1 Introduction

Ecotourism is a form of development in which income is generated for local people and/or governments from visitors (e.g., tourists) attracted by natural ecosystems. Ceballos-Lascurain (1987) presented an early definition of ecotourism as “traveling to relatively undisturbed or uncontaminated natural areas with the specific objective of studying, admiring, and enjoying the scenery and its wild plants and animals, as well as any existing cultural manifestations (both past and present) found in these areas”. More recently, the conceptual basis of ecotourism has expanded along conservation, sustainability, and even ethical lines of thought (Blamey 2001). The concept has evolved rapidly, in particular as conservation scientists have recognized the potential of ecotourism to help protect sensitive environments and to support local economies, often in underdeveloped areas where other forms of development are not possible to achieve. As an example of this conceptual growth, Honey (1999) suggested the following seven characteristics for ecotourism: (1) involves travel to natural destinations, (2) minimizes impact, (3) builds environmental awareness, (4) provides direct financial benefits for conservation, (5) provides financial benefits and empowerment for local people, (6) respects local culture, and (7) supports human rights and democratic movements.

Ecotourism has grown to be an important economic force that globally involves millions of visitors and billions of dollars annually (Filion et al. 1994). Questions remain about the ability of this form of development to be sustainable, however, because of the various costs of travel, and of the potential limitations in managing the environmental impacts of ecotourists on the human communities and ecosystems that they visit (Beekhuis 1981; Duffy 2002; Gossling 1999, 2000; Young 2003). For this industry to provide a stable basis for the economy, it must be able to generate business and income on a long-term basis. In order to examine these long-term prospects, a computer simulation of ecotourism in Belize was developed and studied.

2 Methods

A model for the industry of ecotourism in Belize is shown in Fig. 1, using the energy circuit language for systems modeling (Odum 1994). For this model development, the major factors involved in the dynamics of ecotourism in Belize were identified, and storages and material flows were diagrammed. The energy circuit–diagramming method shows the major energy flows external to a system as forcing functions, flows internal to a system as material or energetic transfers between components, and state variables as accumulating storages of material or energy. The direction of energetic or material transfer between state variables can be defined by formalizing a system of first-order ordinary differential equations that allows computational simulation.

Fig. 1
figure 1

Energy circuit diagram representing the model of the ecotourism industry in Belize

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The model is centered around two-state variables modeled as storages that were determined as most relevant to the Belizean tourism industry: the natural ecosystems of the country, represented by N, and tourism infrastructure, represented by I. Natural sources of energy (sun, wind, rain) are the major inputs to the natural ecosystems, assumed here to represent the terrestrial rainforest. Other energy sources include labor, goods, and services as inputs to tourist infrastructure and tourists as a flow through the system interacting with components through material, energetic, and economic transfers. The energetic inputs to the maintenance and growth of local tourist infrastructure include the investment of local labor (modeled as the flow-limited source L 0 since Belize has a small population, and thus, there is a maximum number of man-hours of labor per year), and investment of goods and services from investors and developers based outside of Belize.

To describe the dynamics that draw tourists to Belize, it is assumed that it is the perception of some combination of extant tourist infrastructure and natural ecosystem that attracts tourists. The flow of tourists through Belize is simulated as a continuous source-limited flow (J T) into and out of Belize and pulled from an overall pool of possible tourists. In the model diagram, the tourist flow enters the system on the right-hand side and interacts with the system through a series of three workgates representing the ecotourism experience before leaving the system. The ecotourism workgates have multiplier inputs from natural ecosystems (N) and from tourist infrastructure (I) and a divisor input from the price of oil (P O) in the global economy, shown in the top right of the diagram. In a functional sense, this means that tourists are attracted to the system in direct proportion to (1) the available pool of tourists (T), (2) the natural ecosystems that they would see during their visit (N), (3) the infrastructure in terms of lodging, etc. that they would use during their visit (I) and in inverse proportion to (4) the global price of oil (P O). Mathematically, the expression for the flow of ecotourists (J T) is:

$$ J_{\text{T}} = k_{\text{T}} (T*N*I)/P_{\text{O}} $$

where k T is a first-order proportionally constant that corrects for the dimensions of the units. Thus, this expression indicates that the flow of tourists into the Belize economy will increase if T, N, or I increases but it will decrease if P O increases. This mathematical form of the ecotourist experience recognizes the critical relationship of the global price of oil in regulating the costs involved in the travel of tourists from their home countries to Belize. The mathematics thus capture the idea that as the global supply of oil declines, the price of oil increases, and in turn, the costs of travel increase. A submodel that generates the price of oil is shown in the upper right-hand portion of the diagram with oil (O) declining as a first-order loss, representing consumption of the supply by the global economy. Price is determined as the ratio of the consumption of oil (J oil) to the flow of money in the global economy (J $), itself modeled as a first-order growth representing a 1 % annual increase in global gross domestic product (GDP).

Tourists bring money into the system in proportion to expenditures during their visit. This is shown as the dashed line from the tourist source (J D). This money is in payment for services from the companies whose infrastructure helps drive the ecotourism experience. Some of this money ultimately goes for local labor (D 1), and the rest ultimately goes back out to the global economy to pay for investments, savings, etc.

Natural ecosystems (N) are obviously an important input to the ecotourism experience, but no money goes back to nature in this model. Optimal ecotourism involves these kinds of feedbacks, as discussed earlier, but most operations do not conduct activities that directly support ecosystems. In fact, ecotourism actually stresses ecosystems through impacts from infrastructure (J 3) and through impacts of the tourists themselves (J 11). In real terms, these impacts might include rainforest that is cleared for construction of hotels and resorts, for agricultural food production to support the tourism services, or reduced forest productivity because of damage from tourists themselves (for example, degradation and erosion from roads and trails). By reducing N, these impacts indirectly affect the total flow of ecotourists and the money they bring into the system.

The overall model shown in Fig. 1 is a set of hypotheses about the causal basis of the ecotourism industry in Belize. A system of equations (Fig. 2) was translated from the diagram according to the methodology described in Odum (1994) and Odum and Odum (2000), in which the change in time of each state variable is described by a first-order differential equation describing inflows and outflows. Each flow pathway is described by a first-order transfer coefficient determined through calibration with values for flows and storages developed from the literature. For this calibration, each of the flows on the right side of each of differential equations is equated to a numerical value determined for that flow from the literature. The value of each flow was divided by the known values of the storages to calculate the estimated value of the transfer coefficient for that process (Rivera et al. 2007). Calibration values for forcing functions, state variables, flows, and transfer coefficients calculated from these are provided (“Appendix 1”). The equations and coefficients were programmed into an EXCEL spreadsheet for numerical solutions using finite difference equations and the Euler method for integration of ordinary differential equations. The model was calibrated to conditions as close to the year 2000 as possible. It was then simulated over a time period of 100 years using a time step of 1 year.

Fig. 2
figure 2

System of equations derived from the systems model to represent the ecotourism industry in Belize

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Following calibration, a baseline simulation was run using calibrated values to determine dynamics and expected results. Additional simulations to test model sensitivity and to examine hypotheses about different scenarios were made by varying individual parameters and recording changes in output results. Three scenarios were tested for model sensitivity. First, the impact of increased oil prices that might result from lower estimates of remaining in-ground oil reserves was examined by decreasing the initial value for the state variable O in the oil supply sub-model. Second, the impact of greater availability of local labor for the support of the tourist industry was examined through increasing the value of the forcing function L 0. Finally, the impact of decreased environmental impacts, which might result from improved natural resource management policies, was examined through decreasing the transfer coefficients for flows J 3 and J 11 that represent drains on the natural ecosystems precipitated by interactions with the tourist industry. For each of these scenarios, the model was run several times with incremental changes in the relevant parameter values to demonstrate the trend of the response of the system.

3 Results and discussion

The results for the baseline simulation, using initial values calibrated to year 2000, are shown in Fig. 3a–d. These figures show that, as tourism infrastructure (I) increases over time, the remaining natural ecosystems decrease over time (Fig. 3a). The flow of tourists into the country shows a steady decline for the entire simulation run (Fig. 3b). The flow of ecotourism money into Belize follows the same trend as the flow of tourists (Fig. 3c), decreasing steadily after an initial increase. Continual payments to local labor cause the exported money (in the form of investors’ profits) to eventually become negative as returns from tourism drops. Finally, the price of oil increases over time as production drops due to a continually reduced supply (Fig. 3d). These baseline results are consistent with expectations. Tourism is high so long as both the amount of natural ecosystems (N) and tourist infrastructure (I) are moderate or high. Infrastructure development and increased tourist flow have an effect on the natural ecosystems, which cannot regenerate fast enough to keep up with environmental impacts. As natural ecosystems decline over time, the flow of tourists decreases, even despite the continually increasing tourist infrastructure development. Because tourist income is directly proportional to the flow of tourists, total money and exported money (profit to foreign investors) follow this same declining trend over time. Money paid to local labor approaches a constant, as it is a function only of the number of rooms and the percent of total work force employed. Overall, this simulation indicates that there is a balance point between tourist development and ecosystem conservation that maximizes tourist flow, and thus tourist dollar flow, into Belize; too much sustained impact on the natural ecosystems will eventually erode the tourist economic base as tourism falls.

Fig. 3
figure 3

Baseline results graphs for the simulation model of the Belize ecotourism industry, showing over time a natural ecosystems (N) and tourism infrastructure (I); b tourist flow (J T); c local (D 1), exported (D 2), and total (J D) money derived from tourism; d oil production (J oil) and oil price (P O)

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The results from the scenario examining the impact of increased oil prices caused by a decreased total oil supply are shown in Fig. 4a–d. These results show that, as the total oil supply decreases, the impact upon natural ecosystems is lessened, although no change is seen in the hotel development I (Fig. 4a). The flow of tourists is seen to decrease with decreasing oil supply (Fig. 4b), thus explaining the decreasing impacts of natural ecosystems. Declining tourism also explains declining receipts of money along with decreasing oil supply (Fig. 4c), shortening the time when profits to foreign investors as export dollars fall below zero. Declining production of oil, as a result of lessened reserves in ground storage, creates increasing prices for oil over time (Fig. 4d). These results are also consistent with expectations. As oil prices increase, tourism decreases, thereby decreasing total and exported revenues accordingly. The amount and rate of tourist infrastructure development, and thus the money paid to local laborers, remains constant as with the baseline simulation. In one sense, this is reasonable where hotels and resorts are built by foreign investors who speculate on the future demand for ecotourism. In reality, however, few developments might be undertaken unless perceived demand exists. This points to one possible improvement to the model: the growth of tourist infrastructure, I, should be moderated by a feedback from the perceived tourist flow, J T, or tourist dollar flow, J D. This change would produce a growth in infrastructure that is scaled to a demand by the tourists.

Fig. 4
figure 4

The effects of decreasing projected world oil supply on various parameters of the Belize ecotourism economy, showing over time a natural ecosystems (N) and tourism infrastructure (I); b tourist flow (J T); c local (D 1), exported (D 2), and total (J D) money derived from tourism; (d) oil production (J oil) and oil price (P O)

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The results from the scenario examining the impact of the availability of local labor revealed that the model dynamics are highly sensitive to the total available labor pool in Belize (Fig. 5a–d). For example, the rate of hotel infrastructure development (Fig. 5a) and tourist flow (Fig. 5b) increase significantly for moderate increases in the total labor pool. This result suggests that the local labor is a limiting factor to the growth of tourism infrastructure, the effects of which propagate through the model simulation. The total work force in Belize was estimated at 90,000 in 2001 with a 13 % unemployment rate (CIA 2005), but only a portion of this number is readily available for work in ecotourism. If shortages do occur, the demand for labor might be met by immigrants from nearby countries, and thus, the limiting effect of labor may be an unrealistic result of the model simulation. The additional feedback discussed previously may help to mitigate the sensitivity of the model to the labor parameter.

Fig. 5
figure 5

The effects of an increased local labor force on various parameters of the Belize ecotourism economy, showing over time a natural ecosystems (N) and tourism infrastructure (I); b tourist flow (J T); c local (D 1), exported (D 2), and total (J D) money derived from tourism; d oil production (J oil) and oil price (P O)

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The results from the scenario examining the impact of decreased environmental impacts caused by ecotourism are shown in Fig. 6a–d. The decrease of environmental impacts results in reduced rates of decline of natural ecosystems over time even though tourist infrastructure increases gradually to a steady state (Fig. 6a) and oil prices rise (Fig. 6d) as in the baseline run of the model. The flow of tourists and their income is maintained over longer time periods with lessened environmental impacts (Fig. 6b, c), because of the improved conditions of the natural ecosystems.

Fig. 6
figure 6

The effects of decreased environmental impacts due to ecotourism on various parameters of the Belize ecotourism economy, showing over time a natural ecosystems (N) and tourism infrastructure (I); b tourist flow (J T); c local (D 1), exported (D 2), and total (J D) money derived from tourism; d oil production (J oil) and oil price (P O)

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While the model is an initial attempt at representing the role of ecotourism in Belize, a number of refinements in the conceptualization can be suggested for possible improvement in the fidelity of the results. First, a possible shortfall of the model is the collection of all productive environmental energies as one state variable with lumped pathways to describe environmental impacts. The environmental resources of Belize that draw significant tourist attraction include both the inland rainforests and the coastal environment and barrier reef. It is arguable that the tourist presence in the country has rates of impact that are different for each of these two distinct ecosystem types, with the barrier reef possibly more sensitive to human presence than the terrestrial rainforest. Further development of the model concept using multiple environmental producer state variables to represent different ecosystems and their sensitivity to human impact would help to refine model predictions for more spatially refined applications in Belize. Another possible improvement to the model is the refinement of descriptive parameters and flows used as calibration values. Some flows used for calibration are based on assumptions as a result of incomplete or unspecified data. For example, to assess the environmental impacts due to tourism, it is assumed that 50 % of the loss of ecosystem productivity results from either the direct impact of tourists or from the clearing of land as a result of development for the tourist industry. This assumption can be tested and refined through improved data collection on the type of losses experienced by the Belizean ecosystems and their contributing causes. It is expected that changes in these parameters describing environmental impacts of the tourist industry might result in dynamic changes to results as demonstrated in the scenario testing on this model.

The benefits of ecotourism in Belize have been demonstrated over the last 20 years (Horwich and Lyon 1998; Lindberg and Enriquez 1994). In fact, our own work has quantified a case study that continues to operate in a small village in central Belize (Kangas et al. 1995). However, the overall conclusions of the modeling experiments described in this paper are that benefits of ecotourism are limited and temporary over the long run. The dominant factor controlling the simulations was the decline in oil production that drives up the cost of travel. None of the simulated experiments (increasing labor supply or decreasing environmental impacts of tourism) were capable of overcoming the effects of decline in oil production, though the economic benefits of ecotourism can be extended by policies that would result in these kinds of structural changes in the system. Even the possibility of increasing efficiency in travel over the next few decades would not appreciably change this dynamic, as the continued increase in the price of oil would affect overall costs of local and regional transportation. The model predicts that the decline in the ecotourism economy of Belize will be apparent within a few decades of the initial conditions, which were calibrated for the year 2000, and will take place gradually. Because of the proximity of Belize to the ecotourism market in the United States, economic inflows to the country will continue but ultimately the industry will be limited. Thus, while important to Belize in the short run, ecotourism is not sustainable in the long run. Although not shown in the simulations, the tourist infrastructure will ultimately decline and natural ecosystems will be able to recover, assuming no other land use emerges. History may then repeat itself, as occurred after the fall of the Maya civilization, and the forest will again cover over the developments built by humans.