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Applied Spatial Analysis and Policy

, Volume 11, Issue 4, pp 713–729 | Cite as

Spatial Interaction Models: from Numerical Experiments to Commercial Applications

  • Martin ClarkeEmail author
  • Mark Birkin
Article
  • 89 Downloads

Abstract

Spatial interaction models have seen extensive use in public and private sector planning over the past 50 years. This paper reviews a number of facets of the application of these models. In particular we focus on developments in testing how well the models work in a number of different contexts related to applied spatial analysis and planning. We also speculate on the future of spatial interaction modelling in an era of ‘Big Data’.

Keywords

Spatial interaction models Numerical experiments Retail applications Big data 

Introduction

This paper was one of several presented at the 2017 European Colloquium on Theoretical and Quantitative Geography to mark the 50th anniversary of Wilson’s 1967 seminal paper on entropy maximizing models in the journal ‘Transportation Research’ (Wilson 1967). That paper proved to be something of a landmark in providing a strong theoretical grounding for a family of spatial interaction models that would subsequently see applications in a whole variety of areas including transportation, retailing, health and urban and regional planning. In this paper, the main aim is to provide an account of the ways in which spatial interaction models have been used in applied contexts from the mid-1970s up to the present, and to provide lessons for the future. This is important at a time of great opportunity, in view of the centrality of spatial interaction modelling to applied geographical analysis over the last 50 years. Massive transformations over the last decade in technology, data, infrastructure and consumer behaviour makes this a timely juncture in which to take stock of achievements and future prospects.

The paper is structured as follows. The second section provides a summary of the state of play in the mid-1970s in terms of data availability and computational power that, when combined, could be used to apply spatial interaction models at that time. In the third section, the focus changes to the design of numerical experiments in a data-lite/computational limited environment and an investigation of the properties of the Harris and Wilson (1978) model in particular. Emphasis is placed on the recognition that much theoretical exploration of urban and regional models had taken place but little work had been undertaken in the application of these models using real (or as identified in due course, imaginary) data. The fourth section contains a discussion of how the landscape changed in the 1980s as more data became available on both the demand and supply side of the equation and as computational storage and power increased significantly. Examples from the commercial application of spatial interaction models are provided along with extensions to the models that made them robust and fit for purpose. In the fifth section, consideration is given to the question of the continuing role for spatial interaction models in both public and private sector planning in a world of profuse ‘Big Data’ and increasingly complex consumer behaviour. Some concluding remarks are offered in the final section.

Background: The 1970s

Both of the authors began academic careers in the 1970s at a time of considerable flux in the discipline of geography. Following the ‘quantitative revolution’ of the 1950s and 1960s (Johnston and Sidaway 2004) our subject was becoming increasingly attractive to physicians, mathematicians and operations researchers, who were drawn to applications of statistical theory (Wilson 1967), entropy maximization (Wilson 1970) and mathematical modelling (Wilson 1974). But also what became apparent was that despite all the impressive theoretical developments in urban modelling, there was a rather limited amount of applied work. There were several reasons for this. The first was fairly obvious – there was a limited amount of data on consumer behavior; apart from the 1971 Census of Population there were no data on consumer demand, spatial interaction flows (such as the journey to work, or retail flows) and data on travel times or costs. All these types of data were essential ingredients for calibrating and operationalizing spatial interaction models.

The capability of mainframe computers in the 1970s was a world away from the technology which is now ubiquitous to nearly all desktops, households and indeed pockets and handbags. Data and programming code were typically submitted by punched cards into a batch system for overnight processing. The cycle of debugging errors in the programming code, or simply minor errors in the punching, was therefore drawn out and frustrating. Interoperability between different computer operating systems was still largely an unknown concept, so a program that would work on one mainframe computer could not be expected to run on another. This meant that software development was a very insular process unlike today’s world of PCs and Open Source software. A third factor was visualization tools. Today’s ubiquitous GIS software and other impressive tools allow us to examine data and model outputs in all sorts of interesting ways. In the 1970s, this was nigh on impossible. With all these obstacles it’s not difficult to see why there were few attempts to operationalize spatial interaction models despite the impressive theoretical advances that had been made (see, amongst others, Wilson 1970, 1974).

In view of these limitations, it seems almost ironic looking back that such rudimentary models as could be deployed were also the subject of fierce attack on the grounds of such perceived vices as ‘hypercomprehensiveness’ and ‘complicatedness’ (Lee 1973). The criticism that spatial models exploited irrelevant concepts imported directly from the natural sciences (e.g. Sayer 1976,) fuelled a scepticism about the value of spatial analytics which is still widespread today.

Despite the difficulties, some steady progress was made through the 1970s. Programs such as SPAINT (Stillwell 1983) and SIMODEL (Fotheringham and Knudsen 1986) were able to run any of the family of spatial interaction models on mainframe computers. The programming task was not straightforward and very time consuming but it did offer an opportunity for applied work, despite the lack of data.

In the late 1970s, concepts from catastrophe theory and bifurcation analysis within the context of non-linear systems had become very popular in urban and regional modelling (Wilson 1981). Some initial attempts to operationalize these using imaginary data for an eight zone Leeds retail system were presented in Wilson and Clarke (1979). But as time moved on and computational power improved substantially there was a need to become more ambitious. In the next section we describe how this next stage of exploring the properties of spatial interaction models unfolded.

The Dynamics of Urban Spatial Structure

Amongst the many potential variants of the family of spatial interaction models (Wilson 1974) the Production-Constrained SIM (PCSIM) has always enjoyed great popularity as a device for representing flows of people and expenditure in a retail or service delivery context. This model can be written in its most straightforward form as:
$$ {\mathrm{S}}_{\mathrm{i}\mathrm{j}}={\mathrm{A}}_{\mathrm{i}}{\mathrm{O}}_{\mathrm{i}}{{\mathrm{W}}_{\mathrm{j}}}^{\upalpha}\mathrm{e}{-^{\upbeta \mathrm{c}}}_{\mathrm{i}\mathrm{j}} $$
(1)
in which Sij is the flow of expenditure between origin zone i and centre j; where Oi is the retail demand in origin zone i; Wj is the attractiveness or size of centre j; cij is the travel time or cost between origin zone i and centre j and a balancing factor, Ai is defined as:
$$ {\mathrm{A}}_{\mathrm{i}=1/}{\Sigma}_{\mathrm{j}}{{\mathrm{W}}_{\mathrm{j}}}^{\upalpha}{{\mathrm{e}}^{-\upbeta \mathrm{c}}}_{\mathrm{i}\mathrm{j}} $$
(2)

α is a parameter that reflects the importance of centre size for consumers; and β is a parameter that reflects the importance of travel costs for consumers. The ability to calibrate these parameters, and the use of the balancing factor to allocate demand, makes the model more flexible and more consistent than the ‘gravity models’ which became popular in the early 1960s (Huff 1964; Lakshmanan and Hansen 1964).

In order to operationalise the model, certain basic information is clearly required on the location of population and associated expenditure patterns, the distribution of retail floorspace, the trade-off between physical accessibility and economies of scale through β and α, and the shape and influence of the transport network. As noted above, early progress was stymied by limited access to even these most basic of data.

In the absence of suitable data, much attention focused instead on the dynamic properties of the models. Harris and Wilson (1978) presented an elegant but simple extension to the PCSIM. They argued that equilibrium in a retail system would be achieved when revenue would equal costs for each retail centre. This can be represented algebraically as
$$ {\mathrm{D}}_{\mathrm{j}}={\mathrm{kW}}_{\mathrm{j}}={\Sigma}_{\mathrm{i}}{\mathrm{S}}_{\mathrm{i}\mathrm{j}} $$
(3)
where Dj is revenue accruing to centre j; k is a cost parameter that converts floorspace into an operating cost.
A lot was known about the theoretical properties of the Harris-Wilson model (e.g., Clarke 1981) but in the absence of real world data implementation was a challenge. So the challenge was to create an artificial but realistic environment to undertake experiments that would allow the exploration of the properties of the model in a numerical rather than theoretical way. The operationalisation of the model within a FORTRAN program required the design a spatial system that could be used as the test bed for the model. After a lot of consideration a 729 zone system was created. This is basically a 27 × 27 symmetric system and is shown in Fig. 1.
Fig. 1

The 27 × 27 hypothetical spatial system (Source: Clarke 1984)

The x’s within this rectangular grid represent cells which are excluded to create a circular and symmetrical landscape with a single central zone and 13 zones in every direction from that centre. Homogeneous and uniform circular cityscapes of this type were popular in location theory and urban economics at the time (e.g. Richardson 1976). Each zone was both a demand point (of equal size in all cases) and also a potential supply point, apart from the crosses on the figure which were just demand zones. Distances between origins and potential supply points were calculated using Euclidean distance. The interaction matrix (Sij) therefore included 729 × 729 (or 531,441) flows, which was just about at the limits of what the university’s Amdahl mainframe could handle in the early1980s! To the author’s knowledge this represented the largest spatial interaction model that had been operationalised at the time.

A final challenge was finding a way to visualize the results of running the model. This was seen as an essential part of the process of interpreting the model’s behaviour under different conditions, which are described below. There was a software package available on the mainframe called SYMVU that allowed the three-dimensional plotting of data and thus provided the best available tool to represent the outputs of the model. In the days before the Windows operating system, ‘cut-and-paste’ was literally that, so scissors, glue and a photocopier were all important components of the visualization process!

Once this was all put together, the strategy was to run the Harris-Wilson model under a number of different scenarios, essentially varying the values of the two parameters, α and β, and exploring the outcomes. α is a parameter that represents the scale economies that a retail centre enjoys; as α increases above one, then larger centres become more attractive to consumers. β is a parameter that takes account of the importance of travel distance to consumers; as β increases, travel time or costs become more important to consumers so they are more likely to make shorter trips, and vice versa.

The results of these experiments were first published in Clarke and Wilson (1983). Figure 2 provides a useful summary of the results. From left to right, the value of α is constant at 1.3 but β varies from 3.5 to 0.5. As can be seen the number of retail centres decreases as beta reduces, eventually ending with just a single centre. Keeping β constant at 2.5 but varying α from 1.1 to 1.5 shows a rather different pattern (top to bottom); as α increases, the number of centres decreases but still leaving a larger number of centres than through the reduction of the value of β. So these numerical experiments do confirm the theoretical interpretation of the Harris-Wilson model that the number of ‘development possible’ states (in which Dj and Wj are non-zero) is reduced with increasing attractiveness and accessibility.
Fig. 2

Results displaying different retail spatial structure under varying model parameters (Source: Clarke and Wilson 1983)

From Numerical Experiments to Real World Applications of Spatial Interaction Models

Although the numerical experiments described above were interesting, the dearth of real world application of spatial interaction models was a growing concern. However, during the mid to late 1980s a series of related events transpired to make this, at last, possible. These included an explosion of data, computational developments, including GIS and visualization methods, and significant changes in the retail sector.

The Data Explosion

During the mid-1980s, both government and commercial organisations began to realize the value and importance of the data they collected on a routine basis. One commercial organization, Pinpoint Ltd., undertook a large scale survey of where consumers shopped, both in terms of their primary and secondary destinations. The outcome was something known as LUPIN which effectively was an origin-destination matrix (postal sector to retail centre) for the whole of the UK. This allowed spatial interaction modellers to properly calibrate their models for the first time, by identifying the parameters that would prove the best fit between observed and predicted interaction matrices. Furthermore retailers themselves recognized that data collected from electronic point of sale (EPOS) data and emerging loyalty card and credit card data could be of immense value in understanding consumer behaviour. The data explosion had begun and has increased exponentially ever since, a topic which is explored further in the next section.

The Development of Personal Computers

Up until the mid-1980s, modelling practitioners were dependent on using mainframe computers, and as noted earlier the concept of interoperability between different mainframe computers and operating systems was not yet developed. This, in itself, was a major constraint to the diffusion of modelling skills between institutions and between academic and commercial organisations. In 1984, the landscape shifted in seismographical proportions with the launch of the IBM PC and its disc operating system (DOS). The IBM PC was not particularly powerful and in some ways rather clumsy with floppy discs used to store and transfer software and data. But it had the unique advantage of compatibility. A software programme developed in Manchester could now run on a PC in Melbourne. Whilst PCs were at first incredibly slow relative to the power of mainframes, this changed very quickly as processing power accelerated quickly in accordance with Moore’s Law.

GIS and Visualisation

As discussed previously, the visualization tools available to spatial modellers were very primitive in the late 1970s and early 1980s. By the mid-1980s, this began to change. Companies such as ESRI and MapInfo developed pioneering Geographical Information Systems (GIS) software for mainframes and workstations. Expensive software licences became more affordable in the 1990s with the rapid growth in PC power, making GIS software widely available to academics and businesses. There was considerable debate about how best to integrate spatial modelling tools in general and spatial interaction models in particular with GIS software (see, for example, Birkin et al. 1996; 2002). A lot of the debate centred around whether it was possible to build ‘generic’ spatial interaction models within GIS packages or if a more customized approach was necessary. In addition to GIS, there were other developments in visualization software through packages such as Excel which made the interpretation of both data inputs and model outputs much easier.

Retail Competition and the Lack of Analytical Skills

In the 1970s and 1980s the expansion of the UK supermarket network was a dominant feature of the retail landscape. New sites were relatively easy to find and planning constraints were fairly lax. This then started to change and resulted in what became known as ‘store wars’ (Wrigley 1994). Although there was little evidence that the supermarket system was becoming saturated (Langston et al. 1997), it had certainly become more competitive and new planning regulations, most notably PPG6, discouraged retailers from developing out-of-town locations. The investment in developing a new store is substantial, typically many millions of pounds, so retailers were reluctant to take risks in getting it wrong. So there was a need to undertake more analysis on whether a new store would make an acceptable return on the investment required to develop it. This created a demand for a more rigorous approach to location analysis. However, many retailers simply did not have the internal capability to respond to this requirement. As a consequence they turned to third party organisations that did.

It was out of these related events that academics at the University of Leeds recognized an opportunity to explore the possibility of deploying spatial interaction models in a commercial environment with retail partners. Working through a university spin out company this operation employed around 120 staff by 1997, mainly geographers who had been trained in spatial modelling skills as undergraduates or postgraduates. Many UK and global retailers quickly recognized the value of linking with the skill sets of academics. But it was still necessary to prove that spatial interaction models could actually add value to retail investment decisions even in this new age of data, software and computational power. Getting the models to work in a commercial environment was a real challenge.

The first point to understand is that consumer behaviour in retailing is quite complex and varies between different types of retail activities, such as supermarkets, banking, automotive, high street and petrol forecourt. Table 1 attempts to summarize the different factors that influence sales in each of these different sectors. It can be seen that in some markets, such as supermarkets, the physical attributes of the destination are key components of attractiveness, in particular size of outlet, parking and accessibility. In other markets, such as financial services, the physical attributes of the outlet are of lesser importance as they tend to attract consumers who are doing something else in that centre. Brand has an important role to play in some sectors, supermarkets and automotive in particular, but less so in petrol retailing.
Table 1

Importance of model drivers by different retail market (Source: Birkin et al. 1996)

 

Supermarket

Retail

Auto

Finance

Petrol

Spatial aggregation

Fine zones

Medium zones

Coarse zones

Medium zones

Medium zones and network

Brand loyalty

Moderate/ strong

Moderate

Moderate

Strong (transactions)

Moderate

Attraction components

Space

5

3

4

1

4

Parking

5

1

3

1

5

Accessibility

5

4

2

3

5

Product range

4

2

4

2

1

Prices

5

5

5

5

5

Adjacencies

1

5

1

5

2

Opening hours

4

3

1

3

5

Complexity of distribution

Simple/ moderate

Simple/ moderate

Simple/ moderate

Complex

Simple

Travel distance

Short

Moderate

Long

Moderate

Long

Trip type

Single purpose

Multi-purpose

Single-purpose

Multi-purpose

Distress

Segmentation

Important

Fundamental

Important

Moderate

Marginal

1 = Relatively unimportant 5 = Very unimportant

Earlier, the question posed was: is it possible to develop a generic spatial interaction model that would work in all of these different retail sectors? It quickly became clear that the answer to this question was ‘no’. There was a clear need to develop customized models for different retail sectors. Some major elements of variation between key market sectors are identified in Table 1.

An obvious and related question is whether it is easier to develop more robust models for certain applications. Some features which are generally conducive to effective modelling are a small number of competing outlets (encouraging large and well-defined catchment areas), weak branding (emphasising the spatial element of the choice process), single-purpose trips (limiting the need to assess complex externalities) and the provision of good data (for model testing and calibration). Working for a DIY retailer in a substantial pilot study of south east England, it was possible to exploit these features to produce a model with exceptional predictive capabilities (Fig. 4).

Elsewhere, the challenges are greater. In the automotive sector, the loyalty to brands is much stronger, to the extent that major manufacturers can maintain substantial in isolated geographical areas – the Isle of Wight for example – even in the absence of local representation. In financial services, transactions are quite likely to be connected to shopping, work or leisure activities, and supported by a huge array of branches and other channels. In such circumstances, it was necessary to extend the models with complex disaggregation and filtering the relatively important factors relating to a particular sector as outlined in Fig. 2. As an example measuring ‘attractiveness’ in the Harris-Wilson model was simply a function of the size or square footage of the outlet. Reality is much more complex than that. Fig. 3 illustrates the type of attractiveness function that is required to robustly model high street retailing. Factors such a centre performance, store performance, brand, store maturity and store agglomeration all influence sales alongside the size of the outlet. In this paper there is not the space to discuss the details of these factors but a useful summary is provided in Birkin et al. (2010). Furthermore, the appearance of additional parameters in these models made the process of model calibration challenging at the best and onerous at worst.
Fig. 3

A typical attractiveness function for a high street model (Source: Birkin et al. 2010)

In extreme circumstances, the rationale for simulating the choice patterns of individual consumers through a spatial interaction models breaks down irrevocably. For a consumer filling the car with fuel goes beyond multi-purpose trip-making to a distress purchase based largely on convenience and price. The commodity – fuel – is relatively homogeneous and available through many thousands of outlets. Even with the more widespread adoption of loyalty cards, customer data is still patchy and incomplete. So, in this market, a different spatial modelling approach is required; a multivariate model was developed that took account of factors such as traffic counts, facility characteristics, other retail offers at the site (C-store, ATM, car wash) amongst others. This alternative model performed very well in a case study for the city of Palermo in Sicily, Italy. Figure 5 shows the results of a new forecourt opening. The light sectors of the circles are the predicted sales reductions from the new opening. In this case, note that the biggest impacts are not necessarily in the nearest locations.

Another important feature of the applied models is their international relevance. The university company worked with clients in every European country, North America, Japan, Australia and South Africa. The principles of spatial interaction modelling at one level are universal but their implementation demands a level of customisation to reflect differences in consumer behaviour, the retail landscape and variations in data availability. The company worked with many household names: Ford, Walmart, Toyota, Sainsburys, HSBC, ExxonMobil, WHSmith, to name but a few.

Interestingly, most successful applications took place in the private sector with comparatively less success in the public sector. This is difficult to explain but might relate to the fact that if you can demonstrate to a commercial organization that you can improve their return on investment then they are prepared to release funds for this to happen. In the public sector the criteria for ‘success’ are much more complex and difficult to enumerate. In the DIY example introduced above, the retail partner sought confidence in the modelling approach by setting a typical challenge. They provided sales data for eight stores in South East England and asked for predictions of the revenues for another six stores in the same study area. The results of this ‘exam paper’ are presented in Fig. 4, which shows observed and model predicted store revenues for all the stores in the study area. The store names have been anonymized to protect the commercial interests of the client. The results of the predictive analysis were impressive, with all but one of the missing store revenues predicted with plus or minus 5% of their actual revenues. On the basis of this modelling exercise, the retailer confidently invested in a new store deployment programme across the country (Fig. 5).
Fig. 4

Observed and model predicted store revenues for DIY stores

Fig. 5

The modelled impact of a new petrol station in Palermo, Italy (Source: Birkin et al. 1996)

The Future

It was clear from all the applied work undertaken with retail clients in the 1990s and beyond that spatial interaction models, intelligently applied did actually work and add significant value in terms of helping with investment planning. But it is interesting to ask if this is still the case in an era when omni-channel retailing and consumer behaviour has changed. Indeed Matthew Hopkinson (2017) from the Local Data Company goes as far as saying that “gravity modelling has no relevance to modern retail planning”. A discussion of the changes that have taken place in retailing in the UK and more generally has recently been published by Birkin et al. (2017). In summary these changes relate to the growth of new channels, especially on-line retailing, the growth of convenience retailing (Hood et al. 2016) and changing demographics with a growing but increasingly elderly population. A decade of ‘austerity’ has taken its toll and many well-known brands such as Woolworths, Blockbuster and Thresher have disappeared from the UK high street. New deep discount supermarkets such as Aldi and Lidl have challenged the dominance of the ‘big four’ and have expanded their retail networks substantially over the last decade.

However, there have been other changes that suggest that there are reasons to be optimistic about the future for spatial modelling in general and spatial interaction models in particular. As was noted in earlier, one of the reasons for the renewed interest in spatial interaction modelling in the 1980s and 1990s was the increase in data available to successfully implement them. In the 2010s the data explosion has continued apace with the emergence of what is termed ‘Big Data’. These new data sets offer new insights into changing consumer behaviour, not only in retailing but transportation, migration and other areas where spatial interaction models are still relevant. The importance and potential of new and emerging data sources is illustrated in the examples which follow.

The first example uses supermarket loyalty card data to look at seasonal variations in retail shopping patterns in coastal resorts, in this case in Cornwall in South West England. The retail partner had four supermarkets in the region and was planning to open a fifth. However, stores in the area showed markedly different patterns of seasonal revenue. Stores in tourist resorts show peaks in the summer months and in school holidays. Using loyalty card data it is possible to understand where consumers are coming from based on their residential location. Figure 6 shows residential locations of consumers at a coastal store for three different weeks in January, August and October in 2010 respectively. The patterns are quite clearly different. In winter the majority of consumers are locally based whereas in summer consumers have residential locations throughout the country, especially in the South East. The models developed around this data were used to forecast the revenues of the new store on a monthly basis. The results were sufficiently encouraging to persuade the retailer to go ahead with the new store development.
Fig. 6

Seasonal variations in customer origins at a coastal supermarket in Cornwall (Source: Newing et al. 2015)

Another new source of data is that captured by mobile devices such as phones and i-pads. The beauty about these data is that they are largely captured in real time so can give insights into how customers behave at different times of the day, different days of the week and different months of the year. Also, unlike loyalty cards the data are not specific to a particular retailer but cover the universe of an individual mobile phone provider’s customers. To illustrate the potential power of these new data, Fig. 7 shows the number of customers using different shopping areas in Leeds city centre in the spring of 2013. In late March, a new centre – the Trinity Centre – opened. The number of customers visiting the centre on the opening day, the first weekend and Easter weekend have been collected and can be compared with the same patterns in other retail centres.
Fig. 7

Daily customer counts from mobile phone data, Leeds city Centre, spring 2013 (Source: Birkin et al. 2017)

A third example involves the origins and destinations of transport users, in this case the train. Train operating companies have a reasonable database on the numbers of passengers who travel between different station but have little knowledge of the residential locations of the passengers or their final destination when they alight their train. Using mobile phone data, it is possible to identify the residential origin of travellers and their final destinations as well as the train stations they used. Figure 8 illustrates journey starting points for passengers travelling on the East Coast Mainline, while Fig. 9 shows the final destination of passengers who alighted at Kings Cross. Insights from data of this type is potentially invaluable in addressing issues ranging from ticket pricing and local economic development to land use planning and long-term infrastructure investments such as HS2.
Fig. 8

Origins of passengers travelling on the East Coast mainline to kings cross. (inset shows passenger origins for those passengers travelling from York station) (Source: Birkin et al. 2017)

Fig. 9

Final destinations for passengers alighting at kings cross

In many ways, the potential of ‘Big Data’ for spatial modelling is enormous as we gain deep insights into consumer behaviour. There are obviously some important issues about privacy, data protection and the extent to which these new data sets can be validated (Lovelace et al. 2016). To illustrate the point a comparison is presented between mobile phone data with 2011 Census data to see how well it reproduced what is considered as the ‘gold standard’ of population data in the UK. Figure 10 looks at comparisons between the daytime locations of population in London between these two data sets. As can be seen there is a good fit between day time populations in both data sets but further work is needed in the validation process. So an element of caution is required before the euphoria of Big Data gets us all carried away.
Fig. 10

Comparison of 2011 census and mobile phone data at LSOA level in London (Source: Lovelace et al. 2016)

Discussion and Conclusions

In the early days of applied spatial interaction modelling, data were scarce, and interesting results were obtained through theoretical exploration of model structures, backed by numerical experiments with idealized landscapes. Significant applied progress became possible with an injection of data from real world business organisations. Nevertheless model operationalization has never been a straightforward ‘one size fits all’ endeavour, but requires a creative, eclectic and pragmatic approach.. Knowledge of how different application areas operate is important and this probably requires engagement with service operators – work in an academic vacuum is unlikely to prove productive.

These lessons are important in considering current trends and future opportunities for spatial analysis. Data is now more abundant than ever, but typically rests under the control of business and commercial organisations. Engagement with real world partners is therefore more important than ever for the long-term development of new spatial modelling approaches, for example in representing real-time dynamics and predictive analytics.

Whilst emerging methods in data science and AI seem attractive – not least to government and large organisations – one size fits all will be no more robust as an ethos than it ever was. The next generation of spatial modellers must continue to set the bar high in their ambition and inventiveness and to be open to engagement and a collaborative approach to real world innovation. They will need to be mindful that the abundance of data is not necessarily matched by its quality, but should be encouraged by the relative facility in generation, storage and processing of data, and that methods and the associated software codes may now be shared very much more easily than in previous times.

Notes

Compliance with Ethical Standards

Conflict of Interest

The authors declare that they have no conflict of interest.

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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.School of GeographyUniversity of LeedsLeedsUK

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