Edward Ullman identified three bases of spatial interaction. They are:

Complementarity, intervening opportunity and transferability

Connectivity, accessibility and diameter

Push, pull and intervening obstacles

Complementarity, intervening opportunity and transferability

A city stops buying timber from a distant region once a nearer forest region begins supplying the same timber. In Ullman's terms this illustrates:

Distance decay in the gravity model

A transport network with a beta index (e ÷ v) of less than 1 is:

A branching tree or a disconnected network with no circuits

A complete network in which every pair of nodes is linked

A highly connected network with many circuits

A network with exactly one circuit

In a transport network, the node with the lowest Shimbel index is:

The node at the end of the network's diameter

In a gravity model with a distance exponent of 2, doubling the distance between two cities of fixed size changes the predicted interaction to:

One-quarter of its former value

The World Trade Organisation came into existence on 1 January 1995 as the successor to:

The Organisation for Economic Co-operation and Development

The United Nations Conference on Trade and Development

The International Monetary Fund

Which of the following are core non-discrimination principles of the WTO? Select all that apply.

Fixed exchange rates among members

Export subsidies for all manufactured goods

Assertion (A): In Taaffe, Morrill and Gould's model of transport development, the first stage consists of scattered small ports along the coast. Reason (R): Colonial transport lines were built to carry primary produce from the interior to the ports. Choose the correct option.

Both A and R are true, but R is not the correct explanation of A

Both A and R are true, and R is the correct explanation of A

Both A and R are true, but R is not the correct explanation of A

Geography of Transport and Trade: Spatial Interaction (Ullman and Hurst), Connectivity and Accessibility, Gravity Models, the WTO and World Trade Patterns

The transport-and-trade block of Unit VI names theories and models of spatial interaction (Edward Ullman and M.E. Hurst); measures and indices of connectivity and accessibility; spatial flow models — the gravity model and its variants; the World Trade Organisation; globalisation, liberalisation and world trade patterns; and the problems and prospects of inter- and intra-regional cooperation and trade. It is the most arithmetic block of Unit VI: the graph-theoretic indices of Kansky and the gravity and breaking-point formulas are all worked through here with numbers.

1. Theories and models of spatial interaction: Ullman and Hurst

Edward L. Ullman ("The Role of Transportation and the Bases for Interaction", 1956) asked why goods, people and information move between some places and not others, and answered with three bases. Complementarity: one place must have a surplus of something that another place demands — regional differences in resources, climate or specialisation create it. Intervening opportunity (a concept Ullman borrowed from Stouffer): an alternative source or destination lying between two complementary places diverts interaction, so the Pacific Northwest might ship timber to California only as long as no nearer forest could supply it. Transferability: the movement must be possible at an acceptable cost and time — distance is measured not in kilometres but in the real cost of transfer, and a good whose transport cost is too high relative to its value will not move however complementary the places.

The document pairs Ullman with M.E. (Michael Eliot) Hurst, whose A Geography of Economic Behavior (1972) and edited Transportation Geography: Comments and Readings (1974) placed transport within a behavioural approach to economic geography. In that approach movement is a decision taken on perceived as well as actual costs and opportunities, flows depend on the structure of the network through which they pass, and the geography of transport is the study of spatial interaction as a whole rather than of routes and carriers alone. A widely used companion model is that of Taaffe, Morrill and Gould (1963), drawn from Ghana and Nigeria, on how transport networks grow in a developing economy:
(1) scattered ports along the coast with small hinterlands;
(2) penetration lines built inland to mines and cash-crop areas, and the ports at their heads grow at the expense of others;
(3) feeder routes and lateral links develop, and interconnection begins;
(4) a fully interconnected network with high-priority trunk routes between the main centres.

⚠️ Intervening opportunity is not intervening obstacle

Ullman's intervening opportunity (from Stouffer) is an alternative place that captures the flow; Lee's intervening obstacle, in migration theory, is a barrier such as distance, cost or law that impedes it. Both reduce interaction between two places, but by different mechanisms, and questions pair them deliberately.

2. Measures and indices of connectivity and accessibility

K.J. Kansky (Structure of Transportation Networks, 1963) applied graph theory to transport networks, reducing them to vertices (nodes: towns, junctions), edges (links: road or rail segments) and sub-graphs (separate, unconnected parts). For a connected planar network with v vertices, e edges and p sub-graphs, the standard indices are set out below. Worked example: a road network with v = 10 towns and e = 12 links in one connected piece (p = 1) has β = 12 ÷ 10 = 1.2; cyclomatic number μ = 12 − 10 + 1 = 3 circuits; α = 3 ÷ (2 × 10 − 5) = 3 ÷ 15 = 0.2 (20 per cent of the possible circuits); and γ = 12 ÷ [3 × (10 − 2)] = 12 ÷ 24 = 0.5 (half of the possible links).

Index	Formula (planar graph)	Interpretation
Beta (β)	e ÷ v	Below 1: a tree or disconnected network; exactly 1: one circuit; above 1: a complex network
Cyclomatic number (μ)	e − v + p	The number of independent circuits
Alpha (α)	(e − v + p) ÷ (2v − 5)	Actual circuits as a share of the maximum possible (0 to 1)
Gamma (γ)	e ÷ 3(v − 2)	Actual edges as a share of the maximum possible (0 to 1)
Eta (η)	Total network length ÷ e	Mean length of an edge
Diameter (δ)	Edges in the shortest path between the two most distant nodes	Smaller diameter means a more compact network

Accessibility describes a node's position within the network. The König number (associated number) of a node is the number of edges in the shortest path from it to the most distant node — the lower it is, the more central the node. The Shimbel index sums the shortest-path distances (in edges or kilometres) from a node to all other nodes; the node with the lowest Shimbel index is the most accessible, and the sum of all nodes' Shimbel indices, the dispersion index, measures the connectivity of the whole network. The detour index compares the straight-line distance between two places with the actual route distance (straight-line ÷ route × 100): values near 100 mean direct routes, low values circuitous ones. In India the Golden Quadrilateral and the dedicated freight corridors were designed precisely to reduce the diameter and raise the accessibility of the national network.

3. Spatial flow models: the gravity model and its variants

The gravity model borrows Newton's law: interaction between two places varies directly with the product of their "masses" (usually populations) and inversely with a power of the distance between them, Iᵢⱼ = k Pᵢ Pⱼ ÷ dᵢⱼᵇ. The exponent b measures the friction of distance (distance decay); with b = 2, doubling the distance cuts interaction to one-quarter, and trebling it to one-ninth. The idea goes back to H.C. Carey's "social physics" (1858) and Ravenstein's migration laws. W.J. Reilly's law of retail gravitation (1931) applied it to shopping: two cities attract trade from an intermediate town in direct proportion to their populations and in inverse proportion to the square of their distances from it. P.D. Converse (1949) derived the breaking point between two cities, where their influence is equal: measured from the smaller city B, d_B = d_AB ÷ (1 + √(P_A ÷ P_B)). For A with 90,000 people and B with 10,000, 40 km apart, √9 = 3 and the breaking point lies 40 ÷ 4 = 10 km from B.

Variant	Author	What it adds
Law of retail gravitation	W.J. Reilly, 1931	Division of trade from an intermediate town between two cities
Breaking-point formula	P.D. Converse, 1949	The boundary of equal influence between two cities
Population potential	J.Q. Stewart and W. Warntz, 1940s–50s	Vᵢ = Σ Pⱼ ÷ dᵢⱼ — the accessibility of a place to the whole population
Probabilistic shopping model	David Huff, 1963	The probability that a consumer chooses a centre, given all competing centres
Entropy-maximising spatial interaction models	A.G. Wilson, 1967–70	Origin- and destination-constrained forms with a statistical foundation

4. The WTO, globalisation, world trade patterns and regional cooperation

The World Trade Organisation came into being on 1 January 1995, created by the Marrakesh Agreement that concluded the Uruguay Round (1986–94) of the General Agreement on Tariffs and Trade (GATT, 1947). Where GATT covered trade in goods, the WTO added the General Agreement on Trade in Services (GATS), Trade-Related Aspects of Intellectual Property Rights (TRIPS), Trade-Related Investment Measures and the Agreement on Agriculture (with its amber, blue and green boxes of subsidies), and a binding dispute settlement mechanism. Its core principles are most-favoured-nation treatment (a concession to one member extends to all) and national treatment (imports treated no worse than domestic goods once they have entered). The Doha Development Round launched in 2001 has stalled, and the Appellate Body has been unable to function since December 2019 because appointments to it have been blocked.

Globalisation and liberalisation — the lowering of tariffs and capital controls, India's own reforms of 1991 among them — have reshaped world trade patterns. Trade has grown faster than output for most of the post-war period; manufactured goods and, increasingly, services dominate; much of it is intra-industry trade in parts and components within global value chains; China has become the largest exporter of goods and the United States the largest importer; and South–South trade has risen sharply. Regional trade agreements have multiplied alongside the WTO — the European single market (1993), NAFTA (1994, replaced by USMCA in 2020), the ASEAN Free Trade Area (1992), MERCOSUR (1991), the South Asian Free Trade Area (in force from 2006), the African Continental Free Trade Area (2021) and the Regional Comprehensive Economic Partnership (signed 2020, which India left in 2019). The problems of regional cooperation are sharpest in South Asia, where intra-regional trade is only about 5 per cent of the region's total trade: similar export baskets, non-tariff barriers, poor transport links and political hostility. The prospects lie in trade facilitation, transport corridors and sub-regional groupings such as the Bangladesh–Bhutan–India–Nepal framework.

Key takeaways

Ullman (1956): complementarity, intervening opportunity and transferability; Hurst set transport in a behavioural economic geography; Taaffe, Morrill and Gould (1963): scattered ports, penetration lines, feeders and interconnection, trunk routes.
Kansky: β = e/v, μ = e − v + p, α = (e − v + p)/(2v − 5), γ = e/3(v − 2); for v = 10, e = 12: β 1.2, μ 3, α 0.2, γ 0.5.
Accessibility: the lowest König number and lowest Shimbel index mark the most central node; the detour index compares straight-line with route distance.
Gravity: I = kPᵢPⱼ/dᵇ; Reilly (1931) retail gravitation; Converse (1949) breaking point d_B = d_AB/(1 + √(P_A/P_B)); Stewart's potential, Huff's probabilities and Wilson's entropy models are variants.
WTO (1995, from GATT 1947 and the Uruguay Round): MFN and national treatment, GATS, TRIPS, agriculture, dispute settlement; trade patterns are shaped by value chains, China's rise and regional agreements, while South Asian integration remains weak.

Practice questions (11)

Attempt each one before opening the answer. Every explanation names the tempting wrong option as well as the right one, because that is where marks are lost.

Edward Ullman identified three bases of spatial interaction. They are:
1. Connectivity, accessibility and diameter
2. Push, pull and intervening obstacles
3. Threshold, range and hierarchy
4. Complementarity, intervening opportunity and transferability
Show answer
Answer: D — Complementarity, intervening opportunity and transferability
Ullman's triad (1956) explains why flows occur between particular places. Threshold and range belong to central place theory, and push, pull and intervening obstacles to Lee's migration theory.
A city stops buying timber from a distant region once a nearer forest region begins supplying the same timber. In Ullman's terms this illustrates:
1. Transferability
2. Intervening opportunity
3. Complementarity
4. Distance decay in the gravity model
Show answer
Answer: B — Intervening opportunity
An alternative source located between the two complementary places captures the flow — Ullman's intervening opportunity, taken from Stouffer. Complementarity still exists with the distant region, but a closer opportunity now satisfies the demand.
A connected planar road network has 10 vertices (towns) and 12 edges (links). What is its gamma index, γ = e ÷ 3(v − 2)? Type a number.
Numerical answer — type the value.
Show answer
Answer: 0.5
γ = 12 ÷ [3 × (10 − 2)] = 12 ÷ 24 = 0.5, so the network has half of the maximum number of links a planar graph of 10 nodes could have. Its beta index is 1.2 and its alpha index 0.2.
A transport network with a beta index (e ÷ v) of less than 1 is:
1. A branching tree or a disconnected network with no circuits
2. A complete network in which every pair of nodes is linked
3. A highly connected network with many circuits
4. A network with exactly one circuit
Show answer
Answer: A — A branching tree or a disconnected network with no circuits
With fewer edges than vertices a network cannot contain a circuit; it is a tree (for example a colonial penetration line with branches) or is broken into parts. β = 1 means one circuit and β above 1 a complex, well-connected network.
In a transport network, the node with the lowest Shimbel index is:
1. The node at the end of the network's diameter
2. The most accessible node
3. The node with the fewest links
4. The least accessible node
Show answer
Answer: B — The most accessible node
The Shimbel index adds up the shortest-path distances from a node to every other node; a low total means the node is close to all the others, i.e. most accessible. Nodes at the ends of the diameter tend to have high values.
City A has 90,000 people and city B has 10,000; they are 40 km apart. Using Converse's formula d_B = d_AB ÷ (1 + √(P_A ÷ P_B)), how far from B (in km) is the breaking point? Type a number.
Numerical answer — type the value.
Show answer
Answer: 10
√(90,000 ÷ 10,000) = √9 = 3, so d_B = 40 ÷ (1 + 3) = 10 km from B, and therefore 30 km from A. The larger city's trade area extends three times as far towards the smaller one.
In a gravity model with a distance exponent of 2, doubling the distance between two cities of fixed size changes the predicted interaction to:
1. Twice its former value
2. Unchanged
3. One-half of its former value
4. One-quarter of its former value
Show answer
Answer: D — One-quarter of its former value
Interaction varies with 1 ÷ d², so doubling d divides it by 2² = 4. A lower exponent, as with cheap modern transport or telecommunications, means weaker distance decay.
The World Trade Organisation came into existence on 1 January 1995 as the successor to:
1. The Organisation for Economic Co-operation and Development
2. The United Nations Conference on Trade and Development
3. The General Agreement on Tariffs and Trade (GATT)
4. The International Monetary Fund
Show answer
Answer: C — The General Agreement on Tariffs and Trade (GATT)
The WTO was created by the Marrakesh Agreement at the end of GATT's Uruguay Round (1986–94), extending the rules from goods to services and intellectual property and adding binding dispute settlement.
Which of the following are core non-discrimination principles of the WTO? Select all that apply.
1. National treatment
2. Fixed exchange rates among members
3. Most-favoured-nation treatment
4. Export subsidies for all manufactured goods
Show answer
Answer: A — National treatment; C — Most-favoured-nation treatment
MFN extends any concession to all members, and national treatment requires imports to be treated like domestic goods once inside the market. Export subsidies on manufactures are prohibited rather than promoted, and exchange rates are the IMF's concern, not the WTO's.
Assertion (A): In Taaffe, Morrill and Gould's model of transport development, the first stage consists of scattered small ports along the coast. Reason (R): Colonial transport lines were built to carry primary produce from the interior to the ports. Choose the correct option.
1. Both A and R are true, and R is the correct explanation of A
2. Both A and R are true, but R is not the correct explanation of A
3. A is true, but R is false
4. A is false, but R is true
Show answer
Answer: B — Both A and R are true, but R is not the correct explanation of A
Both are true, but R explains the second stage — the penetration lines built inland to mines and cash-crop areas — not the first. The first stage is defined by small ports with limited hinterlands before any penetration lines exist.
In the Taaffe–Morrill–Gould model, the stage in which a few ports grow at the expense of others because inland routes to mines and plantations start from them is the stage of:
1. High-priority trunk routes
2. Scattered ports
3. Interconnection by feeders
4. Penetration lines
Show answer
Answer: D — Penetration lines
In the second stage penetration lines reach inland, extending the hinterlands of the ports at their heads, which then outgrow the rest. Feeders and interconnection follow in the third stage and trunk routes in the fourth.