Schedule for: 21w5191 - Mathematics of Human Environmental Systems (Online)

A brief introduction video from BIRS staff with important logistical information

Human-ecological Interactions - Introduction by the Organizers

Illegal logging is a serious threat to plantations in the tropics. Here, we study the coupled dynamics of Social-Ecological systems shedding light of two different aspects. [1] We examined the roles of profit-sharing in plantation management strategy in a dynamic game model. The model assumes that the owner chooses the age of the trees to be harvested and the local people choose their level of monitoring effort to prevent illegal logging with surveillance. After the trees are removed, the owner hires local people to replant young trees. Dynamic optimization analysis revealed that, under the pressure of illegal logging, the owner may find it profitable to share harvesting profits with the local people to enhance their surveillance effort. The profit-sharing rate optimal to the owner depends on the rate of natural disturbance, faster future discount rate, and a higher cost of replanting. [2] Cooperation can be sustained by institutions that punish free-riders. Such institutions, however, tend to be subverted by corruption if they are not closely watched. Monitoring can uphold the enforcement of binding agreements ensuring cooperation, but this usually comes at a price. The temptation to skip monitoring and take the institution’s integrity for granted leads to outbreaks of corruption and the breakdown of cooperation. We model the corresponding mechanism by means of evolutionary game theory, using analytical methods and numerical simulations, and find that it leads to sustained or damped oscillations. The results confirm the view that corruption is endemic and transparency a major factor in reducing it. Lee, J-H., Y. Kubo, T. Fujiwara, R.M. Septianad, S. Riyantod, and Y. Iwasa. 2018. Profit sharing as a management strategy for a state-owned teak plantation at high risk for illegal logging. Ecological Economics 149, 140-148. Lee, J-H, Y. Iwasa, U. Dieckmann, and K. Sigmund. 2019 Social evolution leads to persistent corruption. PNAS 116, 13276-13281.

Cyanobacterial (CB) blooms are becoming a global concern due to the increasing prevalence of eutrophication. The dependence of CB dynamics on phosphorus and light inputs is modeled via a stoichiometric approach and the transient dynamics are discussed. We then couple the CB model to a socio-economic model governing the anthropogenic nutrient inputs. We assume that the human population is made up of cooperators and defectors and that each strategy has an associated cost dependent on social pressure and norms, concern for CB, and effort. We find that the human population at a single lake exhibits bistability. Further, in considering a network of lakes the level of cooperation is highly dependent on social norms.

Please turn on your cameras for the "group photo" -- a screenshot in Zoom's Gallery view.

Infectious disease modeling efforts are emblematic of the challenges of modeling coupled human-environmental systems. These challenges exist conceptually, theoretically, and empirically, and are made more challenging by disciplinary norms. COVID-19 has pumped substantial amounts of energy into interdisciplinary and multidisciplinary approaches to epidemiological modeling. However, I see many of the over-simplifications, related to challenges we have struggled with for over 10 years, finding their way into high profile reports and publications that are guiding policy response. The challenges start with implicit disciplinary disagreement about what is being modeled and why. They are further complicated by scaling issues, which are tightly connected to disciplinary views of model assessment that point back to the reasons for modeling. In this talk, I will describe my lessons learned and outline a research program for couple human-epidemiological modeling going forward with the goal of providing insights for other human-environmental modeling and for public health.

CHANS models frequently incorporate the human component using a game theoretic framework. In this work, we present a different approach where opinion dynamics are modeled explicitly, giving us access to social behaviours such as amplification and polarization. We study the behaviour of the opinion dynamics in isolation, and then couple them to disease dynamics to study the interaction between the two. We propose that our approach allows for the inclusion of human behaviours that are difficult to access via traditional CHANS modelling, and that might have important consequences for the management of ecological systems. Co-Authors: Noah Marshall, Stephen M. Krone, Bert O. Baumgaertner

Human behavior can be modeled by describing, on a collective level, the adoption of certain strategies by individual agents. Many models use either the replicator dynamics (RD) or the logit formulation of the best-response (BR). How do RD and BR differ, and does the distinction matter? This talk gives a brief overview of the two behavioral models, both of which originate from evolutionary game theory. Their differences are illustrated in the context of a social-ecological model for eutrophication in shallow lakes, where the anthropogenic discharge of pollutants into the water is determined by RD or BR. It will be shown that the replicator equation is a limit case of the best-response model, when agents are assumed to behave with infinite rationality. If agents act less rationally in BR, the correspondence with RD decreases; the two model versions can differ substantially regarding the number of possible equilibria, the potential for multistability, and the type of sustained oscillations. Consequently, the choice of the behavioral model may profoundly affect the overall dynamics of a coupled human-environment system and deserves careful consideration. Joint work with Anthony Sun

If sustainable harvesters could benefit more than the unsustainable ones, even in the short term, the overharvesting problem in ecosystem would be solved. However, it is not an easy task. There is a special case: swiftlets in Sarawak, Malaysia, where sustainable harvesters are believed to obtain a more return than unsustainable harvesters in the short term. Edible nests built by adult swiftlets are used as ingredients for a Chinese traditional soup. There is a local knowledge that, once unsustainable harvesters harvest the nests on the cave ceilings, swiftlets escape from the cave and never come back to the same place. This ecological behavior works as the swiftlet's indirect punishment against unsustainable harvesters. We make a stage-structured population model and examines the effect of property rights and the indirect punishment by swiftlets on the population dynamics of the swiftlets, and on the short-term return of both sustainable and unsustainable harvesters. Following are our findings: both the indirect punishment by swiftlets and the property rights system are required to provide sustainable harvesters with a higher short-term return than unsustainable harvesters. We would like to discuss the possibility to apply this model to other ecosystem managements.

Landscape change is the outcome of both natural and anthropogenic disturbances. Natural disturbances (e.g., forest fires, land slides, and floods) are episodic and stochastic events that occur across a wide range of spatial and temporal scales. Anthropogenic disturbances (e.g., forest clearance for agriculture, timber harvest, or pasture) also occur at various temporal and spatial scales, but often at a faster rate and a more extensive scale than natural disturbances. Deforestation is especially an important environmental problem because of its impact on biodiversity, carbon cycling associated with global climate, biogeochemical cycling, and other ecosystem functions. A key factor inducing landscape change is the human behavior that underlies these changes. The simplest way to consider this is to develop a model which traces the responses of landowners to the change of socioeconomic and ecological conditions. We introduce a Markov chain model for land-use dynamics in a forested landscape [1─4]. The model emphasizes the importance of coupling socioeconomic and ecological processes underlying landscape changes. References [1] Satake A, Iwasa Y (2006) Coupled ecological and social dynamics in a forested landscape: the deviation of the individual decisions from the social optimum. Ecological Research 21, 370–379. [2] Satake A, Rudel TK (2007) Modelling the forest transition: forest scarcity and ecosystem service hypotheses. Ecological Applications 17, 2024–2036. [3] Satake A, Janssen MA, Levin SA, Iwasa Y (2007) Collective deforestation induced by social learning under uncertainty of forest-use value. Ecological Economics 63, 452–462. [4] Satake A, Rudel TK, Onuma A (2008) Scale mismatches and their ecological and economic effects on landscapes: a spatially explicit model. Global Environmental Change 18, 768–775.

I will show how understanding transient behavior is important in the management of ecological systems and discuss recent results that provide a general framework for understanding transient dynamics. The simplest transients arise in linear systems, where the cessation of fishing after implementation of a marine reserve provides an example which is both illustrative and important. I will discuss how dynamics after or near a ‘tipping point’ are another key example. More generally, I will show how human-environmental systems are typically a mix of different time scales which makes transients likely. I will emphasize how the need to understand dynamics on different time scales makes an understanding of transients essential, and illustrate this and other aspects with examples.

Modelling coupled human-environment systems is becoming an increasingly urgent research priority. Coupling human dynamics to environmental dynamics in mathematical models introduces higher dimensionality and thus novel dynamics. This creates both challenges and opportunities for predicting critical transitions with early warning signals based on effects like critical slowing down. In this talk, I will summarize work that shows how feedback from human systems can muffle early warning signals of collapse in an environmental system; how feedback can ‘doom’ a human-environment system to self-evolved criticality; how timescale differences mean that early warning signals of human-environment collapse can be more apparent in the human system than the environment system; and how machine learning algorithms, in concert with dynamical systems insights, can be used to enhance our ability to provide early warning of such transitions.

Eco-evolutionary game theory provides a framework for the analysis of human-environmental dynamics. In an eco-evolutionary game, strategies of individuals impact the environment and the state of the environment alters the payoff structure that individuals face, generating feedback. This feedback can lead to persistent cyclical environmental overshoot. In the model of eco-evolutionary games that I will present, we examine the impact of environmental forecasting on cyclic human-environmental dynamics. We find that if individuals make forecasts of the environment and integrate these forecasts into their strategy updating process, environmental stability can be achieved. Next, I will share a model of competition between forecasting and non-forecasting types in a human-environmental system to explore whether forecasting types can invade and generate environmental stability. Coauthors: Vitor Vasconcelos, Erol Akcay, Joshua Plotkin

Humans shape nearly every aspect of our environment, from purposeful elimination of rural predators to the altered soil chemistry of urban settings. These changes have both direct and indirect effects on the evolution and ecology of pathogens. In this talk, we will touch briefly on the obvious, direct efforts to control pathogen systems (e.g., antibiotics use) and then spend the majority of time discussing indirect impacts of modern human systems that can profoundly impact the evolution and ecology of pathogens. We will discuss a few toy models that highlight these effects and discuss a potential framework for understanding the cascading impacts and bidirectional feedbacks between humans and the pathogen landscape in which we live.

A novel probabilistic approach is presented for obtaining the probability distribu- tion of infection time for SI disease epidemics on a finite network specified as a fixed weighted digraph. Individuals (network nodes) are classified as either susceptible or infectious, with transmission rates along weighted network arcs. The model is ap- propriate for diseases with no recovery, or for the initial outbreak of diseases with recovery. Our method to analyze the model yields the exact probability distribution for the time at which a given individual in the network becomes infected. This can also be used to compute the probability that any given individual is infected as well as the expected number of infectious individuals at any time. Examples of simple networks illustrate the utility of the method. Nodes can also be identified more generally, such as farms or cities, and the method can be applied to biological networks with estimated transmission rates on the network arcs.

We investigate the dynamics of epidemiological bifurcations in systems where individuals optimally alter behavior in the face of endogenous disease risk. The bifurcations can lead to aggregate instability, which introduces the potential for less predictable outcomes from public health policies and welfare losses. For instance, health policies designed to lower the transmission probability or policies designed to raise the quality-of-life following infection generate endogenous human responses that may push endemic equilibria from being stable to exhibiting instability or indeterminacy with the possibility of unintended consequences from public health policy.

It is becoming increasingly clear that humans and ecosystems form a single, coupled human-environment system (HES) where humans not only cause negative ecosystem impacts, but also react to them. Humans have highly diverse identities and complex social structures that affect our decision-making. We also have the ability to modify our environments (and those of other organisms) in ways fundamentally different from what other organisms do. This can lead to shifts in norms in how humans use, abuse and/or protect ecological systems and in turn feedback on human behaviour. Despite this, there are still far fewer examples of coupled mathematical models of human and ecological systems than mathematical models of ecological systems themselves. We will present recent case studies in human-environment systems from our own work in forest pest and climate change mitigation. I discuss the challenges of this kind of research and suggest areas and pathways through which mathematical models of human-environment sustainability could be enhanced in future research.

While climate models have rapidly advanced in sophistication over recent decades, they lack dynamic representation of human behavior and social systems despite strong feedbacks between social processes and climate. The impacts of climate change alter perceptions of risk and emissions behavior that, in turn, influence the rate and magnitude of climate change. Addressing this deficiency in climate models requires a substantial interdisciplinary effort to couple models of climate and human behavior. I will discuss efforts by a group of highly-interdisciplinary collaborators to create linked models of human behavior, risk perception and global climate. Our results indicate that inclusion of human behavioral change arising from the perception and experience of extreme events could have large impacts on temperature trajectories. Furthermore, uncertainties in global temperature trajectories arising from impacts of human behavior are similar in magnitude to those arising from uncertainties of the physical components of climate models.

The agricultural establishment has made significant progress in its efforts to improve agricultural productivity and efficiency. Yet, with about one billion people hungry, two billion people with insufficient nutrients, and over two billion people already overweight or obese, undernutrition and malnutrition are affecting more than half the world's population. Clearly, when enough food is produced but sizable fractions of the population suffer from malnutrition or are overweight, we need to get a better understanding of the global food system. In this talk, I will describe some recent efforts at modeling food systems and highlight research issues for MPE. (Joint work with Hans Engler, Georgetown University)

Concluding Remarks by the Organizers