ABSTRACT
In a broad sense, sustainable tourism is an industry devoted to minimizing its impact on the environment and on local culture, connected with new income and employment opportunities for the development and preservation of a site. However, tourism may have different impacts, either positive or negative, on the ecological system of a country (see, for example, Hughes, 2002: 457). As a result, it may be difficult, if not impossible, to formulate policies that allow tourism to be maintained over a long period without severely affecting the environment (e.g. Papatheodoru, 2003: 407; Hillary et al., 2001: 853).1 In this view, deriving a theoretical approach to tourism sustainability is not an easy task. To this end, we need to properly identify the link between tourism flows, T, and the stock of the available natural resources, E, for we assume here that high levels of E may stimulate an increase in tourist visits, even though negatively impinging on future recreation for the environment as a whole.2 To begin with, we start our analysis by giving an explicit algebraic interpretation of the stated tourism flows. Formally, let us define tourism as a slight modification of the Schaefer harvest function:
T vE= (9.2)
where v ∈ [0, 1] is the number (i.e. percentage) of new-coming tourists visiting (i.e. harvesting) the selected natural site, E.3 On the other hand, without any loss of generality, evolutionary dynamics of the environmental good, E, is assumed here to be also influenced by tourism, T, and explicitly given by
E f E T E T= = − ∈( , ) ( ) [ , ]δ δ1 0 1 (9.3)
where fT < 0, for any increase in the number of tourists diminishes the selfreproduction capacity of the ecosystem, or rather nature’s capacity to recover from tourists’ resource exploitation (e.g. Smulders 1995, p. 163). To make a whole representation of the entire dynamics described so far, we substitute (9.2) into (9.3) and let f (·) behave as a 3D characterization of the common Verhulst logistic function (see Verhulst, 1838: 113):
E E vE f E v= − ≡δ ( ) ( , )1 (9.4)
where δ can be interpreted as the usual parameter for the internal growth rate of a natural resource, while ν can be finally interpreted as a choice variable representing a measure for the carrying capacity of the place being considered.4 As a matter of fact, determining the correct tourist carrying capacity can be quite complicated. It might be worth fixing the appropriate lower bound of natural resource exploitation, below which the system incurs the risk of an inevitable qualitative deterioration (see also Bretschger and Smulders, 2007: 1). We
can thus proxy the carrying capacity by the size of arrivals – that is, the density of tourists – that a specific destination may host per unit of land, as synthesized by 1/ν, which is commonly referred to in the literature as a ‘welcoming capacity’ (e.g. Costa and Manente, 2000).5
