Differential urbanisation for settlement planning – A Western Cape case study

The differential urbanisation model is a means to assess settlement growth rates. While the model has been tested primarily at a national level, including in South Africa, this study seeks to apply the analysis to the sub-national scale in the Western Cape province and Cape Winelands district municipality. The study found that the model is applicable to both the province and the district municipality. Settlements of differing size and economic importance grew at varying rates relative to each other in a predictable sequence, which realised the urban hierarchy, over a 20-year period. This finding was unexpected, given that the urban differential model assumes economic growth as well as labour and socio-economic homogeneity – factors that have not been realised evenly sub-nationally. The applicability of the model to these locations may assist in the public division of resources, particularly in small towns, where meaningful urbanisation occurs, yet capital allocations are limited. The applicability of the study is in keeping with national, provincial, and municipal trends in planning that emphasise the interrelationship between settlements of different size and function over time, and the importance of spatial planning in guiding public infrastructure expenditure.


INTRODUCTION
South Africa is urbanising rapidly in the context of a growing population.According to the United Nations (UN), 71.3% of the South African population will live in urban areas by 2030 (RSA, 2022: 51).This estimate varies depending on the source of information used.In an earlier report, the South African Cities Network (SACN), using Council for Scientific and Industrial Research (CSIR) data, stated that "[i]t is estimated that almost 78% of South Africa's population of 51.7 million people live in cities and towns in both urban and rural areas, with only 14% of the population living further than 20 kilometres away from a town or city" (SACN, 2016: 33).
The variation in urban growth statistics is partly a function of the decade between national population censuses, resulting in less reliable data to project rapid population change.It is also a function of differing metrics and the spatial frames used to analyse data.This requires researchers to apply a range of approaches to estimate different facets of this change and to seek consistency in categorisation and measurement.
A population change model focused on cities and towns applied to South Africa over the past three decades is the differential urbanisation model.The model describes how categories of settlements experience successive periods of fast and slow growth relative to each other in a continuum of development during the evolution of an urban system (Geyer, 2003).The model was developed by Thomas Kontuly and Hermanus Geyer (1993), expanding on an earlier paper by Geyer (1990) and detailed in subsequent publications (Kontuly & Geyer, 2003;Geyer, 2003;Geyer et al., 2012;Geyer & Geyer Jr, 2015;Jacobs, 2014).
The differential urbanisation model was applied in its assessment of South African settlements, and with greater sophistication of analysis at the metropolitan scale (for example, Geyer et al., 2012), considering different attributes such as race and economic factors to describe settlement change.
The importance of realistic models such as differential urbanisation, which also considers population estimates to facilitate effective settlement planning and public infrastructure provision, is acknowledged for both project and programme planning (Biermann & Landre, 2002), as well as infrastructure asset management (RSA, 2018).As such, population growth has been a long-term consideration nationally, as currently recognised in the National Spatial Development Framework (NSDF) (RSA, 2022), and in provincial policy, and is a legislated requirement of municipal spatial development frameworks in terms of section 21(e) of the Spatial Planning and Land Use Management Act, Act 16 of 2013 (SPLUMA).Therefore, the need for a range of robust population growth models applicable to different geographical scales to understand urbanisation is important for the national and municipal planning profession.
This study fills a gap in previous research in applying the differential urbanisation model to the provincial and district municipality scale.The intent is to determine whether the model is applicable sub-nationally and to analyse how urbanisation patterns have changed in the Western Cape between 1996 and 2016.

Differential urbanisation
The differential urbanisation model, derived from urban economic geography, describes the changing relationship between settlements of different sizes with time, and originally used to describe urbanisation in developing countries (Kontuly & Geyer, 1993: 164).It builds on the central place theory applying ideas related to the role of market forces, locational attributes, innovation diffusion, development axes, and agglomeration economies (Kontuly & Geyer, 1993: 159).It is a modernist theory, drawn from a period when urbanisation was conflated with development and population growth (Fair, 1982), premised on economic growth occurring in a formal, rational manner.The model differs from linear growth theory in its promotion of a cyclical concept, whereby settlements of differing size and economic importance grow at varying rates relative to each other in a recurring sequence which realises a settlement hierarchy.The hierarchy is not static and is open to changing socio-economic dynamics.
The recurring sequence of the model described by Geyer (2003: 91-92) is polarisation (or urbanisation) (U), polarisation reversal (PR), and counter-urbanisation (CU).In turn, each phase of the sequence has two urban stages.The full sequence is depicted in Figure 1 (Kontuly & Geyer, 1993: 164-166): where the population of a core settlement/s (city/cities) grows fastest, and urbanisation is focused on select locations in the urban system.where the growth rate of intermediate cities is greater than that of small cities, which, in turn, is greater than that of the primary city/cities.3. The final phase of the urban system cycle, where the urban system reaches maturity, is termed counter-urbanisation.
Migration to smaller towns ensures that this category of settlement grows at a higher rate than core settlements and intermediate cities.Like the other phases, the phase is divided into an early small city stage (ESC), where the growth rate of small cities is greater than intermediate cities, which is, in turn, greater than that of the primary city/cities, and an advanced small city stage (ASC), where the growth rate of small cities is greater than that of primary cities, which, in turn, is greater than that of intermediate cities.
The differential urbanisation model functions on the premise of "a cumulative causation process", where one or more primary settlements in a nation state realises "the polarization of labour and any surplus capital from other regions", establishing a core-periphery relationship in an evolving urban system (Geyer, 2003: 89-90).Over time, the primate city/ cities grow to the extent that the conurbation becomes inefficient and costly relative to other regional settlements, due to rising congestion costs and land values, resulting in critical economic activities and associated populations relocating to these more competitive settlements (Kontuly & Geyer, 1993: 159-160).
In turn, this causes the growth rates of regional settlements to be greater than the core settlement/s, resulting in polarisation reversal.In turn, improved efficiencies in the urban system, for example improved transit, combined with improved economies of agglomeration in some smaller settlements, realises movement to these places, which grow at higher rates than primary and/or regional cities, and is termed counterurbanisation (Geyer, 2003: 91-92).
Migration is framed as flows that aid concentration, notably the movement of low-income earners to primary cities in search of employment, as well as those flows that aid deconcentration to smaller settlements in the hierarchy, for example middle-and highincome earners moving to rural or small settlements as a lifestyle choice (Geyer, 2003: 97-98).
The nature of such migrations varies temporally and spatially.Kontuly and Geyer (2003: 92) also note that "caution must be exercised when applying the model to reality because the temporal characterization of the differential urbanization model refers to an ideal situation where urban areas are evenly distributed in an area with relatively evenly distributed natural resources".
In applying the model to reality, deviations should be anticipated and factored into assessment.
The model has been tested internationally (Kontuly & Geyer, 2003).The studies found that a differential urbanisation cycle is observable, although with variations and discontinuities.Finland was the only country reviewed where polarisation reversal and counterurbanisation occurred in sequence before the cycle re-initiated with a further phase of polarisation.In Turkey, Italy, and India, the shift from the polarisation stage to the polarisation reversal phase progressed without a counterurbanisation phase being identified.
For Russia and the Federal Republic of Germany, the disruption of the Second World War was used to explain the countries' deviation from the model.When the economic, social, and political disruptions caused by the war ended the crisisrelated population deconcentration, the countries entered a polarisation phase (Kontuly & Geyer, 2003).
The studies suggested that, when testing the differential urbanisation model, death and birth rates should be analysed alongside population growth rates, although this was not deemed a necessity (Kontuly & Geyer, 2003).In addition, the possibility of a nationwide assessment being applicable at a regional scale was suggested.From the application of the differential urbanisation model to South Africa, three observations can be made.First, the analysis is dependent on reliable demographic data (Geyer, 2003).During apartheid, Black South Africans were treated primarily as urban migrants and not as residents.This required other means of confirming urban populations.

Differential urbanisation in South Africa
Secondly, the determination of boundaries in the formation of homelands from the late 1960s to the early 1980s meant that the designation of towns and cities, or portions thereof, could change a designation from a core city to a rural location (Geyer, 2003: 95).
The vagaries of apartheid planning also highlight that the delimitation of settlements and the subsequent determination of categories is, to an extent, arbitrary and dependent on the perspective of the researcher.This holds in the case of the differential urbanisation model which is applied retrospectively and there is existent knowledge of the growth trajectory of a given settlement, where a three-to four-tier categorisation is optimal to observe relative changes in growth rate, even if a settlement's population size and economic function is not significantly different.
A sub-national application of the model in the South African context has been applied to the primary metropolitan areas (Geyer, 1990;Geyer, 1993;Geyer et al., 2012;Geyer & Roux, 2017;Geyer & Mosidi, 2018).In these studies, population change in conurbations has been differentiated through a range of available socio-economic indicators, including race and income (Geyer, 1990;Geyer, 1993;Geyer et al., 2012), household size (Geyer & Roux, 2017), and gender (Geyer & Mosidi, 2018).These studies add value to the retrospective economic focus of the national application of the differential urbanisation model from a range of socio-economic and cultural perspectives, which may assist in making informed decisions regarding land-use change and infrastructure provision in metropolitan areas.
Besides the metropolitan focus, the application of the differential urbanisation model at a sub-national scale has had limited consideration.
An exception is research undertaken by Jacobs (2014), which applied the model in considering in-migration to the Western Cape province between 2001 and 2011, with the focus on the origins and destination of immigrants to the province.Two distinct streams of migrants were identified.A primary stream of migrants came to the province in search of jobs, education, and better services.They were mainly young, low-income earners, aged between 25 and 29 years, originating primarily from the Eastern Cape, settling in the City of Cape Town, Saldanha Bay, George, and Ceres (Jacobs, 2014).A sub-stream of migrants, consisting of relatively affluent, highly skilled, married, and older migrants from the metropolitan cities in the country, especially Gauteng, was also identified.This group was attracted to intermediate sized municipalities such as Overstrand, Mossel Bay, Knysna, and Bitou (Jacobs, 2014).
The research was concerned with the nature of urbanisation trends beyond the provincial borders of the Western Cape and did not consider whether the differential urbanisation model was applicable to the province's urban system.

The application of differential urbanisation to settlement and spatial planning in South African policy
The importance of accurate population projections to facilitate effective settlement planning and public infrastructure provision is acknowledged (Biermann & Landre, 2002: 330) 1951-19801980-19911996-2001Second cycle 2001-20072007-2011 Source: Compiled by the authors (Information on urban stages is derived from Geyer, 2003;Geyer & Geyer, 2015.)cost modelling for bulk and connector services and social facilities.Population projections guide the capacity demand for infrastructure services for the settlement, and/or a project, influencing density calculations in tandem with a consideration of existing infrastructure supply (and condition) and the settlement units to be provided, or serviced, within budgetary constraints (Biermann & Landre, 2002).In turn, such modelling is underpinned by norms, standards, and guidelines for types of infrastructure and social facilities, providing a level of equity in the provision of services (Wüst, 2020) (RSA, 2016: 7).This emphasis on the interrelated, networked nature of nuclear settlement aligns the policy to the differential urbanisation model and its emphasis on the relations of different sized settlements in an urban system.
The IUDF notes that settlements differ markedly in South Africa, suggesting that standard theories such as the differential urbanisation model will not necessarily be applicable to all settlements.
Of most significance to the model, the IUDF considers three means of categorising settlement (RSA, 2016: 24-27).One typology is based on the settlement's location in relation to 'the core' and to 'the  Historically, the differential urbanisation model has been applied primarily at the national and metropolitan levels in South Africa.The idea of an urban system, or hierarchy, on which the model is based, has been incorporated into national policy as concerns of urban sustainability and the complexity of the jurisdictions under administration have changed in the 20 years between 1996 and 2016.A gap in the consideration of differential urbanisation theory in South Africa is its application to the sub-regional urban system.Such an assessment would provide municipalities and provinces with a more nuanced perspective to urban change than that provided by national policy.The case study below highlights such an attempt, using available data, undertaken for the Western Cape province and the Cape Winelands district municipality.

CASE STUDY AREA
The Western Cape province is a coastal province located in the south-west of the Republic of South Africa (Figure 2).The total population of the province was 5.8 million at the last census in 2011 (Stats SA, 2012).The primate or primary city of the province is Cape Town, with an estimated population, in terms of the 2016 Community Survey, of 4.2 million (WCG, 2021a

Research questions
The following research questions were used to guide the study: • Is the differential urbanisation model applicable to the Western Cape? • What are the sub-national conditions under which the model might fail?• How might spatial planning benefit from a consideration of the model?

Research design
The

Data collection
The spatial distribution of population groups was considered, by analysing changes in population size in Western Cape settlements, using Statistics South Africa Census data for the years 1996 (Stats SA, 1997), 2001 (Stats SA, 2002), and 2011 (Stats SA, 2012) 2018), where population data sets are assigned to mesozones based on an algorithm developed on the principles of dasymetric mapping.Stats SA 1996, 2001, 2011, and 2016 population figures were used as the input data for the respective years.These data sets have different spatial demarcations.The data has thus been re-aligned to the mesozones to create a comparable data set, using the secondary data (Van Huyssteen et al., 2018).

Calculations
The population growth rates for each of the settlements that fall within the primary, intermediate, and small settlement categories were calculated.Once the population growth rates of the three settlement categories were determined, the differential urbanisation model was applied to determine the recurring sequence (see Table 4).

Settlement classification Classification category City regions
Primary settlement Cities and very large regional centres Large regional centres

Data analysis
In calculating the growth rate for the settlements in the three categories, the following information will be analysed: Pattern: The three settlement categories will be classified as either urbanisation (U), polarisation reversal (PR), or counter-urbanisation (CU) for the respective years, according to the differential urbanisation model.

Urban stage:
The three settlement categories will be classified as either early or advanced for the respective years, according to the differential urbanisation model.

Urban development cycle:
According to the differential urbanisation model, counterurbanisation represents the final phase in the first cycle of urban development and is followed by a second cycle in which urbanisation dominates once again.

Limitations
There are inherent limitations in undertaking such a study, due to data and the nature of the model being assessed.Secondly, due to a decade-long period between censuses, the latest data for the 2016 community survey is outdated and based on a relatively expected, given the larger number of settlements and the smaller population sizes in the small settlement category relative to the other categories.Relatively small changes in population size will have a greater statistical impact in the small settlement category than in the other categories.It is interesting to note that the primary settlement (namely, the Cape Town Metro) had a higher growth rate for the period relative to the intermediate settlements, a reflection of the urban centre's importance as a locus of urbanisation in the province.
Figure 4 graphically represents the relationship between the growth rates of the Western Cape settlement categories, as an interpretation of the province's differential urbanisation narrative.
Between 1996 and 2001, the Western Cape urban system experienced a counter-urbanisation phase, where the rate of growth of small settlements (5.56%) was higher (for example, mid-year population estimates) may realise different interpretations of the differential urbanisation model as it applies to the Western Cape and to the Cape Winelands district municipality.Further analysis and discussion are required to understand different interpretations of settlement trends.

Western Cape
The change in growth rates between the three categories of settlement was calculated for the settlements in the Western Cape province (see Table 5).While populations continued to grow in the settlements in the Western Cape, the rate of population growth declined for all three categories between 1996 and 2016.
In comparing the settlement categories, the greatest change in growth rates for the period 1996 to 2016 was experienced in the small settlements (4.29%).This is small sample, and the 2022 census data is yet to be analysed.As a result, there is uncertainty regarding the quality of the recent data used and as such, the assumptions made based on this information.
Thirdly, population figures for settlements were extracted from the SA CSIR MesoZone 2018v1 Dataset, where STATS SA 's 1996, 2001, 2011, and 2016 population figures were re-aligned to mesozones to create a comparable data set.As a result, the population figures used in the study are not identical to the census figures (which are ward based), but the data is spatially comparable, ensuring that data can be applied satisfactorily for the purpose of the current analysis.
Fourthly, the growth rate calculations should ideally incorporate births and deaths at the settlement level.However, in some of the national case studies applying the model, only population growth rate was used in the analysis, and this was considered adequate in the literature (Kontuly & Geyer, 2003).Similarly, the study could have used other data such as economic growth, unemployment, ethnicity, and income distribution to obtain a more detailed perspective on the nature of differential urbanisation in the Western Cape.
Fifthly, the differential urbanisation model is a theoretical application, based on assumptions regarding the economy and the nature of settlements.The reality of the study is that, in some cases, settlements were contiguous (where settlements in the City of Cape Town merge with settlements in the Cape Winelands district), that the majority employed did not necessarily work within the catchment of the settlement, due to commuting and the influence of the internet economy, and that settlements and resources were not evenly located across the province.
As such, deviation from the model in the study should be expected.
Lastly, the analysis carried out in relation to the case studies is an extrapolation, based on a reading of available data.Other analyses of settlement population using different spatial definitions, settlement footprints, or population estimates   During this period, intermediate settlements had a higher growth rate than the primary settlements, which classifies the urban system during the period as being in the early small city stage (Phase V).
From 2001 to 2011, the Western Cape urban system went through an urbanisation phase, where the growth of primary settlement was higher than the intermediate (2.37%) and small settlement (1.80%) categories.As the intermediate settlements showed higher growth rates than the small settlements, the urban system is identified as being in an advanced large city stage (Phase II) during the period.
From 2011 to 2016, the Western Cape urban system experienced polarisation reversal, where the rate of growth of intermediate settlements (2.25%) was higher than that of primary (1.48%) and small settlements (1.27%).Primary settlements realised a marginally higher growth rate than small settlements, placing the Western Cape urban system in the early intermediate city (III) stage.In terms of the differential urbanisation model, the stage marks a turning point in the spatial patterns of growth and development, as continuing concentration ceases and urban deconcentration from primary settlements commences.
If the differential urbanisation model holds, it is expected that, post-2016, the Western Cape will have moved into a counterurbanisation phase again.This shift will be confirmed once the census 2022 data is available.
When comparing the provincial findings with the national application of the differential urbanisation model undertaken by Geyer and Geyer (2015), the phases experienced are the same for the 1996-2001 and the 2001-2007 periods.However, for the 2007-2011 period, the national urban system experienced polarisation reversal, while, in terms of the provincial case study, the polarisation reversal was identified later in the period 2011-2016.

Cape Winelands district municipality
The settlements, was highly variable (see Table 6 and Figure 5).Between 2011 and 2016, the growth rates of all three categories of settlement converged in a band between 2.31% and 2.48% (see Figure 5).
The Cape Winelands district municipality mirrored the phases and stages realised by the analysis at the provincial scale.Between 1996 and2001, counter-urbanisation was experienced;between 2001 and2011, polarisation, and  Source: Compiled by the authors growth rate for that tier in the settlement hierarchy within a given period.This creates a generalisation as to the nature of population change in this settlement type across the geographical area.While models are premised on such generalisations, it is important to reflect on why given outcomes are observed.The observation also highlights the importance of rational determination and explanation in defining a settlement hierarchy's categories.
The above argument assumes that the application of the differential urbanisation model in the case of the Western Cape province and the Cape Winelands district municipality is unusual, and that its realisation could be disrupted by a range of factors, including crime in primary settlements; the residual negative effects of the COVID pandemic; impacts of interest rate shifts and other housing market dynamics; reduction in tourism; increases in unemployment; political instability, and financial constraints in the public and private sectors.

The differential urbanisation model and planning
Differential urbanisation as a retrospective economic geographic model is not a planning tool.
Nevertheless, as the model applies to the study areas, it can be used to identify settlements that have populations growing faster than others.This can be used as an indicator of settlements that require additional capital investment relative to existing infrastructure and facility capacity.This would have a significant impact on rural settlements that may be experiencing unexpected in-migration not considered in sector masterplans, infrastructure asset management plans, and small capital budget allocations from national and provincial government.Annual, medium-and long-term budgets would need to be sensitised to these variations in settlement growth rates and the implication for budget spending, especially with regard to infrastructure that supports economic growth: water, electricity, transport, and local economic development support.

Differential urbanisation model
Despite the expectation for deviation from the differential urbanisation model, when applied to Western Cape province and the Cape Winelands district municipality, the model held true.The hierarchy of settlements chosen demonstrated cyclical shifts in population growth rates for the two sub-national regions.This indicates that the urban system grew at differing and predictable rates over a twodecade period, realising periods of attraction and dispersal relative to the primary settlement, Cape Town.
As of the 2011-2016 period, the Western Cape and the Cape Winelands district urban systems are maturing, with primary cities experiencing declining growth rates, whereas intermediate cities experience higher growth rates.
Where deviation did occur, it was in relation to the application of the differential urbanisation model to the national urban system, where polarisation reversal was observed in a later period at the provincial and district municipality levels, than that experienced at the national scale.This misalignment could be a function of the study being unable to apply the STATS SA community survey data, but it could also be an indication of an urbanisation pattern specific to the Western Cape.If the sample for the Western Cape is valid, Census 2022 data will be required to verify this deviation.
A reason for the Western Cape urban settlement alignment to the differential urbanisation model is that it should meet the underlying assumption of the model that the economies of the settlements in question were growing during the period.While this may have been the case in some periods for specific settlements in the province (for example, Cape Town, Stellenbosch, Paarl), low to negative economic growth was experienced for other periods in specific settlements (WCG, 2021b).It could also be that shifts in economic activity to greater informalisation and an increase in information technologybased enterprise may be distorting settlement growth patterns.In the case of the informal economy, this could mean that the settlements' economy is growing faster than predicted but was not reported.
In terms of the model, this would realise greater settlement growth of low-income housing and informal settlement.The impact of informalisation is arguably most visible in smaller settlements such as De Doorns and Tulbagh, where the formal economies of the towns and hinterlands do not support the populations residing in these towns.
In relation to technology-based enterprise, employment may be based elsewhere, nationally or overseas, and may have limited physical connection to the settlement in which the labour is undertaken, an underlying assumption of the urban differential model, so that while economic activity, and perhaps growth may occur, this does not necessarily realise change in settlement populations.This may have a disproportionate impact on the increase in settlement form through a growth in lifestyle estates premised on high levels of internet connectivity and increased security.
A further possibility for the application of the differential urbanisation model is the movement of middleincome and wealthy groups to select locations in the Western Cape (for example, Hermanus, Stellenbosch, Paarl, and McGregor) as a lifestyle choice, a population flow identified by Jacobs (2014).
The application of the model to the study areas may simply reflect a distinctive regional urban system of largely independent centres that, due to historical and topographical reasons, are relatively evenly distributed, and, while not evenly resourced, are physically well connected.However, the above possibilities are speculative and require further research.
The study highlights the impact of relatively small increases in population on small towns.This dictates an increase in the population From a spatial (or strategic) planning perspective, the cyclical, urban systems focus of the differential urbanisation model has offered a more complex view of settlement than national urban policy applied prior to 2016.This policy focused on nationwide service delivery to address apartheid settlement segregation, with investment focused on primary metropolitan areas at the expense of relative economic growth in rural settlements.Since the introduction of the IUDF and the subsequent NSDF, policy has considered an urban system approach that emphasises the relational and hierarchical aspects of settlement.While these policies do not apply the differential urbanisation model, they do create a scenario where applying the model may be useful in applicable geographies.
The study suggests that, given the success of applying the model at the provincial and district municipal levels in the Western Cape, district and metropolitan spatial planning initiatives such as the joint district and metropolitan approach (the local version of the national district development model), as well as district and provincial spatial developments would be suitable vehicles to incorporate the differential urbanisation model.This would contribute to historical attempts within municipalities and provinces to understand local settlement dynamics.

CONCLUSIONS AND RECOMMENDATIONS
This study sought to apply the differential urbanisation model to the provincial and district municipality contexts of the Western Cape between 1996 and 2016, expanding past applications to the national and metropolitan urban systems.The study found that the model applies to the province and the case of the Cape Winelands district municipality.
The study highlighted that urbanisation within the Western Cape province occurs in the context of a long-term declining population growth rate across settlements.Placed in a hierarchy of primary, intermediate and small settlements, population growth rates for these categories follow a cyclical process of concentration and deconcentration relative to the other categories.These processes can be termed polarisation, polarisation reversal, and counter-polarisation.
While the differential urbanisation model is not a planning tool, it provides a means of assessing which settlements require additional capital funding for services and facilities, in order to meet the needs of settlements with unexpected increases in population.This would be especially useful for smaller municipalities that have limited capital budgets.The model could best inform the revision of district and provincial spatial development frameworks.
In applying the differential urbanisation model in other provinces and districts, practitioners would need to ascertain whether the model would apply, as urban systems vary across South Africa (Geyer, 2003;RSA, 2022)

Figure 2 :Figure 2 :
Figure 2: Map of South Africa indicating the administrative region of the Western Cape province and the Cape Winelands district municipality Source: Compiled by the authors 4. METHODOLOGY 4.1 Research questions The following research questions were used to guide the study:  Is the differential urbanisation model applicable to the Western Cape?  What are the sub-national conditions under which the model might fail? How might spatial planning benefit from a consideration of the model?4.2 Research design The following calculations were used to determine the percentage change between the census years (for example, between 1996 and 2016), and average growth rate (%) per annum: Percentage change = (2016 population final value -1996 population starting value)/1996 population starting value Average annual rate of growth (%) = percentage change/time (years)

Figure 3 :
Figure 3: Settlement categories used in the application of the differential urbanisation model to the Western Cape province Source: Compiled by the authors (Settlement data from CSIR MesoZone 2018v1 Dataset)4.6SampleTable3is an extract from the Excel document that was used in the study to list all settlements in the Western Cape, their classification, their population figures for 1996,

First
, the study makes use of available census and community survey data for 1996, 2001, 2011, and 2016.The 2007 community survey was excluded, due to concerns related to its credibility (Mail and Guardian, 2008) and small sample size, which made disaggregation of the data difficult.

Figure 4 :
Figure 4: Rate of growth for settlements in the Western Cape (1996-2016) Source:Compiled by the authors

Figure 4 :Figure 5 :
Figure 4: Rate of growth for settlements in the Cape Winelands district municipality (1996-2016) Source: Compiled by the authors The Cape Winelands district municipality mirrored the phases and stages realised by the analysis at the provincial scale.Between 1996 and 2001, counter-urbanisation was experienced; between 2001 and 2011, polarisation, and between 2011 and 2016, polarisation reversal.Between 2011 and 2016, intermediate settlements such as Wolseley (2.87%), Ceres,

Table 2 :
Classification of settlements in the Western Cape province Source:Compiled by the authors (CSIR functional town typology derived fromVan Huyssteen et al., 2018: online)

Table 4 :
Criteria used for data analysis in the application of the differential urbanisation model to the Western Cape II. Advanced primate city stageGrowth of primary > intermediate > small Polarisation reversal (PR) III.Early intermediate city stage Growth of intermediate > primary > small IV.Advanced intermediate city stage Growth of intermediate > small > primary Counter-urbanisation (CU) V. Early small city stage Growth of small > intermediate > primary VI.Advanced small city stage Growth of small > primary > intermediate Source: Compiled by the authors (differential urbanisation criteria retrieved from Mookherjee & Geyer, 2011) distribution of the subsequent classification of settlements.
Table3is an extract from the Excel document that was used in the study to list all settlements in the Western Cape, their classification, their population figuresfor 1996,  2001, 2011, and 2016, as well as the calculated average annual rate of growth between census periods (see Annexure A for a complete list).

Table 3 :
Sample of data and formulas used in research

Table 5 :
Western Cape stages of differential urbanisation for 1996-2016 Figure 4: Rate of growth for settlements in the Western Cape (1996-2016) Source: Compiled by the authors and may differ from the Western Cape experience.