improving consistency with observations and highlighting the biogeochemical implications of dynamic N:P. We applied ATOM‐COBALT to explore the impacts of different physiological mechanisms hypothesized to underlie N:P variation, finding that two mechanisms together drove the observed patterns: proportionality of P‐rich ribosomes in phytoplankton cells to growth rates and reductions in P‐storage during scarcity. A third mechanism which linked temperature with phytoplankton biomass allocations to non‐ribosomal proteins, led only to relatively modest impacts because this mechanism decreased the temperature dependence of phytoplankton growth rates, compensating for changes in N:P. We find that there are quantitative response differences that associate distinctive biogeochemical footprints with each mechanism, which are most apparent in highly productive low‐latitude regions. These results suggest that variable phytoplankton N:P makes phytoplankton productivity and export resilient to environmental changes, and support further research on the physiological and environmental drivers of phytoplankton stoichiometry and biogeochemical role. Marine phytoplankton are single‐celled photosynthetic organisms that live near the ocean's surface, where they absorb carbon dioxide and other nutrients. This exerts a large influence on ocean chemistry and, through the ocean's capacity to absorb carbon dioxide from the atmosphere, the Earth's climate. We explored how phytoplankton vary their requirements for two essential nutrients, nitrogen and phosphorus, based on environmental conditions, and how that variation affects the export of carbon from the surface ocean to depth. We found that flexibility in phytoplankton nutrient uptake ratios makes them use phosphorus more efficiently, driving an increase in carbon export. It also stimulates nitrogen fixation, causing an increase in nitrogen available to phytoplankton. As a result, our simulations predicted significantly less phosphorus limitation and more export from low‐latitude parts of the ocean, increasing agreement with observations. Flexible phytoplankton nutrient requirements change how marine ecosystems respond to the environment, and understanding how these nutrient requirements vary is key to predicting how the ocean will respond to future changes. Implemented a trait‐based model of dynamic phytoplankton elemental stoichiometry within global biogeochemical simulationsDynamic stoichiometry decreased phytoplankton P‐limitation in the tropics and subtropics and increased N‐fixation and exportFrugal P‐utilization in low P environments and increased P‐rich ribosomes at high growth rates leave distinct biogeochemical fingerprints Implemented a trait‐based model of dynamic phytoplankton elemental stoichiometry within global biogeochemical simulations Dynamic stoichiometry decreased phytoplankton P‐limitation in the tropics and subtropics and increased N‐fixation and export Frugal P‐utilization in low P environments and increased P‐rich ribosomes at high growth rates leave distinct biogeochemical fingerprints

Climate change is anticipated to impact smallholder farmer livelihoods substantially. However, empirical evidence is inconclusive regarding how increased climate stress affects smallholder farmers’ deployment of various livelihood strategies, including rural–urban migration. Here we use an agent-based model to show that in a South Asian agricultural community experiencing a 1.5 oC temperature increase by 2050, climate impacts are likely to decrease household income in 2050 by an average of 28%, with fewer households investing in both economic migration and cash crops, relative to a stationary climate. Pairing a small cash transfer with risk transfer mechanisms significantly increases the adoption of migration and cash crops, improves community incomes and reduces community inequality. While specific results depend on contextual factors such as risk preferences and climate risk exposure, these interventions are robust in improving adaptation outcomes and alleviating immobility, by addressing the intersection of risk aversion, financial constraints and climate impacts.

Climate change is reshaping the comparative advantage of regions and hence driving migration flows, principally toward urban areas. Migration has multiple benefits and costs in both origin and destination regions. Coordinated policies that recognize how and why people move can reduce future costs and facilitate adaptation to climate change both within borders and internationally.

An actively controlled Susceptible-Infected-Susceptible (actSIS) contagion model is presented for studying epidemic dynamics with continuous-time feedback control of infection rates. Our work is inspired by the observation that epidemics can be controlled through decentralized disease-control strategies such as quarantining, sheltering in place, social distancing, etc., where individuals can actively modify their contact rates in response to observations of the infection levels in the population. Accounting for a time lag in observations and categorizing individuals into distinct sub-populations based on their risk profiles, we show that the actSIS model manifests qualitatively different features as compared with the SIS model. In a homogeneous population of risk-averters, the endemic equilibrium is always reduced, although the transient infection level can overshoot or undershoot. In a homogeneous population of risk-tolerating individuals, the system exhibits bistability, which can also lead to reduced infection. For a heterogeneous population comprised of risk-tolerators and risk-averters, we prove conditions on model parameters for the existence of a Hopf bifurcation and sustained oscillations in the infected population.

Available online: November 1, 2019

We derive an exact upper bound on the epidemic overshoot for the Kermack–McKendrick SIR model. This maximal overshoot value of 0.2984 · · · occurs at R0∗=2.151⋯. In considering the utility of the notion of overshoot, a rudimentary analysis of data from the first wave of the COVID-19 pandemic in Manaus, Brazil highlights the public health hazard posed by overshoot for epidemics with R0near 2. Using the general analysis framework presented within, we then consider more complex SIR models that incorporate vaccination.

MRI and laboratory features have been incorporated into international diagnostic criteria for multiple sclerosis. We assessed the pattern of MRI lesions and contributions of cerebrospinal fluid (CSF) and serum antibody findings that best identifies children with multiple sclerosis, and the applicability of international diagnostic criteria in the paediatric context.

As the SARS-CoV-2 trajectory continues, the longer-term immuno-epidemiology of COVID-19, the dynamics of Long COVID, and the impact of escape variants are important outstanding questions. We examine these remaining uncertainties with a simple modelling framework that accounts for multiple (antigenic) exposures via infection or vaccination. If immunity (to infection or Long COVID) accumulates rapidly with the valency of exposure, we find that infection levels and the burden of Long COVID are markedly reduced in the medium term. More pessimistic assumptions on host adaptive immune responses illustrate that the longer-term burden of COVID-19 may be elevated for years to come. However, we also find that these outcomes could be mitigated by the eventual introduction of a vaccine eliciting robust (i.e. durable, transmission-blocking and/or ‘evolution-proof’) immunity. Overall, our work stresses the wide range of future scenarios that still remain, the importance of collecting real-world epidemiological data to identify likely outcomes, and the crucial need for the development of a highly effective transmission-blocking, durable and broadly protective vaccine.

This study investigated the performance of Cepheid Xpert human papillomavirus (HPV) assay in South African human immunodeficiency virus (HIV)-infected women and compared its performance with that of hybrid capture-2 (hc2). Methods: Stored cervical specimens from HIV-infected women that had previously been tested using hc2 were tested using Xpert. Results: The overall HR-HPV prevalence was found to be 62.0% (720/1161) by Xpert and 61.2% (711/1161) by hc2. 13.6% (158/1161) were HPV16 positive, 18.8% (218/1161) were HPV18/45, 37.3% (434/1161) were HPV31/33/35/52/58, 12.7% (147/1161) were HPV51/59 and 23.3% (270/1161) were HPV39/68/56/66. Overall agreement with hc2 was 90%; Cohen’s kappa was 0.78 (95% CI 0.74–0.82) indicating substantial agreement. Detection of HPV16, HPV18/45, and HPV31/33/35/52/58 were independently associated with cervical intraepithelial neoplasia (CIN)−2+ (P<0.0001 for each); while HPV51/59 and HPV39/68/56/66 were not. Women infected with HPV16, HPV18/45 or HPV31/33/35/52/58 were found to have significantly higher amounts of HPV DNA detected for those with CIN2+ compared to those without CIN2+, P<0.0001 for each. Xpert and hc2 were similarly sensitive (88.3% and 91.5%, respectively) and specific (48.4% and 51.0%) for CIN2+ and CIN3 (sensitivity: 95.8% and 97.9%; specificity: 41.4% and 42.8%). Conclusions: Xpert is a promising screening test in HIV-infected women that performs similarly to hc2.

The article offers information on the importance of professionalism in pottery and sculpture. Topics discussed include supporting better galleries with cost, time, and passion; providing strong foundation for galleries by having a website, promoting gallery on social media websites; and need for evaluating long-term goals and responsibility.

Climate change is often described as the greatest environmental challenge of our time. In addition, a changing climate can reallocate natural capital, change the value of all forms of capital and lead to mass redistribution of wealth. Here we explain how the inclusive wealth framework provides a means to measure shifts in the amounts and distribution of wealth induced by climate change. Biophysical effects on prices, pre-existing institutions and socio-ecological changes related to shifts in climate cause wealth to change in ways not correlated with biophysical changes. This implies that sustainable development in the face of climate change requires a coherent approach that integrates biophysical and social measurement. Inclusive wealth provides a measure that indicates sustainability and has the added benefit of providing an organizational framework for integrating the multiple disciplines studying global change.

Responsibility for training general paediatricians in Canada lies primarily with the 17 paediatric academic health sciences centres with more programmatic emphasis on subspecialty training and less on preparing residents for general paediatrics. However, the greatest unmet demand in the paediatric workforce will be for consulting paediatric generalists. Here, we define the need for paediatric generalists and list deficiencies in current models to promote more consulting community general paediatricians. The limited presence of general paediatricians as role models reduces the potential for learners to better understand the role of generalists in our specialty. Nationally, we need to advocate for change in teaching models to guide the career choices of our graduates to meet societal needs through better mentorship and educational models that heavily include community-based paediatric consulting generalists. This will be essential to meet our responsibility of supporting primary care colleagues closer to home for our funders, patients and families.

Sustainably managing coupled ecological–economic systems requires not only an understanding of the environmental factors that affect them, but also knowledge of the interactions and feedback cycles that operate between resource dynamics and activities attributable to human intervention. The socioeconomic dynamics, in turn, call for an investigation of the behavioural drivers behind human action. We argue that a multidisciplinary approach is needed in order to tackle the increasingly pressing and intertwined environmental challenges faced by modern societies. Academic contributions to climate change policy have been constrained by methodological and terminological differences, so we discuss how programmes aimed at cross-disciplinary education and involvement in governance may help to unlock scholars' potential to propose new solutions.

The article discusses the use of wood firing in the creation of ceramic art pieces with a focus on wadding, which is the material that stops pots from sticking to shelves or other pots while they are being fired. Topics discussed include the various techniques used by ceramics artists including Pete Pinnell, Linda Christianson, and Kenyon Hansen.

The objective of this study was to examine the association between convulsive status epilepticus (CSE) and health-related quality of life (HRQL) during a 24-month follow-up in a multisite incident cohort of children with epilepsy.

ABSTRACTThe within-host dynamics of an infection with the malaria parasite Plasmodium falciparumare the result of a complex interplay between the host immune system and parasite. Continual variation of the P. falciparumerythrocyte membrane protein (PfEMP1) antigens displayed on the surface of infected red blood cells enables the parasite to evade the immune system and prolong infection. Despite the importance of antigenic variation in generating the dynamics of infection, our understanding of the mechanisms by which antigenic variation generates long-term chronic infections is still limited. We developed a model to examine the role of cross-reactivity in generating infection dynamics that are comparable to those of experimental infections. The hybrid computational model we developed is attuned to the biology of malaria by mixing discrete replication events, which mimics the synchrony of parasite replication and invasion, with continuous interaction with the immune system. Using simulations, we evaluated the dynamics of a single malaria infection over time. We then examined three major mechanisms by which the dynamics of a malaria infection can be structured: cross-reactivity of the immune response to PfEMP1, differences in parasite clearance rates, and heterogeneity in the rate at which antigens switch. The results of our simulations demonstrate that cross-reactive immune responses play a primary role in generating the dynamics observed in experimentally untreated infections and in lengthening the period of infection. Importantly, we also find that it is the primary response to the initially expressed PfEMP1, or small subset thereof, that structures the cascading cross-immune dynamics and allows for elongation of the infection.

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 nutrient-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.

In this article, the author presents a personal narrative in which he reflects upon his experiences as a potter dealing with topics including how he self evaluates his work, his artistic technique and his experiences collaborating with the ceramic artist Amy Smith.

To assess health-related quality of life (HRQL) over 2 years in children 4−12 years old with new-onset epilepsy and risk factors.

Abstract: Despite recent advances in molecular and metagenomic approaches, it is still unclear how spatiotemporal variations in microbial communities influence the biological pump, exporting organic carbon from the surface to the deep oceans. We address this important problem by constructing a simple model of a prokaryotic metacommunity in which two generalist ecotypes compete for two resources. The first and the second ecotypes have, respectively, a higher preference for particulate organic carbon (POC) and dissolved organic carbon. Sinking of POC would lead to a higher abundance of the first ecotype in the deep layer compared to the surface layer, but vertical mixing in turn generates a net upward flux of this ecotype to the surface layer. This upward movement accelerates the shifts in the community composition during the phytoplankton bloom, contributing to a higher efficiency in POC remineralization at the surface layer and reducing the carbon flux to the deep layer.

Abstract: This paper compares perfect information and passive–adaptive social learning models of forest harvesting using a simple Markov chain model for land-use dynamics. A perfect information model assumes that landowners know true utility values of forest conservation and harvesting. In contrast, a passive–adaptive social learning model assumes that landowners do not know true utility values and they learn these values by their past experiences and by exchanging information with others in a society. We determine conditions under which the same consequences expected from perfect information and passive–adaptive social learning models. We found that the outcome from a perfect information model resembles that from passive–adaptive social learning model only when the perfect information model incorporates little discounting for future values. The stability analysis of landscape dynamics predicts a cyclic overexploitation of forest resources in a passive–adaptive social learning model with short-term memory, while instability of landscapes is never expected in a perfect information model. We discuss the role of discounting the future and discounting the past in the context of forest management.

We study a single species in a chemostat, limited by two nutrients, and separate nutrient uptake from growth. For a broad class of uptake and growth functions it is proved that a nontrivial equilibrium may exist. Moreover, if it exists it is unique and globally stable, generalizing a result in [15].

A variety of decision models have been formulated for the optimal selection of nature reserve sites to represent a diversity of species or other conservation features. Unfortunately, many of these models tend to select scattered sites and do not take into account important spatial attributes such as reserve shape and connectivity. These attributes are likely to affect not only the persistence of species but also the general ecological functioning of reserves and the ability to effectively manage them. In response, researchers have begun formulating reserve design models that improve spatial coherence by controlling spatial attributes. We review the spatial attributes that are thought to be important in reserve design and also review reserve design models that incorporate one or more of these attributes. Spatial modeling issues, computational issues, and the trade-offs among competing optimization objectives are discussed. Directions for future research are identified. Ultimately, an argument is made for the development of models that capture the dynamic interdependencies among sites and species populations and thus incorporate the reasons why spatial attributes are important.A variety of decision models have been formulated for the optimal selection of nature reserve sites to represent a diversity of species or other conservation features. Unfortunately, many of these models tend to select scattered sites and do not take into account important spatial attributes such as reserve shape and connectivity. These attributes are likely to affect not only the persistence of species but also the general ecological functioning of reserves and the ability to effectively manage them. In response, researchers have begun formulating reserve design models that improve spatial coherence by controlling spatial attributes. We review the spatial attributes that are thought to be important in reserve design and also review reserve design models that incorporate one or more of these attributes. Spatial modeling issues, computational issues, and the trade-offs among competing optimization objectives are discussed. Directions for future research are identified. Ultimately, an argument is made for the development of models that capture the dynamic interdependencies among sites and species populations and thus incorporate the reasons why spatial attributes are important.

We demonstrate how direct simulation of stochastic, individual–based models can be combined with continuum numerical–analysis techniques to study the dynamics of evolving diseases. Sidestepping the necessity of obtaining explicit population–level models, the approach analyses the (unavailable in closed form) ‘coarse’ macroscopic equations, estimating the necessary quantities through appropriately initialized short ‘bursts’ of individual–based dynamic simulation. We illustrate this approach by analysing a stochastic and discrete model for the evolution of disease agents caused by point mutations within individual hosts. Building up from classical susceptible–infected–recovered and susceptible–infected–recovered–susceptible models, our example uses a one–dimensional lattice for variant space, and assumes a finite number of individuals. Macroscopic computational tasks enabled through this approach include stationary–state computation, coarse projective integration, parametric continuation and stability analysis.

The evolution of the etiological agents of disease presents one of the greatest challenges for their control, and makes essential complementing standard epidemiological investigations with broader approaches that allow for evolutionary change. Given the stunning genetic diversity that is possible for many such agents, such as the influenza virus, it is impossible to represent all of the diversity manifest at the level of amino acid sequences. We show that drift-variant influenza strains naturally cluster into groups which are associated with functionally important epitopic regions. Dominant clusters typically replace each other every 2–5 years, and this feature is fundamental to the development of vaccination strategies. We furthermore show that stochastic fluctuations can greatly magnify small interference effects among strains, or even among subtypes, leading for example to competitive exclusion in situations where such effects would be unexpected based on the usual deterministic models. We suggest that this effect might be involved in the explanations of some persistent empirical anomalies. [Copyright &y& Elsevier]

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.

Many planktivorous fishes forage in currents, where they actively maintain position and visually strike at current-entrained zooplankton. In general, the zooplankton are wafted by the foraging fish at a rate equivalent to the current velocity. From a fish's viewpoint the plankton approach either head-on or offset at varied distances from the fish's position. We present a model that describes the relative motion of particles as they approach and pass a foraging fish at different offset distances, and the rate of change in apparent size as they close on a fish. In addition, a series of experiments of fish feeding on plankton in a flume at increasing current velocities revealed that two basic tactics are utilized. At low current velocities (<10-14 cm s m 1), the fish swims toward the prey, whereas at higher current velocities the fish tends to fall back with the current to capture a prey item. The model and experimental results are discussed in terms of the visual problems associated with the detection and tracking of items in motion.

The problem of multiple scales permeates the study of ecological process and pattern, uniting aspects of space, time, and organizational complexity. In particular, it supports the maintenance of biological diversity, allowing for the magnification of underlying patterns of variation in the physical environment to create many resources from few, through the evolutionary diversification of species' niches and life histories. Specialization to particular stages of a successional gradient facilitates coexistence of multiple types in the presence of uncorrelated local disturbances, such as gap formation, which reinitiate successional sequences. Superimposed upon such successional dynamics are the effects of multiple stable states and multiple successional pathways (Levin 1976), which increase diversity even more. Multiple stable states more generally raise the possibility of sudden flips of systems from one stable configuration to another, and with such changes may come huge changes in the biotic composition. On larger spatial scales and longer time scales, these flips may become correlated, resulting in the transformation of the landscape, or may result in sustained spatiotemporal mosaics of states. Instability at the local level may lead to the maintenance of biodiversity on broader scales. Finally, the ultimate scale mismatch involves that between the dynamics of natural systems and the cultural dynamics of human societies. Our ability to live sustainably in a global commons is dependent upon adjusting normative behavior, and tightening feedback loops more generally, so that individual actions serve the common good.

It is well known that if reacting species experience unequal diffusion rates, then dynamics that lead to a constant steady state in a “well-mixed” environment can in a spatial setting lead to interesting patterns. In this paper, we focus on complementary pattern formation mechanisms that operate even when the diffusion rates are equal. In particular, we can say that when the mean-field ODE has an attracting periodic orbit then the stochastic spatial model will have large-scale spatial structures in equilibrium. We explore this mechanism in depth through the dynamics of the simulator WATOR.

Abstract: We describe the dynamics of competing species in terms of interactions between spatial moments. We close the moment hierarchy by employing a Gaussian approximation which assumes that fluctuations are independent and distributed normally about the mean values. The Gaussian approximation provides the lowest-order systematic correction to the mean-field approximation by incorporating the effect of fluctuations. When there are no fluctuations in the system, the mean equations agree with the Gaussian approximation as the fluctuations are weak. As the fluctuations gain strength, they influence the mean quantities and hence the Gaussian approximation departs from the mean-field approximation. At large fluctuation levels, the Gaussian approximation breaks down, as may be explained by the bimodality and skewness of the fluctuation distribution of the partial differential equation.

The diversity of functional forms and strategies in plant communities is essential to the maintenance of the services that ecosystems provide humanity, and ultimately to the homeostasis of the biosphere. This diversity emerges from evolutionary forces operating at lower levels; these exploit the opportunities for specialization presented by exogenous and endogenous spatial and temporal heterogeneity. Two major theoretical approaches have been taken to understand how strategies arise and are maintained: optimization models, which consider the fitnesses of types in isolation, and game-theoretic methods, which take frequency dependence into account. The gametheoretic approach is more powerful, but also more challenging to apply. For some relatively simple problems in the study of biodiversity, we show how the game-theoretic formulation can be translated into an equivalent problem in optimization. More generally, however, new techniques will be needed to explore the dynamics of multiple coexisting types and strategies.

Pathogens evolve different life-history strategies, which depend in part on differences in their host populations. A central feature of hosts is their population structure (e.g. spatial). Additionally, hosts themselves can exhibit different degrees of symptoms when newly infected; this latency is a key life-history property of pathogens. With an evolutionary-epidemiological model, we examine the role of population structure on the evolutionary dynamics of latency. We focus on specific power-law-like formulations for transmission and progression from the first infectious stage as a function of latency, assuming that the across-group to within-group transmission ratio increases if hosts are less symptomatic. We find that simple population heterogeneity can lead to local evolutionarily stable strategies (ESSs) at zero and infinite latency in situations where a unique ESS exists in the corresponding homogeneous case. Furthermore, there can exist more than one interior evolutionarily singular strategy. We find that this diversity of outcomes is due to the (possibly slight) advantage of across-group transmission for pathogens that produce fewer symptoms in a first infectious stage. Thus, our work reveals that allowing individuals without symptoms to travel can have important unintended evolutionary effects and is thus fundamentally problematic in view of the evolutionary dynamics of latency.

We study a model for competing species that explicitly accounts for effects due to discreteness, stochasticity and spatial extension of populations. If a species does better locally than the other by an amount ε, the global outcome depends on the initial densities (uniformly distributed in space), εand the size of the system. The transition point moves to lower values of the initial density of the superior species with increasing system size. Away from the transition point, the dynamics can be described by a mean-field approximation. The transition zone is dominated by formation of clusters and is characterized by nucleation effects and relaxation from meta-stability. Following cluster formation, the dynamics are dominated by motion of cluster interfaces through a combination of planar wave motion and motion through mean curvature. Clusters of the superior species bigger than a certain critical threshold grow whereas smaller clusters shrink. The reaction–diffusion system obtained from the mean-field dynamics agrees well with the particle system. The statistics of clusters at an early time soon after cluster-formation follow a percolation-like diffusive scaling law. We derive bounds on the time-to-extinction based on cluster properties at this early time. We also deduce finite-size scaling from infinite system behavior.

This work investigates approaches to simplifying individual-based models in which the rate of disturbance depends on local densities. To this purpose, an individual-based model for a benthic population is developed that is both spatial and stochastic. With this model, three possible ways of approximating the dynamics of mean numbers are examined: a mean-field approximation that ignores space completely, a second-order approximation that represents spatial variation in terms of variances and covariances, and a patch-based approximation that retains information about the age structure of the patch population. Results show that space is important and that a temporal model relying on mean disturbance rates provides a poor approximation to the dynamics of mean numbers. It is possible, however, to represent relevant spatial variation with second-order moments, particularly when recruitment rates are low and/or when disturbances are large and weak. Even better approximations are obtained by retaining patch age information.

In sessile organisms such as plants, interactions occur locally so that important ecological aspects like frequency dependence are manifest within local neighborhoods. Using probabilistic cellular automata models, we investigated how local frequency-dependent competition influenced whether two species could coexist. Individuals of the two species were randomly placed on a grid and allowed to interact according to local frequency-dependent rules. For four different frequency-dependent scenarios, the results indicated that over a broad parameter range the two species could coexist. Comparisons between explicit spatial simulations and the mean-field approximation indicate that coexistence occurs over a broader region in the explicit spatial simulation.

We, as a society, find ourselves confronted with a spectrum of potentially catastrophic and irreversible environmental problems, for which conventional approaches will not suffice in providing solutions. These problems are characterized, above all, by their unpredictability. This means that surprise is to be expected, and that sudden qualitative shifts in dynamics present serious problems for management. In general, it is difficult to detect strong signals of change early enough to motivate effective solutions, or even to develop scientific consensus on a time scale rapid enough to allow effective solution. Furthermore, such signals, even when detected, are likely to be displaced in space or sector from the source, so that the motivation for action is small. Conventional market mechanisms thus will be inadequate to address these challenges.

An individual–based model of plant–herbivore interactions was developed to test the potentially interactive effects of explicit space and coevolution on population and community dynamics. Individual plants and herbivores resided in cells on a lattice and carried linked interaction genes. Interaction strength between individual plants and herbivores depended on concordance between these genes (gene–for–gene coevolution). Mating and dispersal among individuals were controlled spatially within variably sized neighbourhoods. Without evolution we observed high–frequency plant–herbivore oscillations (blue spectra) with small individual neighbourhoods, and stochastic fluctuations (white spectra) with large neighbourhoods. Evolution resulted in decreased interaction strength, decreased herbivore–induced plant mortality, increased population sizes, and longer–term fluctuations (reddened spectra). Small herbivore neighbourhoods led to herbivore extinction only with evolution. To explore the increased population size response to evolution we ran simulations without evolution while tuning plant–herbivore interaction strength from high to none. We found that herbivore populations were maximized at intermediate levels of interaction strength that coincided with the interaction strength achieved when the system tuned itself through evolution. Overall, our model shows that the small–scale details of phenotypically variable individual–level interactions, leading to evolutionary dynamics, affect large–scale population and community dynamics.