Michael Monticino

Coupled human and natural systems: A multi-agent-based approach

A major force affecting many forest ecosystems is the encroachment of residential, commercial and industrial development. Analysis of the complex interactions between development decisions and ecosystems, and how the environmental consequences of these decisions influence human values and subsequent decisions will lead to a better understanding of the environmental consequences of private choices and public policies. Determining conditions of the interactions between human decisions and natural systems that lead to long-term sustainability of forest ecosystems is one goal of this work. Interactions between human stakeholders are represented using multi-agent models that act on forest landscape models in the form of land-use change. Feedback on the effects of these actions is received through ecological habitat metrics and hydrological responses. Results are presented on the dynamics of land-use change under different growth management strategies based on an area of the Dallas-Fort Worth (Texas, U.S.A.) region facing intense residential development.

Assessing physiological complexity.

SUMMARY Physiologists both admire and fear complexity, but we have made relatively few attempts to understand it. Inherently complex systems are more difficult to study and less predictable. However, a deeper understanding of physiological systems can be achieved by modifying experimental design and analysis to account for complexity. We begin this essay with a tour of some mathematical views of complexity. After briefly exploring chaotic systems, information theory and emergent behavior, we reluctantly conclude that, while a mathematical view of complexity provides useful perspectives and some narrowly focused tools, there are too few generally practical take-home messages for physiologists studying complex systems. Consequently, we attempt to provide guidelines as to how complex systems might be best approached by physiologists. After describing complexity based on the sum of a physiological systems structures and processes, we highlight increasingly refined approaches based on the pattern of interactions between structures and processes. We then provide a series of examples illustrating how appreciating physiological complexity can improve physiological research, including choosing experimental models, guiding data collection, improving data interpretations and constructing more rigorous system models. Finally, we conclude with an invitation for physiologists, applied mathematicians and physicists to collaborate on describing, studying and learning from studies of physiological complexity.

Biocomplexity and conservation of biodiversity hotspots: three case studies from the Americas

The perspective of ‘biocomplexity’ in the form of ‘coupled natural and human systems’ represents a resource for the future conservation of biodiversity hotspots in three direct ways: (i) modelling the impact on biodiversity of private land-use decisions and public land-use policies, (ii) indicating how the biocultural history of a biodiversity hotspot may be a resource for its future conservation, and (iii) identifying and deploying the nodes of both the material and psycho-spiritual connectivity between human and natural systems in service to conservation goals. Three biocomplexity case studies of areas notable for their biodiversity, selected for their variability along a latitudinal climate gradient and a human-impact gradient, are developed: the Big Thicket in southeast Texas, the Upper Botanamo River Basin in eastern Venezuela, and the Cape Horn Archipelago at the austral tip of Chile. More deeply, the biocomplexity perspective reveals alternative ways of understanding biodiversity itself, because it directs attention to the human concepts through which biodiversity is perceived and understood. The very meaning of biodiversity is contestable and varies according to the cognitive lenses through which it is perceived.

Randomly generated distributions

A new scheme for randomly generating probability distributions on the interval [0, 1] is introduced. The scheme can also be viewed as a way to generate homeomorphisms at random. Conditions are given so that a continuous measure with full support is generated almost surely. Geometric properties of the generated probability measures are examined, including the dimension and derivative structure of the measures and their respective distribution functions. For example, we give conditions so that almost all the distribution functions of the measures generated are strictly singular. Applications include determining average case errors for numerical methods of equation solving and Bayesian statistics.

Constructing prior distributions with trees of exchangeable processes

Abstract This paper introduces a scheme for constructing prior distributions on a space of probability measures using a tree of exchangeable processes. The exchangeable tree scheme provides a natural generalization of the Polya tree priors presented by Mauldin et al. (1992) . Exchangeable tree priors provide useful conjugate families of priors for statistical models in which an experiment proceeds in several stages with each stage dependent on the previous outcomes. The exchangeable tree construction has some advantages over other constructions. For instance, exchangeable tree priors can give probability one to the set of continuous measures unlike, say, Dirichlet processes. Moreover, the scheme’s perspective is both a conceptual aid in sampling applications and a useful tool in deriving properties of the priors. The exchangeable tree scheme also gives an alternate way of constructing the random rescaling priors defined by Graf et al. (1986) and more generally by Mauldin and Monticino (1995) . Here, some basic properties of exchangeable tree priors are developed and connections with other schemes – in particular, with random rescaling – for constructing priors are established.

Biocomplexity in the Big Thicket

Introduction: Overview of the Big Thicket and BiocomplexityThe Big Thicket is an ill-defined region of southeast Texas on the coastal plain of theGulf of Mexico between the Trinity and Sabine rivers, not far from Houston.Because the biological-diversity index of the area is one of the highest in NorthAmerica, the Big Thicket National Preserve (BTNP)—an archipelago of isolatedconservation ‘units’ administered by the US National Park Service—was establishedin 1974. The BTNP is located in a matrix of privately owned timberland, small farms,and a few small towns. The major human impacts on the region, beginning in the late19th century and continuing into the 21st, have been logging and milling by largeindustrial timber operations and oil and gas extraction. Because of its proximity tothe refineries of Port Arthur and the city of Beaumont and the steady increase in theavailability of automobiles after World War II, residential development has alsobeen a major impact in the region—and now represents the most potent driver ofland-use/land-cover change.Few ecosystems are now free of extensive human influence. However, the wayhuman activity affects natural systems and the way those anthropogenic changes innatural systems reciprocally affect human behavior is poorly understood. Therefore,the aggregate impact of the several decisions of private persons, corporations, andgovernments to buy and sell land, to explore for minerals, to harvest timber, to buildhomes, strip malls, factories, and roads is only perceptible after the fact. Detailedprediction of anthropogenic land-use/land-cover change is impossible with currenttools. However, computer models can simulate the complex interactions betweenhuman and natural systems reliably enough to enable stakeholders and policy

The adequacy of universal strategies in analystic gambling problems

Suppose measurability structures are imposed upon a Dubins and Savage gambling problem. A long-standing question asks whether strategies which are measurable with respect to these structures enable the gambler to maximize his return. Measurable strategies have the advantage over arbitrary strategies in that they induce countably additive probability measures. In this work, we show that measurable strategies are adequate in order to maximize return if and only if the optimal return function is measurable. Using this result, several examples of gambling problems for which measurable strategies are adequate are given.

Optimal cutoff strategies in capacity expansion problems

Capacity expansion refers to the process of adding facilities or manpower to meet increasing demand. Typical capacity expansion decisions are characterized by uncertain demand forecasts and uncertainty in the eventual cost of expansion projects. This article models capacity expansion within the framework of piecewise deterministic Markov processes and investigates the problem of controlling investment in a succession of same type projects in order to meet increasing demand with minimum cost. In particular, we investigate the optimality of a class of investment strategies called cutoff strategies. These strategies have the property that there exists some undercapacity level M such that the strategy invests at the maximum available rate at all levels above M and does not invest at any level below M. Cutoff strategies are appealing because they are straightforward to implement. We determine conditions on the undercapacity penalty function that ensure the existence of optimal cutoff strategies when the cost of completing a project is exponentially distributed. A by-product of the proof is an algorithm for determining the optimal strategy and its cost.