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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.

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Space in unified models of economy and ecology or space the final frontier

Space in Unified Models of Economy and Ecologyor . . . ?Space: The final frontier

A. Xepapadeas*

University of Crete, Department of Economics

*Research presented in this lecture has been conducted jointly with William Brock.


Space in unified models of economy and ecology or space the final frontier

  • 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.


Space in unified models of economy and ecology or space the final frontier

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.


Spatial patterns
Spatial Patterns Interactions take place among units occupying distinct spatial points. Thus geographical patterns of production activities, urban concentrations, or species concentrations occur. My purpose is:

  • 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 analysis in economics
Spatial Analysis in Economics Interactions take place among units occupying distinct spatial points. Thus geographical patterns of production activities, urban concentrations, or species concentrations occur. My purpose is:

  • 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.


Space in unified models of economy and ecology or space the final frontier

  • 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
The Racetrack Economy* no returns to scale, spatial patterns of economic activity cannot emerge. Economic activity should spread evenly across space to minimize transportation costs.

  • 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.


Space in unified models of economy and ecology or space the final frontier

Paul Krugman, “Space: The Final Frontier” no returns to scale, spatial patterns of economic activity cannot emerge. Economic activity should spread evenly across space to minimize transportation costs.Journal of Economic Perspectives, Vol. 12, 2, 1998, pp. 161-174


Spatial analysis in ecology
Spatial Analysis in Ecology no returns to scale, spatial patterns of economic activity cannot emerge. Economic activity should spread evenly across space to minimize transportation costs.

  • 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
How the leopard got its spots no returns to scale, spatial patterns of economic activity cannot emerge. Economic activity should spread evenly across space to minimize transportation costs.


Spatial patterns in kilimanjaro
Spatial patterns in Kilimanjaro no returns to scale, spatial patterns of economic activity cannot emerge. Economic activity should spread evenly across space to minimize transportation costs.


Chlorophyll concentrations in oceans
Chlorophyll concentrations in oceans no returns to scale, spatial patterns of economic activity cannot emerge. Economic activity should spread evenly across space to minimize transportation costs.


Locust distribution in australia
Locust distribution in Australia no returns to scale, spatial patterns of economic activity cannot emerge. Economic activity should spread evenly across space to minimize transportation costs.


Modelling diffusion
Modelling Diffusion no returns to scale, spatial patterns of economic activity cannot emerge. Economic activity should spread evenly across space to minimize transportation costs.

  • 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)


Space in unified models of economy and ecology or space the final frontier

  • 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.


Space in unified models of economy and ecology or space the final frontier

  • 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
Emergence 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. 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.


Space in unified models of economy and ecology or space the final frontier

  • 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
A Bioeconomic Model 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.


The turing mechanism
The Turing Mechanism 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.

  • 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

* 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.

x>x

*

x<x

0

α

α/2

z

Spatial Pattern

Figure 1


Space in unified models of economy and ecology or space the final frontier

x 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.

t

λ=0.5

z


Space in unified models of economy and ecology or space the final frontier

x 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.

t

λ=-0.5

z


Capital accumulation and pollution accumulation
Capital Accumulation and Pollution Accumulation* 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.

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


Space in unified models of economy and ecology or space the final frontier


Control of bioinvasions
Control of Bioinvasions be destabilized by diffusive or Turing instability if:


Space in unified models of economy and ecology or space the final frontier

Figure 2 be destabilized by diffusive or Turing instability if:


Space in unified models of economy and ecology or space the final frontier

Wavefront be destabilized by diffusive or Turing instability if:

Solution

t

z


Space in unified models of economy and ecology or space the final frontier

Wavefront be destabilized by diffusive or Turing instability if:

Solution

z

(1/a) = 0.5 ; 0.48


Conclusions
Conclusions be destabilized by diffusive or Turing instability if:

  • 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


Space in unified models of economy and ecology or space the final frontier

Regulation Issues be destabilized by diffusive or Turing instability if:

  • 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.


Space in unified models of economy and ecology or space the final frontier

  • Control of Bioinvasions be destabilized by diffusive or Turing instability if:

    • 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.


Space in unified models of economy and ecology or space the final frontier

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