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interactions (Smith, 1985). Nevertheless, despite its problems the gravity model remains
widely used in transport planning and retail analysis; 'the great variety of forms means that an
approximate fi t can nearly always be made and the model then used to predict future fl ows'
(Hay, 1986: 186).
Gravity models (Malamud, 1973), locational analysis and the role of distance and distance
decay (Taylor, 1971) in economic and tourist behaviour played a signifi cant role in
early tourism-related economic geography, including the infl uential work of Christaller
(1963) (Hall and Page, 2006); as well as research based on the travel cost method (e.g. Font,
2000) and distance decay functions in tourism (e.g. Zhang
et al.
, 1999; McKercher and
Lew, 2003).
Also connected to this period of spatial analysis, and still strongly resonating in tourism
geography, is Butler's (1980) Tourist Area Cycle of Evolution, the origins of which were
heavily infl uenced by location analysis and Christaller's work in particular (Butler, 2006c;
Hall, 2006b), with the fi rst version of the model (Brougham and Butler, 1972) suggesting that
the destination development process 'may be satisfactorily approximated by the solution of
the logistic equation
Dv
= kV(M
−
V)
(4)
Dt
where V is the number of visitors,
t
is time, M is the maximum number of visitors and K is
an empirically derived parameter representative of the telling rate, or the spread of knowledge
of the resort from tourists to potential tourists (Brougham and Butler, 1972: 6, cited in Butler,
2006a: 17). The solution was proposed as
V
=
MVOV
+ (
M
−
V
) −
Mkt
(5)
where
V
is the number of tourists at time
t
. The comment with respect to the 'telling rate' also
provides a strong connection to the work of Hägerstrand (1968) on the formal analysis of
innovation diffusion as a spatial process, which later developed into his infl uential work on time
geography (discussed below; see also Shoval
, Chapter 22
in this volume). Indeed, in stressing the
importance of a mathematical approach to tourism space, Hall (2006b: 99) argued that 'the
product life-cycle so infl uential in consideration of [Tourist Area Cycle of Evolution] is itself a
space-time wave analog related to innovation diffusion processes . . . a point seemingly lost in
nearly all of the discussion which has taken place on tourism destination product life-cycles. Such
an observation also highlights the potential for spatial interaction modelling to provide a better
understanding of the development of information regarding potential destinations.'
Spatial interaction as statistical mechanics
The next major theoretical framework came with the work of Wilson (1967, 1974, 1975),
who produced a family of spatial interaction models, initially rooted in entropy-maximising
methods, which also functioned as location models, and which were particularly infl uential
with respect to retailing fl ows, transportation analysis and regional economics (O'Kelly,
2010). These models were signifi cant because they provided a theoretical justifi cation for
what had hitherto been an empirical observation, although they have been criticised on the
basis that one analogy, that of gravitational attraction, has merely been replaced by another,
statistical mechanics (Fotheringham
et al.
, 2000). However, from the 1970s onwards
