Finding Pseudorandom Colorings of Pseudorandom Graphs

We consider the problem of recovering a planted pseudorandom 3-coloring in expanding and low threshold-rank graphs. Alon and Kahale [SICOMP 1997] gave a spectral algorithm to recover the coloring for a random graph with a planted random 3-coloring. We show that their analysis can be adapted to work when coloring is pseudorandom i.e., all color classes are of equal size and the size of the intersection of the neighborhood of a random vertex with each color class has small variance. We also extend our results to partial colorings and low threshold-rank graphs to show the following: * For graphs on n vertices with threshold-rank r, for which there exists a 3-coloring that is eps-pseudorandom and properly colors the induced subgraph on (1-gamma)n vertices, we show how to recover the coloring for (1 - O(gamma + eps)) n vertices in time (rn)^{O(r)}. * For expanding graphs on n vertices, which admit a pseudorandom 3-coloring properly coloring all the vertices, we show how to recover such a coloring in polynomial time. Our results are obtained by combining the method of Alon and Kahale, with eigenspace enumeration methods used for solving constraint satisfaction problems on low threshold-rank graphs

Coupling Fishery Dynamics, Human Health And Social Learning In A Model Of Fish-Borne Pollution Exposure

The final publication is available at Springer via http://dx.doi.org/10.1007/s11625-015-0317-5Pollution-induced illnesses are caused by toxicants that result from human activity and are often entirely preventable. However, where industrial priorities have undermined responsible governance, exposed populations must reduce their exposure by resorting to voluntary protective measures and demanding emissions abatement. This paper presents a coupled human-environment system model that represents the effects of water pollution on the health and livelihood of a fishing community. The model is motivated by an incident from 1949 to 1968 in Minamata, Japan, where methylmercury effluent from a local factory poisoned fish populations and humans who ate them. We model the critical role of risk perception in driving both social learning and the protective feedbacks against pollution exposure. These feedbacks are undermined in the presence of social misperceptions such as stigmatization of the injured. Through numerical simulation and scenario analysis, we compare our model results with historical datasets from Minamata, and find that the conditions for an ongoing pollution epidemic are highly unlikely without social misperception. We also find trade-offs between human health outcomes, the viability of the polluting industry and the survival of the fishery. We conclude that an understanding of human-environment interactions and misperception effects is highly relevant to the resolution of contemporary pollution problems, and merits further study.Ontario Graduate Scholarship progra

Convergence of socio-ecological dynamics in disparate ecological systems under strong coupling to human social systems

bioRxiv preprint first posted online Apr. 6, 2018; doi: http://dx.doi.org/10.1101/296202. The copyright holder for this preprint (which was not peer-reviewed) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY-NC-ND 4.0 International license.It is widely recognized that coupled socio-ecological dynamics can be qualitatively different from the dynamics of social or ecological systems in isolation from one another. The influence of the type of ecological dynamics on the dynamics of the larger socio-ecological system is less well studied, however. Here, we carry out such a comparison using a mathematical model of a common pool resource problem. A population must make decisions about harvesting a renewable resource. Individuals may either be cooperators, who harvest at a sustainable level, or defectors, who over-harvest. Cooperators punish defectors through social ostracism. Individuals can switch strategies according the costs and benefits of harvesting and the strength of social ostracism. These mechanisms are represented by a differential equation for social dynamics which is coupled to three different types of resource dynamics: logistic growth, constant inflow, and threshold growth. We find that when human influence is sufficiently weak, the form of natural dynamics leaves a strong imprint on the socio-ecological dynamics, and human social dynamics are qualitatively very different from natural dynamics. However, stronger human influence introduces a broad intermediate parameter regime where dynamical patterns converge to a common type: the three types of ecological systems exhibit similar dynamics, but also, social and ecological dynamics strongly mirror one another. This is a consequence of stronger coupling and is reminiscent of synchrony from other fields, such as the classic problem of coupled oscillators in physics. Socio-ecological convergence has implications for how we understand and manage complex socio-ecological systems. In an era of growing human influence on ecological systems, further empirical and theoretical work is required to determine whether socio-ecological convergence is present in real systems

Spatiotemporal dynamics in a transition zone: patchiness, scale, and an emergent property

Ecological transition zones are believed to be unique in their ability to shed light on the organization of populations and communities. In this paper, we study vegetation dynamics in the Great Plains short-grass steppe and Chihuahuan desert grassland ecotone in New Mexico, USA, using long-term, high resolution transect studies of the Sevilleta Long-Term Ecological Research Program. We focus on spatial pattern and examine this in several ways: patch size distribution, spatial autocorrelation analysis, and fractal scaling. These methods are used to examine patch size distributions in two sites representing distributional limits of the dominant species and for detection of an emergent scaling property. We found no characteristic spatial resolution (quadrat size), but rather a fractal structure of spatial variation in abundance and a trend towards consistency of the pattern in time when species were closer to their distributional limit. In this, we were able to detect a robust power law behaviour (the emergent property), indicating strong spatial organization via anti-persistence. Our investigation was exploratory in nature; we feel the results are highly suggestive of intrinsic organization in ecological dynamics and may also be useful in generating testable hypotheses regarding the behaviour of species along ecotones

Coupled Human-Environment Dynamics Of Forest Pest Spread And Control In A Multi-Patch, Stochastic Setting

Background The transportation of camp firewood infested by non-native forest pests such as Asian long-horned beetle (ALB) and emerald ash borer (EAB) has severe impacts on North American forests. Once invasive forest pests are established, it can be difficult to eradicate them. Hence, preventing the long-distance transport of firewood by individuals is crucial. Methods Here we develop a stochastic simulation model that captures the interaction between forest pest infestations and human decisions regarding firewood transportation. The population of trees is distributed across 10 patches (parks) comprising a "low volume" partition of 5 patches that experience a low volume of park visitors, and a "high volume" partition of 5 patches experiencing a high visitor volume. The infestation spreads within a patch-and also between patches-according to the probability of between-patch firewood transportation. Individuals decide to transport firewood or buy it locally based on the costs of locally purchased versus transported firewood, social norms, social learning, and level of concern for observed infestations. Results We find that the average time until a patch becomes infested depends nonlinearly on many model parameters. In particular, modest increases in the tree removal rate, modest increases in public concern for infestation, and modest decreases in the cost of locally purchased firewood, relative to baseline (current) values, cause very large increases in the average time until a patch becomes infested due to firewood transport from other patches, thereby better preventing long-distance spread. Patches that experience lower visitor volumes benefit more from firewood movement restrictions than patches that experience higher visitor volumes. Also, cross-patch infestations not only seed new infestations, they can also worsen existing infestations to a surprising extent: long-term infestations are more intense in the high volume patches than the low volume patches, even when infestation is already endemic everywhere. Conclusions The success of efforts to prevent long-distance spread of forest pests may depend sensitively on the interaction between outbreak dynamics and human social processes, with similar levels of effort producing very different outcomes depending on where the coupled human and natural system exists in parameter space. Further development of such modeling approaches through better empirical validation should yield more precise recommendations for ways to optimally prevent the long-distance spread of invasive forest pests

Spatial correlation as an early warning signal of regime shifts in a multiplex disease-behaviour network

The final publication is available at Elsevier via https://doi.org/10.1016/j.jtbi.2018.03.032. © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/Early warning signals of sudden regime shifts are a widely studied phenomenon for their ability to quantify a system’s proximity to a tipping point to a new and contrasting dynamical regime. However, this effect has been little studied in the context of the complex interactions between disease dynamics and vaccinating behaviour. Our objective was to determine whether critical slowing down (CSD) occurs in a multiplex network that captures opinion propagation on one network layer and disease spread on a second network layer. We parameterized a network simulation model to represent a hypothetical self-limiting, acute, vaccine-preventable infection with short-lived natural immunity. We tested five different network types: random, lattice, small-world, scale-free, and an empirically derived network. For the first four network types, the model exhibits a regime shift as perceived vaccine risk moves beyond a tipping point from full vaccine acceptance and disease elimination to full vaccine refusal and disease endemicity. This regime shift is preceded by an increase in the spatial correlation in non-vaccinator opinions beginning well before the bifurcation point, indicating CSD. The early warning signals occur across a wide range of parameter values. However, the more gradual transition exhibited in the empirically-derived network underscores the need for further research before it can be determined whether trends in spatial correlation in real-world social networks represent critical slowing down. The potential upside of having this monitoring ability suggests that this is a worthwhile area for further research.Natural Sciences and Engineering Research Council of Canad

Outlook On A Worldwide Forest Transition

It is not clear whether a worldwide "forest transition" to net reforestation will ever occur, and the need to address the main driver-agriculture-is compelling. We present a mathematical model of land use dynamics based on the world food equation that explains historical trends in global land use on the millennial scale. The model predicts that a global forest transition only occurs under a small and very specific range of parameter values (and hence seems unlikely) but if it does occur, it would have to occur within the next 70 years. In our baseline scenario, global forest cover continues to decline until it stabilizes within the next two centuries at 22% of global land cover, and wild pasture at 1.4%. Under other scenarios the model predicts unanticipated dynamics wherein a forest transition may relapse, heralding a second era of deforestation; this brings into question national-level forest transitions observed in recent decades, and suggests we need to expand our lexicon of possibilities beyond the simple "forest transition/no forest transition" dichotomy. This research also underscores that the challenge of feeding a growing population while conserving natural habitat will likely continue for decades to come.Natural Sciences and Engineering Council of Canad

The Impact Of Human-Environment Interactions On The Stability Of Forest-Grassland Mosaic Ecosystems

Forest-grassland mosaic ecosystems can exhibit alternative stables states, whereby under the same environmental conditions, the ecosystem could equally well reside either in one state or another, depending on the initial conditions. We develop a mathematical model that couples a simplified forest-grassland mosaic model to a dynamic model of opinions about conservation priorities in a population, based on perceptions of ecosystem rarity. Weak human influence increases the region of parameter space where alternative stable states are possible. However, strong human influence precludes bistability, such that forest and grassland either co-exist at a single, stable equilibrium, or their relative abundance oscillates. Moreover, a perturbation can shift the system from a stable state to an oscillatory state. We conclude that human-environment interactions can qualitatively alter the composition of forest-grassland mosaic ecosystems. The human role in such systems should be viewed as dynamic, responsive element rather than as a fixed, unchanging entity.Natural Sciences and Engineering Research Council of Canada (NSERC

Interconnections accelerate collapse in a socio-ecological metapopulation

Resource over-exploitation can have profound effects on both ecosystems and the human populations residing in them. Models of population growth based on a depletable resources have been studied previously, but relatively few consider metapopulation effects. Here we analyze a socio-ecological metapopulation model where resources grow logistically on each patch. Each population harvests resources on its own patch to support population growth, but can also harvest resources from other patches when their own patch resources become scarce. We find that allowing populations to harvest from other patches significantly accelerates collapse and also increases the parameter regime for which collapse occurs, compared to a model where populations are not able to harvest resources from other patches. As the number of patches in the metapopulation increases, collapse is more sudden, more severe, and occurs sooner. These effects also persist under scenarios of asymmetry and inequality between patches. We conclude that metapopulation effects in socio-ecological systems can be both helpful and harmful and therefore require urgent study.NSERC Discovery Gran

Dynamics Of The Global Wheat Trade Network And Resilience To Shocks

Agri-food trade networks are increasingly vital to human well-being in a globalising world. Models can help us gain insights into trade network dynamics and predict how they might respond to future disturbances such as extreme weather events. Here we develop a preferential attachment (PA) network model of the global wheat trade network. We find that the PA model can replicate the time evolution of crucial wheat trade network metrics from 1986 to 2011. We use the calibrated PA model to predict the response of wheat trade network metrics to shocks of differing length and severity, including both attacks (outward edge removal on high degree nodes) and errors (outward edge removal on randomly selected nodes). We predict that the network will become less vulnerable to attacks but will continue to exhibit low resilience until 2050. Even short-term shocks strongly increase link diversity and cause long-term structural changes that influence the network's response to subsequent shocks. Attacks have a greater impact than errors. However, with repeated attacks, each attack has a lesser impact than the previous attack. We conclude that dynamic models of multi-annual, commodity-specific networks should be further developed to gain insight into possible futures of global agri-food trade networks.Natural Sciences and Engineering Research Council (NSERC)NSERCUniversity of Guelp