Space in Unified Models of Economy and Ecology or... ? Space: The final frontier A. Xepapadeas* University of Crete, Department of Economics * Research presented in this lecture has been conducted jointly with William Brock.

Economics studies how human societies use scarce resources to produce commodities and distribute them among their members. Ecology is the study of living species, such as animals, plants and micro-organisms and the relations among themselves and their natural environment. An ecosystem includes these species and their nonliving environment, their interactions and evolution in time and space. Human economies and natural ecosystems are inexorably linked, but economic models and ecological models are not usually linked. Ecological economics aims at providing this link.

Economic and ecological systems evolve in time and space. Interactions take place among units occupying distinct spatial points. Thus geographical patterns of production activities, urban concentrations, or species concentrations occur. My purpose is: to discuss approaches for modeling, in a meaningful way, economic and ecological processes evolving in space time. to examine mechanism under which a spatially homogenous state – a flat landscape – acquires a spatial pattern. to examine how this pattern evolves in space-time.

The emergence of spatial patterns in economics has received relatively little systematic analysis, with the notable exception of the new economic geography. Spatial patterns in human economies are profound... Spatial Patterns

Spatial Analysis in Economics However spatial analysis was not given sufficient attention until the early 1990s Main ideas in location theory rely on economies of scale that enforce geographical concentrations Inability of earlier research to work with tractable models of imperfect competition which is implied by unexhausted economies of scale.

In a homogeneous environment with transportation costs but no returns to scale, spatial patterns of economic activity cannot emerge. Economic activity should spread evenly across space to minimize transportation costs. Need for increasing returns to generate spatial patterns Need to model imperfect competition Increasing returns/Imperfect competition – New Industrial Organization – New Trade Theory – New Growth Theory – New Economic Geography

The Racetrack Economy* Many regions equally spaced around the circumference of a circle Transportation takes place around the circumferences From a spatially homogeneous – flat – initial distribution of manufacturing activities, a perturbation generates a spatial structure. Manufacturing is concentrated in two regions. What is the mechanism that generates this spatial pattern? *M. Fujita, P. Krugman and A. Venables, The Spatial Economy, MIT Press 2001.

Paul Krugman, “Space: The Final Frontier” Journal of Economic Perspectives, Vol. 12, 2, 1998, pp

Spatial Analysis in Ecology Pattern formation and the emergence of spatial patterns have received relatively more attention in ecology. Morphogenesis is the study of patterns and form, e.g.: – Mammalian coat patterns – Butterfly wing patterns Spatial patterns in resources. Spatial patterns of species. The concept of diffusion has been used in ecological modeling to explain spatial pattern formation in ecological systems.

How the leopard got its spots

Spatial patterns in Kilimanjaro

Chlorophyll concentrations in oceans

Locust distribution in Australia

Modelling Diffusion Biological resources tend to disperse in space and time under forces promoting "spreading" or "concentrating" (Okubo, 2001); these processes along with intra and inter species interactions induce the formation of spatial patterns. Economic activities also tend to disperse in space and time. Flows of capital, labour, commodities, resources Spatial issues in economic-ecological problems: – resource management in patchy environments (Sanchirico and Wilen 1999, 2001; Sanchirico 2004; Brock and Xepapadeas 2002) – the study of control models for interacting species (Lenhart and Bhat 1992, Lenhart et al. 1999) – the control of surface contamination in water bodies (Bhat et al. 1999)

A central concept in modelling the dispersal of biological or economic resources is that of diffusion. Diffusion is defined as a process where the microscopic irregular movement of particles such as cells, bacteria, chemicals, animals, or commodities, results in some macroscopic regular motion of the group (Okubo and Levin 2001; Murray 1993, 2003). Diffusion is based on random walk models, which when coupled with population growth equations or capital accumulation equations lead to general reaction-diffusion systems.

In general a diffusion process in an ecosystem tends to produce a uniform population density, that is spatial homogeneity. Thus it might be expected that diffusion would "stabilize" ecosystems where species disperse and humans intervene through harvesting. There is however one exception known as diffusion induced instability, or diffusive instability (Okubo et al. 2001). Alan Turing (1952) suggested that under certain conditions reaction-diffusion systems can generate spatially heterogeneous patterns. This is the so- called Turing mechanism for generating diffusion instability.

Emergence of Spatial Patterns We examine conditions under which the Turing mechanism induces diffusive driven instability and creates heterogeneous spatial patterns in Economic/Ecological models. This is a different approach to the one most commonly used to address spatial issues, which is the use of metapopulation models in discrete patchy environments with dispersal among patches.

Thus the Turing mechanism can be used to uncover conditions which generate spatial heterogeneity in models where ecological variables interact with economic variables. When spatial heterogeneity emerges, the concentration of variables of interest (e.g. resource stock and level of harvesting effort), in a steady state, are different in different locations of a given spatial domain. Once the mechanism is uncovered, the impact of regulation in promoting or eliminating spatial heterogeneity can also be analyzed.

A Bioeconomic Model

The Turing Mechanism The Turing mechanism implies that the spatially homogeneous steady state can be destabilized by a spatial perturbation depending on Condition for diffusive instability

Spatial Pattern 0 α/2 α z x>x * x<x * Figure 1

t z x λ=0.5

t z x λ=-0.5

Capital Accumulation and Pollution Accumulation* * Based on current research of S. Levin and A. Xepapadeas

The spatially homogeneous capital- pollution steady state can be destabilized by diffusive or Turing instability if: In this case we have a spatially heterogeneous pattern of capital accumulation (economic activity) and pollution accumulation But we require α 11 >1, increasing returns

Control of Bioinvasions

Figure 2

Wavefront Solution t z

z Wavefront Solution (1/a) = 0.5 ; 0.48

Conclusions This paper develops methods of analyzing spatial dynamical ecological/economic systems. In particular the Turing mechanism for diffusive instability is adopted to bioeconomic problems The potential power of the method is shown in the analysis of spatial pattern formation in –A resource management problem –A spatial growth under pollution accumulation problem –A bioinvasion control problem

Regulation Issues In the resource management problem and the growth pollution problem, spatial pattern creation is possible. –Spatial pattern creation may have welfare implications regarding the spatial distribution of welfare. –Regulation can eliminate spatial patterns and induce spatial homogeneity.

Control of Bioinvasions –When benefits and costs are equated across sites, the invasion could take the form of a travelling wave. –Regulation affects the wave's speed and the spatially homogeneous stable carrying-capacity biomass of the invasive species.

We are living in a spatially heterogeneous world.. The modeling approach presented here might help in gaining some new insights into the interrelations between ecological systems and human economies and might provide a basis for more efficient regulation of environmental externalities in the space – time continuum