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Dorling, D. (1991) The Visualization of Spatial Structure, PhD Thesis, Department of Geography, University of Newcastle upon Tyne

Chapter 6: Cobweb of Flows

The developments of census cartography should be based first and foremost on the use of models of the dynamics of the observed or planned area on the long term as well as the short term. Look upon the population and its various activities as a part of a vertically-rising stream in space-time with oblique tributaries of movements in a short chronological perspective and a longer one (for example, daily journeys to work and migratory moves respectively).
[Szegö J. 1987 p.200]

6.1 What Flow Is

Flow is more than change. It describes the static structure of change; how the change came to be, what changed. Change is a difference; flow is an entity in itself. It is of an order of complexity above change and involves an entire order of magnitude more of information. In our social structures it is the movement between places, rather than alterations within them, which are responsible for the restructuring we see81.

To paint a picture of the static social structure, at any point in time, we need only know the situation in each cell of the structure. To show where that structure is changing we to know the situation at at least two points in time for every cell. To show how that structure changed, what moved from where to where, information is required about the relationships between all cells (Figure 17). Flows are real. The people they measure did move from one place to another (Print CIV). This is the structure of change, the structure of movement82. It forms a cobweb that links places.

The final step in complexity taken here is to look at the change in flows. Again the information required at least doubles; the flows between all pairs of cells at several points in time. The differences between webs are explicitly not counted in actual people. The measure of how many more or less people moved between two places from one pair of years to another provides an abstract quantity, not easy to comprehend.

6.2 What Flows There Are


Social science abounds with flows. Many are not spatial. The flow of votes between political parties would produce a small matrix within each constituency or ward. Each element of the matrix would tell us how many people changed their vote from one party to another, or chose not to vote. Often flows are not given, while change can be derived.

Flows on and off the unemployment register are an aspatial set which are recorded. Here, within every employment area, only two states are given, moving on or off the register. With a long time series, however, these little matrices can tell us a lot about the frequency and length of unemployment, and the spatial distributions of these occurrences.

Flows of spatial movement abound and are usually categorised by purpose of movement. Some have been mapped in the past83, but we have little information about many others, frequent flows to go shopping or to school for instance. Less frequent, but important moves, to holidays, hospitals or further education, for example, are also difficult to obtain data for, or estimate.

The only spatial flows regularly recorded and disseminated are those between home and workplace, and migration from one home to another. Travel to work flows are sampled at the census. They link the basic static points at which people are regularly enumerated, they give day and night time populations and tell us how these change.

Migration is counted at a fine spatial scale by the census. A useful series can be obtained from the National Health Service central register of patients. Migration flows are collected to see how the night time population is changing in the medium term. The creation of flow matrices was a by-product of this. Here I show how the cobweb of migration is wrapped around the honeycomb of social structure in Britain, enabling important insights to be realised (Carrier N.H. & Jeffery J.R. 1953, Davis N. & Walker C. 1975, Redford A. 1976, Gordon I. 1982, Green A.E. 1986, Boden P., Stillwell J. & Rees P. 1987, Stillwell J., Boden P. & Rees P. 1988, Boden P. 1989, Mueser P. 1989, Green A.E. & Owen D. 1990).

6.3 Unravelling the Tangles


Places in Britain can be divided into two; those where more people leave for work in the morning than arrive — residential, and those where more people arrive for work than leave — industrial. Such a map could have two colours, black and white, on a grey background, and would show the rings and sections of the basic pattern. But how much would this picture tell us?

Elaboration can begin by moving from two colours to a continuous scale from black to white. The image is smoother. Just how many people are moving though? I can show the proportion of people moving out of each place, or those moving in, or both. This can be done with the colour of the cells, or their size; size for the proportion involved, darkness for the proportion outgoing, for instance.

Next, we consider where, in general, people are going to and coming from? This is implied by the rings, but may not be as simple as it appears. I can show the average direction of outgoing movement by changing the shape of each cell to an arrow, which points to where the people are travelling.

Finally, how far are people moving, or better still, how long is it taking them to get there? The length of the arrow is another aspect we can alter. The length is in proportion to the average time it takes people to travel; the direction, where they go; the size, how many of them go; and the colour — the darkness — what proportion are outgoing.

This succession of images just described has been concerned with average flow. Such maps are useful, for instance in studying commuting, because most areas are either residential or industrial, most people go in roughly the same direction, and travel the same amount of time. It is only the nature of travel to work which allows it to be mapped like this84. The arrows could not be used to show where people were coming from, or how far they travel to get to the shops for instance, as these aspects are too variable, being concentrated in the centre of cities and large neighbourhoods.

None of what I have described so far has been flow mapping (Thornthwaite C.W. & Slentz H.I. 1934, Schultz G.M. 1961, Matthews G.J. 1970, Morrison A. 1970, 1971, Phillips D.J. 1977, Beddoe D.P. 1978, Craig J. 1981, Tamsma R. 1988). It has been the mapping of gross averages and tendencies. It is similar in assumption to mapping locally varying characteristics of a population at a regional level. This is regional mapping of flow at the local scale, when the ward level is used.

The simple travel to work pattern is as much an artifact of this method as it is a reality. From seeing these pictures you would think you could draw lines dividing the headwaters of the flow to define travel to work catchments. Whether it is possible or not depends on how much flows cross over, how many people travel in the same direction, how you measure flow, indeed, how many people travel at all.

6.4 Drawing the Vortices


What have been discuused up to now have been vectors, single attributes for sets of single areas — average direction and magnitude of flow. Now I attempt to draw the matrix, not just a tangle of lines connecting all places between which people flow, but a picture which shows the static structure of the change in as much detail as possible.

Lines are used to show matrices of flow, as areas were used to depict scales of attributes. Lines have length, width, colour, direction (by arrow-head), and can be given order as they overlap. The first of these qualities, length, conveys the strongest information, but is most difficult to use, as the line links two places, and to alter its length would make that connection ambiguous (Dale L. 1971, Forbes J. 1984, Tobler W.R. 1987a, 1987b, Jobse R.B. & Musterd S. 1989, Becker R.A., Eick S.G., Miller E.O. & Wilks A.R. 1990a, Teeffelen P.B.M. 1991).

The best choice we have, which has most influence over the final image, is whether to draw any particular line at all (Print CV). With areas this is not a choice; there is a place for every area. With lines, there is only enough space for a minority to be shown (between more than a couple of dozen places). A line should be drawn between two places only if the flow between those places is significant. What is a significant flow? There is a second and linked difficulty; this is the most serious effect of the modifiable areal unit problem (largely overcome above by the use of many small areas and cartograms). The problem is that in particular the size, in people, but also the shapes, on the ground, of the arbitrary areas between which flows are recorded, will affect the number of flows counted, as much as does the number of people who are actually moving85. More people will flow from larger areas, but less people move between such areas (since more move within them, Figure 18)), and more will flow from long narrowly shaped areas, than from more compact places. Put simply, the longer the boundaries are over which flows are recorded, the more will be recorded.

One answer is the same as earlier, to use as many small areas as possible, to record as many of the flows which occurred as possible. Here wards represent the finest resolution. With flows, however, long distance movements can come to dominate the image, stretched across many other areas and perhaps more important flows86. Two solutions are used, one visual, the other statistical.

Firstly, we can order the flows; lines can be placed above, and partly obscuring, other lines. This is achieved by drawing a slight white border around the lines. The strongest flows could be uppermost, but is was found most advantageous to put those which were between contiguous areas foremost, those of second order next, and so on. The effect of this is to clarify the image, hide the most deviance and show the most structure. Only strong unusual movements will show through the mesh (Figure 19).

Secondly, we only draw flows which represent more than a particular type of average propensity to move. The proportion of an area’s population travelling to another area to work must be greater than the national average propensity for the line to be drawn. This usually means that over three-quarters of those travelling are represented on the image, and that these are the most typical commuters. This technique is particularly useful when flows between all the wards of Britain are being shown, as there is too little space to use the visual ordering technique effectively, and even the widths of the lines cannot be gauged (Print CVI).

Width can still be used to convey magnitude of flow, and arrow-head to convey the direction. The less the number of areas between which flows are being drawn, the more effective these methods can be. Colour can be reserved to show other things about those who are travelling, what kind of areas they are coming from or going to, what kind of people they are. The length of the line is a good surrogate for the time taken when the population cartogram is used as the base. This base also makes the picture clearer and gives some meaning to the density of lines (Print CVII).

The cobwebs of travel to work are not as simple as they were first drawn here. By looking at a relatively constrained set of flows we have not encountered all the problems this kind of mapping can create. It should also be noted that the picture produced is very sensitive to the denominator used (Prints CVIII & CIX).

6.5 Commuting Chaos


What the commuting flows show us is the well known city structure of Britain, and the extent to which this is a true interpretation. On the population cartogram the flows are much more confused than in Euclidean space. This brings the image closer to the complexity of reality87 (Dickinson R.E. 1957a, Lawton R. 1968b, Watts H.D. 1968, Census Division, OPCS 1976, Becker R.A., Eick S.G., Miller E.O. & Wilks A.R. 1990b, Hodgson M.J. 1990).

Most people, in fact, do not work, and many of those who do, do so within the ward in which they live. Thus even at ward level we are not representing the majority of people. Circles, their areas in proportion to the number of people living and working in the same ward, can give an indication of this phenomenon, while the flow lines between wards are still shown.

At this resolution the direction of flow is implied from the context — where the lines converge. Where lines cross it can be seen that the directions differ. There is a problem when they go in completely the opposite direction, but this is rare. The magnitude of flow is also difficult to see as the lines all appear very thin. This is partly because almost all flows are small, but this could be compensated for by making large flows darker.

Colour can be used effectively to show how the structure of flow relates to other social structures (Prints CX & CXI). The lines can be coloured according to a particular feature of the areas which people leave for work, or about the work they do, where they are going, or even all three aspects simultaneously.

Finally it would be possible, though perhaps too confusing, to place the flow map over a smoothed three colour cartogram of some related aspects of the population involved. If this were done with migration, the cartogram could represent a few of the changes which the flows were producing88.

The flows of travel to work are the heartbeats of the urban system, people being pumped in and out of the cities. If they stopped there would be no cities. The rhythm is well known, five days a week until Christmas. It may miss a beat, but not often. Seeing the flows is fundamental to understanding them. Understanding them shows us how society ticks.

6.6 Migration Networks


What makes flow mapping in other subjects simple compared to geography is that their flows are local, and in one direction — vector fields89. Travel-to-work flows can be seen as an approximation to this; most people go to work near to where they live and travel in the same direction as other commuters. The extent to which this does not apply was shown above. Migration takes us much further from the ideal, simpler, situation to visualize. Migration flows can be much longer, but migration does have a strongly localised tendency. If it did not do so, as we see later, it would be practically impossible to map by the techniques used here (Hollingsworth T.H. 1970, Ogilvy A.A. 1982, Brant J. 1984, Devis T. 1984, Fielding A.J. 1989, Bulusu L. 1990, Salt J. 1990).

The more serious problem of flow mapping in general is that there need not be a single strong net direction of flow. Flow can and does occur in both directions. How can we show bi-directional movement along a line? Various methods can be used when the flows are only between a few dozen places and the arrows are still large enough to have specific characteristics. Placing the smaller flow as an arrow on top of, and in the opposite direction to, the larger flow is the solution preferred here. Net flow is then represented by the differences between the arrows, as it should be, being a difference and not an entity in itself90.

To show just net flows would be simpler, but it would also be highly misleading (Flowerdew R. & Salt J. 1979, Johnson J.H. 1984, Rees P. 1986, Rees P. & Stillwell J. 1987, Owen D.W. & Green A.E. 1989, Rogers A. 1990). The majority of the movements would be cancelled out. We are interested primarily in how the change occurs, in how many people move and where — not in a difference. In fact the net flows in migration are very small in comparison with the absolute movements. Migration flows between two areas tend to be roughly equal in both directions91. We can use this fact to advantage when drawing images of migration between many areas. The basic migration network is successively revealed through a series of images (Prints CXII to CXIX).

One other solution which has been suggested (Tobler 1987b), is to re-route flows by the shortest path through contiguous areas. This was tried, but it was found that for Britain the effect was to imply the opposite of the true picture. Much of the flow went through the middle of the country and the relationship between the metropolitan cities and their hinterlands was reversed. The idea was abandoned.

One problem, which has held back work on the 1981 census migration statistics, has been the method by which flows have been amalgamated when too few people were involved, to a higher spatial resolution. The solution to this problem is similar to that of the changing constituency boundaries earlier — it does not matter. Just as a series of election results can be drawn while the boundaries change, so the lines on the map need not all be between wards, but can be between amalgamations, as long as the basic populations of the areas involved are used to determine their significance. In fact, the Census Office may even have done researchers a favour in amalgamating, creating clearer images of the basic movements, which can be coloured according to the attributes of the migrants92.

6.7 A Space of Flows


Again, images of migration, the average distance and direction can be drawn, at resolutions as fine as the ward level. These pictures show that migration is a much more diffuse process than commuting. Propensity is most useful, coupled with distance it gives us an idea of how often and how far people move house. Without being able to see the structure of individual streams we are blind to the pattern.

Between the ten thousand wards in Britain there could be as many as one hundred million migration streams. In fact only one percent of these actually occur in a year — one million streams carried some five million people between the years 1980 and 1981. The flows are generally equal in both directions. If we amalgamate these two flow propensities as a geometric mean, and plot only those which are significant, merely one hundred thousand lines need be drawn, representing the spatial distribution of the movement of the majority of migrants between those years at the finest available resolution.

These lines need no longer convey direction, and are generally too thin to give an impression of magnitude. Each represents, on average, the change of residence of half a dozen families between two wards. Again they can be coloured. This could be done according to the nature of the area being left and that being entered, or by any aspect of one or the other. Lines from obviously different areas should stand out from the crowd. As we can see, the pattern of movement is deeply embedded in the social structure (Prints CXX & CXXI).

What is striking about the images created is the extent to which migration actually maintains the status quo (Rowley G. 1970, Coombes M.G., Green A.E. & Owen D.W. 1985, Champion A.G. 1989, Hubbuck J. & Coombes M.G. 1989, Allen J. & Hamnett C. (eds) 1991, Fielding A.J. 1991). The vast majority of movements are within similar areas and the boundaries can be clearly seen93. It appears that there is a single, overriding spatial social structure to Britain; a social structure encapsulated by the streams of migration, crossed daily by travel to work. People in Britain must work together, or at least at the same place, but they can and do live apart. The patterns of their movements testify to this. These movements are as much part of the spatial structure as are the pictures of who lives in households or works in offices94.

With information from the National Health Service central register we have an opportunity to depict how the flows of migrants are changing over time. A change of flow is a strange concept. If between 1975 and 1976 two thousand people moved from Liverpool to London, and ten years later only one thousand did, what does that tell us? Firstly we must know whether the level of flow throughout the country has fallen, then we need to know whether the flow from Liverpool has fallen in general, or that to London dropped, and finally what has happened to the movement in the opposite direction.

Mapping change of flow involves two images; one showing between which places, and by how much, the relative increases have occurred and the other showing where there have been decreases in the number of moves. Circles centred on the places themselves can show what has happened to their total in, out, and net flows. It is difficult to know whether, with the use of dark and light arrows, these two images could be put on a single map. What certainly could not be shown is the changes over fifteen consecutive years that have been recorded up to 1990 between the ninety seven mainland family practitioner areas.

What we have seen in this part of the dissertation, has been how the official and conventional place and time based information about people can be turned into pictures depicting the spatial social structure of this country made up from their lives. A rich tapestry has been woven, the warp and weft of which are made up from the flows of people to work and to new homes, different directions — holding the picture together95. Both sets of lines can be placed on a single image, illustrating how the two are linked. Without pictures we would never cope with such complexity.

Much is missing from this as a complete view of British society. Flows of money, wealth and goods would be essential, as well as knowledge about their static distributions. What I have accomplished here, though, is the ability to depict this type of information visually. A change from tables to pictures, numbers to colours, words to drawings, allows us to move from vague impressions to concrete images.

 

Prints

CIV Migration flows between all regions in 1976, sorted by contiguity order.
CV Migration flows between metropolitan counties and other areas, 1975-1976.
CVI Daily commuting flows on an equal land area projection in 1981.
CVII Daily commuting flows on an equal population projection in 1981.
CVIII Daily commuting flows as a proportion of destination employees.
CIX Daily commuting flows as a proportion of destination residents.
CX Daily commuting flows on an equal area projection by occupation, 1981 (Colour).
CXI Daily commuting flows in population space by occupation, 1981 (Colour).
CXII Migration flows between family practitioner areas of 1 in 200 people.
CXIII Migration flows between family practitioner areas of 1 in 300 people.
CXIV Migration flows between family practitioner areas of 1 in 500 people.
CXV Migration flows between family practitioner areas of 1 in 1000 people.
CXVI Migration flows between family practitioner areas of 1 in 2000 people.
CXVII Migration flows between family practitioner areas of 1 in 2777 people.
CXVIII Migration flows between family practitioner areas on an equal area projection.
CXIX Migration flows between English and Welsh counties on an equal area projection.
CXX Yearly migration flows on an equal area projection by occupation, 1981 (Colour).
CXXI Yearly migration flows in population space by occupation, 1981 (Colour).

 

The full matrix of travel to work flows between British wards contains, in theory 10444², or over 100 million separate counts. It was not possible to obtain flows within Scotland from the census records available. Only 434,340 or half of one percent of all possible routes were actually travelled, by the 20,602,790 people working. People tend to work near to where they live. The entire matrix of commuting flows was stored as a run length encoded binary file of only 628,752 bytes (small enough to fit on a floppy disc). This was achieved by sorting the flows from each ward in ward order and recording only the displacement in ward number and size of the flow (each in four bits: a carry option could be set if this size of field were inadequate). The set of flows from any ward could be determined instantly and the entire matrix easily held in computer memory.

The migration streams were somewhat more dispersed and also subdivided by sex. 893,941 streams of 4,210,900 people moving between 1980 and 1981, stored in a file of 1,453,252 bytes (which could also be held in computer memory).

Figure 17: Storing the Flows

A flow between two places is of a significant magnitude if it is larger than you would expect, given the populations of the two places and the general propensity to move between places. Here a flow was deemed to be significant, and thus drawn when:


Where mijst is the flow from place i to j between times s and t, and Pit is the population which could move at place i, time t (n is the total number of places being considered). The equation therefore calculated whether the geometric mean propensity to move between two places is greater than the expected propensity to move.

Problems can occur when this method is applied to commuting flows, particularly in central London where many people are moving into an area of generally low night-time population. It can be useful to use the day-time population estimate (caused by the flow) as the denominator.

Figure 18: A Significant Flow

The diagram shows how the size of migration streams between two places can be shown by a single arrow:

The arrow-head points in the direction of net flow, the size of the larger flow being shown by the width of the black line, and the minor back flow by the width of the grey line placed over it. A white border is placed around the arrow to obscure lines lying beneath it and clarify the image. The order of the arrows is then as that of spatial continuity -flows between neighbours being uppermost followed by second, then third, then fourth order contiguities. The inset below shows part of the country level migration structure north-west of London.

Figure 19: Drawing Overlapping Arrows


 

81 [a] Showing movement is one of the most difficult cartographic challenges:
When the information involves both TIME and spatial or GEOGRAPHIC ORDER, the correspondences translate a MOVEMENT: movement of the pendulum; migratory, demographic, or social movement. ... But when the two planar dimensions are utilized to represent space, no planar dimension remains available to represent the “time” component; this is the basic problem with the representation of movement in cartography. There are three solutions. -Construct a series of images (figure 2). As in the cinema, this solution can be applied to the most complex of movements. But here the number of images is limited by the reading process: with a long series it is difficult to suggest motion. -Represent the path and direction of a moving body (figure 3). This solution can suggest a continuous movement on the plane, i.e., MOTION. However, we must consider both the nature of the moving body, which can be a point, a line, or an area, and also the complexity of the movement (with or without reversal), which can only be perceived with a simple division of the plane. -Utilize a retinal variable (figure 4). The time component is divided into ordered categories represented by the different steps of an ordered retinal variable. This solution depends on the possibility of defining a small number of categories, since the ordered retinal variables are relatively limited. The figure does not generally suggest movement on the plane. [Bertin J. 1983 p.342]

[b] The quotation which began this chapter continues by advising:
Utilize these dynamics as basic conceptual elements — in the analysis of the past as well as in the planning of the future. Document this approach with text, tables, diagrams and maps in a co-ordinated manner. Let all these elements create a linked chain around the basic concept. Do not sort out too much: present even the less-formalized thoughts, sketches, etc. if they help reproduce the dynamics. [Szegö J. 1987 p.200]

[c] Solutions to showing flows through distortion are not new:
For early thematic maps developed in the nineteenth century, concerns were not with planimetric accuracy, but with how and why the environment and society function as they do. For example, Charles Joseph Minard, one of the originators of the flow-line map, placed considerable emphasis on accuracy of data value depiction while freely altering geographical position to allow effective data presentation (Robinson 1967). On his 1850 map of coal exports from England, he enlarged the Strait of Gibralter to a width of almost 500 miles (805 kilometers) in order to allow the flow line to pass through the strait. [MacEachren A.M. 1987 p.102]

82 [a] Most census mapping is of the distribution of night-time population:
This effect, which sometimes distorts at least some aspects of city life, can be overcome in some degree by measuring changes over time and movements in space; the static structure is only a departing point for the analysis of a living city. [Shepherd J., Westaway J. and Lee T. 1974 p.112]

[b] The problems and errors of data collection are usually much greater when looking at flows; many are known and some compensation can be made:
The correlation coefficient (Pearson’s) between inter-regional flows from the two sources is 0.996, and between FPCAs is still 0.980. We can be confident, therefore, in using NHSCR re-registration data to update the picture of internal migration provided by the 1981 census to 1985-86, and they are employed extensively in the chapter. [Rees P. & Stillwell J. 1987 p.5]

[c] A particular example of unreliable information on many peoples’ movement is given by:
The figures for Scotland in 1975 and 1976 show considerable fluctuations which can be attributed to the operation of the recording system rather than to real changes in migrant numbers. [Ogilvy A.A. 1982 p.67]

[d] One unfortunate preoccupation of research is to measure physical distance and relate it to migration — with an accuracy that suggests every minute spent by the removal van is of crucial importance:
Distance is measured as road milage between the zones and historical tests suggest that the negative power decay function (dij-ß) is preferable to the negative exponential form. [Stillwell J.C. 1986 p.181]

[e] Another example is where:
Distances were estimated (in miles) on a straight line basis between population centres of gravity for the counties, with diversions being forced around major estuaries and inlets. [Gordon I. 1982 p.9]

[f] Deviation from the expected propensity to migrate was mapped in some of the illustrations in this dissertation:
To discover any flows of unusual magnitude between certain areas, we calculated expected migration flows. These prognoses are derived from the total out-flow from one area and the total in-flow to another. (These form the expected cell frequencies that are also determined in Chi-square analysis.) The expected frequencies are subsequently compared with the observed frequencies (actual flows). The difference reveals any unusual attraction or repulsion exerted by an area. [Jobse R.B. and Musterd S. 1989 p.247-248]

[g] It is the streams of migration that are real and of importance — not the marginal distributions they produce:
The simple framework that reduces migration to ‘pulls’ towards desirable locations and ‘pushes’ away from less desirable ones cannot adequately explain even total migration, let alone the spatial structure of streams. [Mueser P. 1989 p.196]

83 [a] The limitations of mapping only night-time population were realised at an early stage:
The temporal aspect of thematic map data is also undergoing change. Emphasis has always been on relatively static, easily managed information even though these data may not represent the most crucial environmental variables. Maps of urban population based on night-time residential distribution are good examples. Potentially more interesting and revealing maps of daytime, rush hour, or non-residential night-time populations seldom exist! [Muehrcke P. 1972 p.8]

[b] Maps are not well suited to showing flow:
The map which has been the traditional instrument of expression in geography has the disadvantage of treating all organisms and objects as if they were more or less stationary. Though spatial flows may be mapped, it is still useful to have a mode of expression which is more attuned to a dynamic view of nature and culture. A major advantage with the time geographic notation system is that movements and changes in location can be registered in the paths or trajectories in a time-space map, just as the path of a jet-plane can be seen in the sky a few minutes after it has passed. A sequence of events and activities for individuals and objects thereby becomes frozen into a kind of historic-geographic matrix. This is in contrast to the traditional overcommittment to the two dimensional map as an analytical tool.
In a time-space region, each individual can be visualized as a continuous path starting in a point of birth and ending in a point of death. Depending on the observation period, individual-paths can be referred to as day-paths, year-paths or life-paths. This corresponds to the concept of life-time in demography, an idea initially conceived by the demographers Bexter and Lexis (Lexis 1875), mainly as a temporal concept. Hagerstrand generalized this idea to a time-space concept in his population mobility studies, but he also looked into time perspectives shorter than the year, which is the conventional unit of time in demography and demometrics. [Carlstein T. 1982 p.41]

[c] Again, it is the individual streams that must be visualized:
In studying migration, it is common to focus on the total number of moves to and from locations, ignoring the particular paths traversed by migrants. Such an approach allows analyses to focus on the way that location characteristics influence total number of migrants, abstracting from the complexity of spatial relations among locations. Yet, to understand the meaning of these totals, it is necessary to trace how the aggregates derive from decisions of individuals which, in turn, are shaped by the spatial character of the migration choice. We believe that the regularities in the streams of migration are important in revealing the processes of migration and the way that location characteristics influence migration. [Mueser P. 1989 p.186]

84 [a] Travel-to-work flows are spatially condensed, but showing just the in- and out-flow to places can be problematic:
Map 11 shows in- and outcommuters on one map. The problem arises that, in some cases, the number of in- and outcommuters are almost the same so that they should be represented by the same size of circle. If the same size of circle is used for each, there is no rim left to indicate which group predominates. If it is attempted to show a rim, then the graded circles are not accurate. The main advantage of this method, however, is that in- and outcommuters can be represented on a single map. [Dale L. 1971 pp.17-21] [a technique, similar to the one described, with similar problems, was used in some of the illustrations in this dissertation]

[b] Only a minority of all actual flow streams can be shown between many places:
The cartographic difficulties involved prevent the representation on one map of all net movements from each state to every other state, yet, since it seemed necessary for purposes of comparison to get as much of the movement as possible on one map, it appeared desirable to effect a certain compromise. It was found that the rejection of total movements of less than 10,000 into or out of any state resulted in the omission of only about five percent of the total migration. If the movement from each state to every other state were indicates separately, the multiplicity of lines would have made the map totally illegible, but through combinations of migrations in the same direction it has been possible to preserve legibility and still to show what was intended. [Thornthwaite C.W. & Slentz H.I. 1934 p.14]

[c] Showing only flows above an average propensity produces comprehensible images which still represent the majority of the people under study:
In the second category we have been able to demonstrate that the optimal threshold for the deletion of entries is the average flow size. This data selection rule deletes as much as 80% of the flow arrows. But generally only 20% of the flow volumes. [Tobler W.R. 1987 p.348]

[d] We are only concerned with which places are connected, not about the actual routes travelled:
Tracing the actual itineraries is not sufficient for representing a system of relations. A map of maritime routes, even when weighted, does not show the direction of trade among the centres of activity; it shows the density of ships at sea. The maritime trade among the cities of Europe and the Mediterranean will only appear in its diversity, weight, and geographic direction, when each connection, even through maritime, is represented by a straight line (figure 4). [Bertin J. 1983 p.344]

85 [a] The problem of measuring propensity to move is that:
A “migrant” usually is defined as an individual who moves across the boundary of an areal unit within a specified time period. Clearly, other things being equal, the rate of out-migration (number of persons leaving the area divided by number of persons residing in the area) will be greater for small areal units than for large areal units (see Bogue, 1959a). Conceivably, if one could assume that the propensity to move, i.e., probability of moving, a given distance, p(d), were constant for each individual in the population, and if a simple assumption about the distribution of population within areal units were accepted, an “expected” amount of out-migration could be ascertained by calculating the proportion of moves carrying a mover across the boundary of an areal unit. Expression of actual out-migration as deviation from “expected” out-migration, then, might be regarded as a measure of out-migration standardized for the size of areal unit. The problem is further complicated by the fact that for areas of the same size out-migration rates would be higher for a long and narrow areal unit than for a circular one. [Duncan O.D., Cuzzort R.P., & Duncan B. 1961 p.34]

[b] The problem is far from trivial:
All the variations introduced by spatial, numerical and temporal aggregation procedures operate on origin and destination data in an almost more bewildering variety than they do on static data. Ideally a migration journey should be represented by an arrow going from the point of origin to the point of destination. In practice, individual arrows would be too numerous, and the points too small to draw, so we summarise by trying to pick out the main bundles of arrows moving between pairs of areal units. Thus it depends entirely what size, shape and position of spatial units we use, what apparent bundles we pick up. [Forbes J. 1984 p.99]

[c] Movement is, certainly a geographical problem:
Migration is an event which by definition involves two places — even if only adjoining houses. So spatial location and spatial units are more basic to migration than to other events such as births, deaths and consumers’ expenditure. For these latter events, space is not fundamental to the event itself: it is merely necessary to define the geographical limits of the population to be included, though location may also be used as an explanatory variable. But since migration is a movement of people, analyses by location are intrinsic to it. While aggregate migration to and from an area may suffice for demographic calculations, analysis by place of origin or destination are necessary to understand migration as a social phenomenon. However for the whole country this involves so many figures — even county by county analysis without any sex or age analysis means a 54 x 54 matrix for England and Wales — that the analysis becomes unwieldy. Moreover only a few broad generalizations are possible as migration patterns differ greatly from place to place. There is not some kind of national average with regional differentials. [Craig J. 1981]

86 [a] Experimentation is required to overcome many of the problems of movement mapping:
The question of “what” to map has been specified; it is the “how” of mapping that remains to be done in more detail. As the methods discussed in this paper are attempted, further advantages and disadvantages will be discovered. This process of experimentation will be a most valuable way of determining the best cartographic techniques to apply to journey-to-work data. [Dale L. 1971 p.34]

[b] Many different solutions have been suggested:
For all but the simplest networks these link data displays have many intersecting lines and are difficult to interpret. There are several possibilities for reducing clutter. One is to shorten the line segments, that is, instead of drawing the line segments 50% of the way between nodes, draw them 30% or 10%, say. Another is to draw only lines whose corresponding statistic falls above or below some threshold. The difficulty with these ideas is that it is quite hard to come up with a good heuristic for setting these thresholds or line lengths (or overall line thickness, for that matter) before making the display. [Becker R.A., Eick S.G., Miller E.O. & Wilks A.R. 1990 p.93]

[c] Use of the cartogram opens up previously overcrowded areas of the image.
Most traffic flow maps utilize variations of line width to portray differences in traffic volume. There are times, however, when crowded conditions on a map, extreme constraints in flow, or other factors constitute a cartographic problem and make something other than expected lines desirable. [Schultz G.M. 1961 p.18]

87 [a] The lines appear at an almost constant density on the cartogram, as people move in all directions:
Programming the mapping of other than the most crude versions of such flow maps is not trivial, not least because large flows tend to occur between areas close together on the ground and numerous lines occur if all flows are mapped. Most frequently, they are mapped by arrows whose width is proportional to the flow involved. [Rhind D. 1983 p.176]

[b] Visually, ordering lines according to spatial proximity relieves some of the confusion:
There is a particular problem in using line segments to connect locations on a map: the geographically longer lines are visually dominant. In many data sets, such as migrations or trade flows, the flow between locations varies inversely with distance. One consequence is that, at times, short but important lines may be difficult to see because of the long, less important lines. One possible way to alleviate this problem is to use wide lines for connecting nearby locations. [Becker R.A., Eick S.G., Miller E.O. & Wilks A.R. 1990 p.289]

[c] An alternative idea is used for mapping average road speed:
The map has some resemblance to the familiar traffic flow map on which line width represents flow: but it is in fact more satisfactory than the flow map in cities because the lines on the speed map become narrower as they converge towards city centres, usually the most crowded parts of the map, whereas on the flow map the lines thicken and merge towards city centres. [Morrison A. 1971 p.120]

88 [a] Much social change is thought to be caused by migration flows:
Taylor (1979) compared 1979 with 1966, at a regional scale, and showed that the changing pattern of party support is closely correlated with net migration patterns. The regions of net population loss are those which have remained Labour strongholds; those of net population gain have been those of increasing Conservative strength. [Johnston R.J., Hay A.M. & Taylor P.J. 1982 p.953]

[b] However, most flows reinforce, rather than change, the structure:
Many movements of individuals in the population do not alter the characteristics of the area, since one council tenant often replaces another, and one stockbroker moves only to sell his house to another stockbroker and so on. Even where an atypical individual arrives in an area, his new environment may influence him towards adopting the characteristics of his new neighbours. Correlations and slopes between 1966 census data and partisanship change so little when using election years other than 1966 that we would be surprised to discover large biases due to the ageing of the census. [Miller W.L., Raab G. & Britto K. 1974 p.399]

89 [a] Simple vector mapping can itself still be difficult to comprehend:
We cannot directly display vectorial data on a two-dimensional screen, for example as a set of little arrows, and still interpret the result with the same ease as we would a scalar image. Our visual systems simply are not adapted to interpret large volumes of vectors in this way, whereas we have superb abilities for understanding and interpreting images or depth-cued surface displays. [Helman J. & Hesselink L. 1990 p.62]

[b] Here we are reaching the limits of what can be sensibly drawn:
There is no doubt that graphic complexity would be enormous if large populations in sizeable regions for a long time period were to be drawn as paths; the picture of merely one day in a small village is quite complicated even if computer plotters were programmed to do the actual drawing. But the important task of the graphic notation system is not to thrive on visual complexity, but to reveal the under-lying logic of human society and ecology in space and time. Simple graphs can be strategically employed to pinpoint the elements, relations and mechanisms which have principal importance for social-environmental structure and operation. [Carlstein T. 1982 p.45]

90 [a] Gross migration rates measure the actual numbers of people moving:
Gross migration stream (multiregional) models, on the one hand, more realistically depict the phenomenon being modelled (since there are no net migrants). The rates that they use to represent directional movements are linked to the populations at risk of moving and therefore measure true propensities of migration (a feature that net migration rates lack). [Rogers A. 1990 p.299]

[b] Some migration counts can include the same person several times, so:
Although the number of moves into and out of the country during the last ten years was close to 5 million — equivalent to nearly 10 per cent of the total population — this does not mean that 5 million different people were migrating. [Davis N. & Walker C. 1975 p.2]

[c] There is much speculation over the processes which might influence migration rates and destinations:
The data with which patterns of migration can be investigated in greater detail does not yet exist, but the analysis of gross in-migration rates in the year preceding the 1981 Census indicates that migrants are attracted to areas of employment growth, but avoid areas of rapidly increasing unemployment rates. [Owen D.W. & Green A.E. 1984 p.31]

[d] The relationships are not totally clear cut:
However, the trends in neither employees in employment nor unemployment mirror those we have found in migration. The number of employees in employment continues to rise from 1975 to 1979 while migration rates fall, although a rise in employees parallels the rise in migration levels. If the migration series followed unemployment rates closely, we would expect greater falls in the 1979-82 period and no recovery from 1982-83 in migration activity. [Rees P. & Stillwell J. 1987 p.16]

[e] Housing necessity, rather than employment choice, might be the major factor:
The fact that among men aged under 50 the percentage of migrants who were unemployed was greater for those moving within local authority districts than for all migrants is difficult to reconcile with the hypothesis of movement to find work. Although some districts cover a large area, a more likely explanation for much of this movement could be to find somewhere less expensive to live. [Brant J. 1984 p.30]

91 [a] But the distance migrants move is strongly related to who they are:
The three economic classifications of the population all show a similar pattern, but the socio-economic groups give the most illuminating explanation of differential migration. Apart from the effect of distance, tenure, age, family status, and sex, there seems to be a tendency for self-employed and managerial people to move rather less than many of their subordinates, especially over short distances. This might be termed a social effect, reflecting position in the hierarchy of status and power; at longer distances, more economic effects become stronger, so that the poor move much less often than the comparatively rich. [Hollingsworth T.H. 1970 p.62]

[b] The illustrations drawn here show clearly how the top third of the class structure dominate long distance migration:
The majority of labour migrants are middle class, in the 25-44 age group, and have middle-high incomes. They are professional and managerial workers in a career structure that encourages movement. Their occupational status frequently entitles them to financial and other forms of aid which make migration easier. They move within a housing market that is especially geared to their requirements. [Johnson J.H., Salt J. & Wood P.A. 1974 p.246]

92 [a] Colouring flows by the attributes of migrants may show which divisions are actual, and which are fictional:
An interesting and here easily seen feature not commented on by Hamnett is that skilled workers choose a region in the same way as the professional, managerial, intermediate and own-account workers. The big divide between the well-off and the disadvantaged groups seems to be between skilled and semiskilled workers. [Berge E. 1988 p.976]

[b] Some basic patterns are very clear:
Over Great Britain as a whole, the pattern of gross migration levels seems to reflect the political map remarkably well, for Labour Party strongholds correspond quite closely to places where little migration takes place. [Hollingsworth T.H. 1970 p.33]

[c] As are the social implications:
The process is one of deprived people being left in the urban priority areas as the successful move out to middle Britain. [Halsey A.H. 1989 p.22]

93 [a] People have been able to travel further to work as car ownership has spread:
Social changes are likely to add to economic changes in loosening up the pattern of settlement in the industrial regions of Britain in the next generation. [Lawton R. 1968 p.39]

[b] Most people do not move house when changing job, however:
Most migrants had moved short distances. In 1981, of those moving within Great Britain about 69 per cent moved less than 10 kilometres (six miles) and only 13 per cent moved more than 80 kilometres (50 miles)-distances measured as the straight-line distance between the grid reference of the address a year before census and the grid reference of the enumeration district of the usual address at census. [Brant J. 1984 p.23]

[c] We can speculate about what other factors might operate to affect these decisions:
If migration is to become more predictable, we can however suggest what parameters will be important. In the first instance, distance seems to matter a great deal; but we should probably use distance merely to separate short moves from long and regard distance as relative in our study of occupationally-induced migration. Movement to quite a distant place will still be likely if there are few nearer places that could supply migrants. [Hollingsworth T.H. 1970 p.164]

[d] Migration to and from London is dominant, even when sensible areal units are used to measure it:
Migration to and from London dominated population movement in much of Britain: 56 of the 67 largest flows in 1971 involved the London SMLA. There was a tendency for migration to London to come from a rather broader area than migration from London, thus suggesting a process of population redistribution operating through the Capital (Johnson et al. 1974: Salt & Flowerdew 1980) [Johnson J.H. 1984 p.305]

94 [a] Travel to work flows have even recently been linked to aspects such as political partisanship:
Some researchers have seen the workplace-residence relationship as a key to explaining different patterns of working-class behaviour in general. This is largely due to the importance of the work situation as a determinant of friendship networks, incomes and lifestyles. [Eagles M. & Erfle S. 1989 p.118]

[b] People are arranged in space, through migration, over relatively short distances:
It is also clear that, at the broader regional level, no simple distinction can be made between regions of labour surplus and shortage. Much has been written about the so-called ‘drift to the South’ and the conclusion has been drawn from the use of this generic term that the principal internal currents of migration have been long-distance moves from the depressed to the prosperous areas — for example, from north-eastern to south-eastern England. To a large extent this view stems from the misconception that unemployment is high throughout the assisted areas. In fact this is not so and especially over the last decade, unemployment in Britain has been developing a pattern of greater local variation. Thus, within the assisted areas, now covering virtually all the northern and western parts of Britain, there are adjacent local labour markets with widely differing levels of unemployment (Fig. 1.2). At the same time, within midland and south-eastern England, there are pockets of unemployment considerably above the national average. This situation indicates that spatial equilibrium in the labour market as a whole can be approached through relatively short-distance movements of labour from local areas of unemployment to nearby ones where job opportunities are more plentiful. [Johnson J.H., Salt J. & Wood P.A. 1974 pp.9-11]

[c] The overall result of all these moves, at a gross scale, has been the continued contraction of the major cities:
The single most impressive finding of the 1981 Census in relation to population distribution was the massive decline in population sustained by Britain’s larger cities over the previous decade. The population of Greater London alone fell by almost three-quarters of a million between 1971 and 1981, a drop of almost 1 in 10 (OPCS, 1984). Even bigger relative rates of decline were recorded by some of the provincial centres, notably Glasgow (-22.0 per cent), Liverpool (-16.4) and Manchester (-17.5). To some extent, the latter are related to the North-South drift described in the previous section, but they are also partly the outcome of a general shift in population from more urban to more rural areas. Evidence for the importance of this ‘rural-urban shift’ can be found in the fact that London sustained such heavy population loss in the 1970s despite being located at the heart of the most dynamic region in the UK. [Champion A. G. 1989 p.121]

95 [a] Some thought that housing and labour market areas would roughly coincide:
Highly skilled and highly paid workers are likely to have a much larger potential travel to work area than the less skilled and low paid who are more likely to be constrained by the difficulty and cost of commuting. But, such caveats aside, there is an approximate congruence between housing and labour markets which is imposed by the journey to work. [Allen J. & Hamnett C. (eds) 1991 p.5]

[b] But, again, most people moving house do not do it because of a change in employment:
Only 10.5% were moving house because of a change in their job or location of work, while for 4.3% the prime motivation for moving was to be nearer their place of work. Data from the 1984 LFS reinforce this conclusion, with 10.5% of those reporting a change in address claiming that the move was job-related. [Owen D.W. and Green A.E. 1989 p.119]

[c] Even the majority of moves between regions did not involve a change of employer:
Figure 4.1 indicates that in 1981 over half of inter-regional migrants in the UK (defined as those employed both one year before and at the time of the Labour Force Survey) did not change employer. The figures for 1975 and 1979 were similar. [Salt J. 1990 p.54]

[d] The relationships between commuting, migration and economic growth and decline are strong:
Of particular importance has been the growth of relatively high-level employment in both manufacturing and service sectors in southern England along the M4, M3 and M1 corridors. The strongest performances in the North can mainly be attributed to the surge in residential decentralization which took higher-status people out of the major cities into surrounding towns with a long manufacturing tradition, but some of the more successful freestanding settlements experienced significant growth in their service sectors, partly in connection with the expansion of higher education. The lack of improvement in the more rural and peripheral regions of the north can be associated in part with the swelling of the labour force by low-paid part-time female labour and low-skilled manual jobs for men, while the falling status of the South Coast towns reflects a partial substitution of their traditional high-class retirement role by the wider range of locally based jobs and by long-distance commuters seeking out lower house prices. [Champion A.G., Green A.E., Owen D.W., Ellin D.J. & Coombes M.G. 1987 p.93]

[e] The relationships also serve to constrain what can be done to improve the situation:
The latter policies are unlikely to have a large effect on unemployment in the inner city because of the induced changes in commuting and migration, and often the types of jobs created do not fit the skills of the inner city residents. [Ermisch J. & Maclennan D. 1987 p.198]