System Dynamics Approach to TALC Modeling

sustainability

Article System Dynamics Approach to TALC Modeling

Marko Hell 1 and Lidija Petri´c 2,*

1 Department of Business Informatics, Faculty of Economics, Business and Tourism, University of Split, 21000 Split, Croatia; [email protected] 2 Department of Tourism and Economy, Faculty of Economics, Business and Tourism, University of Split, 21000 Split, Croatia * Correspondence: [email protected]

Abstract: The system dynamics applied in this research on modeling a tourist destination (area) life cycle (TALC) contributes to understanding its behavior and the way that information feedback governs the use of feedback loops, delays and stocks and flows. On this basis, a system dynamic three-staged TALC model is conceptualized, with the number of visitors V as an indicator of the carrying capacities’ dynamics and the flow function V(t) to determine the TALC stages. In the first supply-dominance stage, the model indicated that arrivals are growing until the point of inflexion. After this point, arrivals continue growing (but with diminishing growth rates), indicating the beginning of the demand-dominance stage, ending up with the saturation point, i.e., the maximum number of visitors. The simulated TALC system dynamics model was then applied to five EU destinations (Living Labs) to explain their development along the observed period (2007–2019). The analysis revealed that all observed Living Labs reached the second lifecycle stage, with one entered as early as in 2015 and another in 2018. Lifecycle stage durations may significantly differ across the destinations, as do the policies used either to prevent stagnation or to restructure the offer to become more sustainable and resilient. Citation: Hell, M.; Petrić,L. System Dynamics Approach to TALC Keywords: system dynamics; TALC system dynamics model; living labs/destinations Modeling. Sustainability 2021, 13, 4803. https://doi.org/10.3390/ su13094803

Academic Editors: Bart Neuts, 1. Introduction João Martins, Milada Št’astná and Tourism and a tourist destinations are researched from many standpoints and by John Martin many scientific disciplines. However, most of them have generally taken a reductionist approach, with both tourist destinations and tourism not effectively understood as complex Received: 19 March 2021 phenomena [1]. The reason might lie, as indicated by Farrell and Twinning Ward [2], in Accepted: 21 April 2021 the fact that the majority of tourism researchers are schooled in a tradition of linear, Published: 25 April 2021 specialized, predictable, and deterministic methods, while tourism, in turn, is a complex phenomenon strongly influenced by global and local trends affecting the development Publisher’s Note: MDPI stays neutral of a destination, in both positive and negative manners. Moreover, a tourist destination with regard to jurisdictional claims in (be it a community, a region or a country) encompasses numerous directly and indirectly published maps and institutional affil- involved stakeholders acting interdependently with nonlinear interactions, which is why it iations. is considered a complex adaptive system, whose dynamical behavior is best-delineated using chaos and complexity frameworks [3]. Surprisingly, as stressed by Olmedo and Mateos [4], after seminal papers by Faulkner and Valerio [5] and Parry and Drost [6], only a few papers have applied chaos and com- Copyright: © 2021 by the authors. plexity concepts in the tourism/tourist destination-related literature, with not many more Licensee MDPI, Basel, Switzerland. up to the recent period. Thus, Sedarati et al. [7] indicate that a systematic literature review This article is an open access article of the papers dealing with tourism from the system’s dynamics perspective revealed only distributed under the terms and 27 published from 1994 to 2015, addressing six different categories, being: multisector, conditions of the Creative Commons attractions, adventure and outdoor recreation, transportation, accommodation and events. Attribution (CC BY) license (https:// In addition, a brief analysis of the papers dealing with the system dynamics and chaos and creativecommons.org/licenses/by/ complexity concepts in researching tourism and tourist destination, referenced in the Web 4.0/).

Sustainability 2021, 13, 4803. https://doi.org/10.3390/su13094803 https://www.mdpi.com/journal/sustainability Sustainability 2021, 13, 4803 2 of 22

of Science database in the period 2016–2021, has revealed just a few [8–14], thus indicating that the application of these concepts to tourism is still in an early development phase. Following the above reasoning, with this research, we opt to add to the existing body of knowledge on a tourist destination applying system thinking and chaos and complexity approach, or, as indicated by Olmedo and Mateos [4], a chaordic approach, harnessing a unifying approach to deal with systems where chaos and complexity simultaneously coexist. In this regard, this paper aims to develop a system dynamics model explaining a destination behavior while passing through different life cycle stages. This model leans on Butler’s [15] Tourism Area Life Cycle (TALC) model and is based on the number of visitors V as an indicator of the dynamics of the carrying capacities and the flow function V(t) determining the TALC stages. The TALC system dynamics model we intend to develop may be used by destination managers as a prognostic tool aimed at pointing at two crucial moments of a destination development cycle, i.e., the moment when it reaches its carrying capacities and the moment of saturation after which an innovative cycle begins. Using this tool, managers may timely apply appropriate strategies and policies to enhance the destination’s sustainability and prevent its decline. The paper consists of the introductory part and five other sections. In Section2, we present a tourist destination as a complex, nonlinear system that needs to be managed. In Section3, we explained a destination’s life cycle behavior using the system dynamics approach. Section4 elaborates on the TALC model development based on a causal loop diagram. The fifth section presenting the results, is divided into four subsections. In the first one, the simulated TALC system dynamics model is applied to five EU destinations (Living Labs) to explain their development along the observed period (2007–2019). In the subsequent subsection, the TALC model generic structures are explained based on the UNWTO [16] definition of carrying capacities, thus providing the basis for its empirical validation. The following section presents the model interface in the Powersim program. Finally, simulation scenarios for each LL are analyzed, and the characteristic points on the TALC curve for each one discussed. The last section discusses the results, elaborates on the theoretical and practical implications of the paper and reflects the research gaps and future research directions.

2. Tourist Destination as a Complex System—Theoretical Background Systems differ regarding their complexity. Thus, simple systems are considered as linear, with predictable interactions, consisting only of a few components; they are repeatable and decomposable, while complicated systems, though may also be repeatable and decomposable, have many components, separated cause and effect over time and space [3]. Opposite to simple and complicated systems, complex systems do not have predictable reactions, cannot be decomposed, have nonlinear interactions, are dynamic, adaptable to the environment and produce emergent structures and behaviors [17]. As a complex system, a tourist destination is very sensitive to different disturbances through environmental change and social, economic and political upheaval [18]. Moreover, due to its complexity (nonlinearity), one stress initiates a series of other stresses/impacts (butterﬂy effect). For example, natural disasters may lead to a health crisis, which may cause social crisis (related to crime rate growth), ultimately producing crises of economic/ﬁnancial nature. Chaos theory stresses that it is essentially impossible to formulate long-term predictions about the behavior of a complex system [3,17,19]. However, by adjusting its structure and behavior to external environmental changes, a complex system demonstrates its ability to withstand shocks, i.e., to be more resilient [20]. Furthermore, tourist destinations possess a structure spanning several scales or layers. At every scale, there is a structure as an essential aspect of a complex system, ultimately contributing to emerging behavior. The emerging behavior is a phenomenon special to the scale considered, resulting from global interactions between the scale’s constituents [21]. Considering the complexity of a destination as a system, the use of the panarchy concept helps contribute to Sustainability 2021, 13, 4803 3 of 22

the interdisciplinary understanding of resilience at the community level [22], by drawing attention to cross-scale relationships. As pointed by Baggio [3], global structures in a complex system may emerge when specific parameters go beyond a critical threshold, affecting the appearance of a new hierarchical level. The system then evolves, increasing its complexity to the following self-organization process, potentially affecting the capability to show a degree of robustness to external shocks. Miletti indicated (in [3]) that a system may absorb the shock and remain in a given state or regain the state unpredictably fast, concerning the internal structure of the system and the stimulus of private or public policy decisions. As a complex adaptive system, a tourist destination constantly acts at the edge of the chaos (in the state of fragile equilibrium), i.e., between a chaotic state (disorganization) and a completely ordered one (highest level of organization), a condition that has also been named self-organized criticality [3]. Farrel and Twinning Ward [2] indicate that instead of seeking a single equilibrium in complex systems, stability is believed to be offset by periods of disturbance and disorder associated with the cyclic life of ecosystems. This process is illustrated by the adaptive cycle first described in 1986 by Holling (in [2]). Moreover, Farrel and Twinning Ward [2] pinpointed that the new knowledge derived from ecosystem dynamics might suggest that it could be quite possible for a complex adaptive tourism system to have multiple stable states. According to Faulkner and Russell [23], who introduced chaos and complexity theory into tourism destination-related literature, entrepreneurs are seen as actors of chaos while planners as regulators. Additionally, Russell and Faulkner [24] explained that the stagnation stage or an edge-of-chaos state of a tourist destination life cycle could be viewed as an opportunity to achieve change, eventually pushing it into the next, more innovative cycle. The state of the highest level of the organization should imply that a destination has reached sustainability in all the three major aspects of its development, i.e., economic, social and environmental, which is only a theoretical, hardly reachable goal [25]. Despite an ever-growing interest in sustainable development, the mainstream reductionist scientific approach seems inappropriate in explaining the sustainability of a tourist destination as a complex and uncontrollable system characterized by nonlinear and chaotic behavior [26]. In the same vein, Farell and Twinning Ward [2] criticize the idea that management actions can be accurately predicted and controlled and question the efficiency of tools such as carrying capacity, environmental impact assessment, and tourism planning in reaching sustainability goals. Yet, they [2] do not oppose the idea of using these tools but ask for applying a more experimental approach to carrying capacities’ measurement, which allows continuous revision depending on the new knowledge, locality, seasonality, tourist behavior, and particularly local preferences. Similarly, concerning tourism planning, they suggest it moves towards greater integration of systems techniques where the planning process is a continual one, incorporating constant review and revisions. Finally, the authors [2] suggest that techniques such as limits of acceptable change, recreation and tourism opportunity spectrum, and growth management should adopt a more integrated and participatory approach, instead of still fairly rigid top-down management structures. In addition, Farrel and Twinning Ward [2] suggested some new tools that may be appropriate for tourism, such as adaptive ecosystem cycle theory, scenario planning, simulation models, integrated assessment models, integrated landscape planning, regional information systems, and, recently, resilience analysis and management, with the ‘adaptive management’ standing out as an effective way of managing the comprehensive tourism system towards sustainability goals (pp. 284–285). According to Williams et al., 2007 [27], adaptive management is a six-step learning cycle with the participation of all relevant stakeholders in conflict management, acknowledging that many factors influence the condition of an ecosystem outside the manager’s jurisdiction, requiring a broad systemic, or strategic approach. Although not being the direct object of this study, it is worth noting that the request for the participative approach, especially stressing the role of the local community in managing Sustainability 2021, 13, 4803 4 of 22

sustainable development of a tourist destination, is at focus from as early as 1985 and Peter Murphy’s [28] seminal book up till today [29–35].

3. Tourist Destination Life Cycle Behavior from the System Dynamics Perspective The TALC model [15] has become one of the most cited in tourism literature. It describes the evolution of a tourist area, hereafter destination, through six stages, namely, the ‘exploration’, ‘involvement’, ‘development” and ‘consolidation’, signifying growth expressed by visitor numbers, while the ‘stagnation’ stage represents a gradual decline. The end of the cycle is marked by the ‘post-stagnation’ stage, which comprises a set of five options that a destination may follow [36]. The purpose of the TALC model, as explained by Butler [37], was primarily to draw attention to the dynamic nature of destinations and propose a generalized process of development and potential decline which could be avoided by appropriate interventions (of planning, management and development). Key to this was the concept of a destination’s carrying capacity, in the sense that it if was exceeded, destination’s relative appeal would decline, leading to the loss of its competitiveness, and consequently to declines in visitation, investment, and development. Butler [37] also stresses that carrying capacity was always envisaged as having several components and not just a single number impractical to determine even in wilderness areas, let alone in such a varied setting as a destination. As early as 1980, Butler wrote that three critical factors were determining the TALC model, that is: tourists, residents, and tourism conditions, e.g., attractions and fixed capability ([15], p. 10). To explain the reasoning lying behind the tourist area/destination life cycle (TALC) behavior, we use the system dynamics approach. System dynamics, as an aspect of systems theory, is as a method to understand the dynamic behavior of complex systems, or, as explained by Colye [38], system dynamics is the time-dependent behavior of managed systems, aimed to describe the system, and to understand how information feedback governs. The origins of system dynamics can be traced back to engineering control theory that focuses on the feedback loop control, and transient/steady response [39]. System dynamics took these concepts and applied them to social, managerial domains. Hence, characteristics that make system dynamics different from other approaches to studying dynamic systems is the use of feedback loops, delays and stocks and flows [40]. These elements help describe how even seemingly simple systems display nonlinearity. System dynamics uses both qualitative and quantitative analyses. The qualitative tools are mainly used to capture the model structure, including causal loop diagrams [41], structure–behavior diagram [42], and stock-flow diagram [43] used in model simulation. The quantitative methodologies in system dynamics focus on feedback loop analysis aiming to design an effective policy to adjust the system behavior. According to the “father” of the system dynamics, Forrester [40], the feedback loop is the technical term describing the environment around any decision point in a system. The decision leads to a course of action that changes the state of the surrounding system and gives rise to new information on which future decisions are based. A feedback loop is a closed path, representing a chain of causal-effect relationships. Forrester [43] stated that all decisions take place in the context of feedback loops. A time delay describes a process whose output lags behind its input. Time delays reduce the number of times one can cycle around the learning loop, slowing the ability to accumulate experience, test hypotheses, and improve [44]. By using time delays, it is possible to explain the movement of a destination along the TALC stages. A fundamental task in exploring dynamic systems is to distinguish different types of behavior. It is also essential to eventually identify what types of feedback structures give rise to various behavior and why. As stated by Güneralp (in [45]), ‘structure drives behavior’ is considered a primary principle in the system dynamics paradigm. Although it would be of utmost importance to discover links between dominant feedback loops and shifts in loop dominance to behavior patterns, system dynamics does not currently Sustainability 2021, 13, 4803 5 of 22

provide a method for identifying dominant feedback loops. To do so, it traditionally uses informal approaches such as experimental model exploration, model reduction, or both with their understanding of the behavior patterns typically generated by positive and negative feedback loops [46]. However, they do not seem to be very useful in identifying dominant loops because loop polarity is only loosely coupled to specific behavior patterns. In addition, no formal and unambiguous definition of behavior concerning dominance has been formulated so far. Research has focused far more on the structural aspects of how feedback structures and behavior are linked than on behavioral aspects [46,47]. System dynamics needs an understanding of feedback loop dominance that balances structural and behavioral perspectives. The purpose of the analysis of the feedback loop dominance is to identify feedback structures that dominate behavior. The location of dominance must be identified more specifically than at the level of a model because specific variables in a model can have very different behavior patterns at the same time interval. Therefore, the identification of feedback loop dominance requires the specification of a single system variable for which dominance is considered relevant [48]. A deeper understanding of the logic lying behind feedbacks, delays, and time dimen- sion can help explaining the destination system structure and its impacts on the expected pattern of its behavior. In this way, the analysis is not focused solely on partial observation of one or two variables but on structured sets of variables (FBL feedback loop) characterizing basic patterns of behavior. The structured sets of variables thus obtained enable studying the FLBs dominance. FLB dominance can change over time because the same variables may belong to different FBLs, hence enabling the isolated observation of each of the observed subsystems and the description of the interaction between them. To adapt the general model to an individual destination, descriptive statistics is applied, thus enabling the model verification. Such a model contributes to achieving a balance of the entire destination system by applying variables with different values. In the context of this research, a balanced destination system is the one that is sustainable and resilient. As indicated by Pejić-Bachand Cerić[ˇ 49], the ‘step-by-step’ approach used to develop the system dynamics model proposes three evaluation tests, e.g., the dimensional consistency test, extreme conditions test and the behavior sensibility test. The dimensional consistency test shows the existence of errors, i.e., it checks if the measurement units of variables on both sides of the equation are the same. The extreme conditions test indicates oversights, i.e., it shows whether the model structure allows the model behavior in extreme conditions matching the real system behavior in the same situations. The behavior sensibility test helps to understand the impact of each variable on the model behavior. It focuses on detecting such parameters whose small change cause a significant change in the model behavior. The fewer such parameters, the higher the credibility of the model. However, the behavior sensibility test is acceptable if the real system behaves as the modeled one. The system dynamics aims to identify the parameters which affect the system behavior the most, and as so is the most adequate to be applied in management policies. If the behavior sensibility test reveals that parameters do not affect model behavior, they can be assessed based on subjective judgment ([49], p. 174).

4. The TALC Model Development Based on Causal Loop Diagram Following the theoretical explanation on complex systems and system dynamics, a system dynamic TALC model will be further elaborated in detail. Destination’s attractiveness is usually expressed by tourist attendance, whether re- ported by visitor arrivals or overnights, or by ﬁnancial indicators such as tourist receipts. In this paper, considering data availability and Butler’s [15] original idea, we decided to take the number of visitors V as the reference point, with the logistic curve to explain the destination’s development over time. The logistic function is applied in various sci- entiﬁc disciplines, such as neural networks, biomathematics, demography, economics, statistics, chemistry, medicine, sociology, political science, etc. Butler [15] himself created Sustainability 2021, 13, 4803 6 of 22

the TALC model based on a logistic curve originating from Verhulst (in [50]), as explained by expression (1). L f (x) = (1) 1 + e−k(x−x0)

M V(t) = (2) 1 + e−k(t−t0) The function can be presented in different ways. For the sake of consistency of the measurement units used in the model and of the methodology of system dynamics, in this research we use a logistic differential equation. Such a form is obtained by applying the differential calculus, as follows: The TALC logistic curve is represented by function (2). By deriving the function (2), we come to: dV(t) −e−k(t−t0) = k·M· , dt 1 + e−k(t−t0) and, after arranging the above we come to: ! dV(t) M 1 M 2 = k· − . (3) dt 1 + e−k(t−t0) M 1 + e−k(t−t0)

If (2) is contained within (3), the logistic differential Equation (4) is obtained and will be further used to describe the TALC model. dV(t) V(t) = k ∗ V(t) ∗ 1 − . (4) dt M

In the system dynamics context, after been arranged, Equation (4) can be written as a level Equation (5) Z t2 V(t) V(t) = V(t1) + k·V(t) ∗ 1 − dt, (5) t1 M

where Vt is the actual number of visitors (arrivals), Vt1 is the number of visitors in time t1; t1 is the starting point and t2 is the ending point of the observed period, k is the coefﬁcient of the information spread-out rate about a destination, and M is a maximum number of the potential visitors (arrivals). Following above explanations, basic TALC model structure is described by the casual loop diagram, describing the interaction of the employed variables, as in Figure1. Sustainability 2021, 13, x FOR PEER REVIEW 6 of 22

chemistry, medicine, sociology, political science, etc. Butler [15] himself created the TALC model based on a logistic curve originating from Verhulst (in [50]), as explained by expression (1). 퐿 푓(푥) = (1) 1 + 푒−푘(푥−푥0)

where: L is the maximum value of the curve f(x), x is the argument of the function, x0 is the argument of sigmoid ‘midpoint’, k is the logistic growth rate or steepness of the curve. To align with previous research in this area, f(x), which in this research represents the actual number of visitors, will be denoted by V; L is the maximum value of the number of visitors and will be denoted by M, while the variable x will represent time and will be denoted by t. Based on this, the logistic TALC function has the following form (2) 푀 푉(푡) = (2) 1 + 푒−푘(푡−푡0) The function can be presented in different ways. For the sake of consistency of the measurement units used in the model and of the methodology of system dynamics, in this research we use a logistic differential equation. Such a form is obtained by applying the differential calculus, as follows: The TALC logistic curve is represented by function (2). By deriving the function (2), we come to:

푑푉(푡) −푒−푘(푡−푡0) = 푘 ∙ 푀 ∙ , 푑푡 1+푒−푘(푡−푡0) and, after arranging the above we come to:

푑푉(푡) 푀 1 푀 2 = 푘 ∙ ( − ( ) ). (3) 푑푡 1+푒−푘(푡−푡0) 푀 1+푒−푘(푡−푡0) If (2) is contained within (3), the logistic differential Equation (4) is obtained and will be further used to describe the TALC model.

푑푉(푡) 푉(푡) = 푘 ∗ 푉(푡) ∗ (1 − ). (4) 푑푡 푀 In the system dynamics context, after been arranged, Equation (4) can be written as a level Equation (5)

푡2 푉(푡) 푉(푡) = 푉(푡1) + ∫ 푘 ∙ 푉(푡) ∗ (1 − ) 푑푡, (5) 푡1 푀

where Vt is the actual number of visitors (arrivals), Vt1 is the number of visitors in time t1; t1 is the starting point and t2 is the ending point of the observed period, k is the coefficient of the information spread-out rate about a destination, and M is a maximum number of Sustainability 2021, 13, 4803 the potential visitors (arrivals). 7 of 22 Following above explanations, basic TALC model structure is described by the casual loop diagram, describing the interaction of the employed variables, as in Figure 1.

Sustainability 2021, 13, x FOR PEER REVIEW 7 of 22

Figure 1. Casual loop diagram of the TALC model. Figure 1. Casual loop diagram of the TALC model.

Considering V V is is the the number number of ofactual actual visitors visitors and and M is M the is maximum the maximum expected expected num- numberber of visitors of visitors in a indestination, a destination, 1-V/M 1-V/M is the is difference the difference between between the themaximum maximum number number of ofexpected expected visitors visitors and and the the visitors visitors in the in the previous previous period. period. As AsV increases, V increases, the the1-V/M 1-V/M de- decreases,creases, indicating indicating inverse inverse proportionality, proportionality, expressed expressed by by a aminus minus sign sign next next to to the the arrow. arrow. The difference between the actual number of visitors (V) in thethe previousprevious periodperiod andand thethe maximum number of expected visitors (M) in the following period is the basis of Growth. The describeddescribed processprocess will will depend depend on on the the information information spread-out spread-out rate rate k, which k, which synthesizes synthe- allsizes elements all elements influencing influencing Growth. Growth. Economics, Economics, business, business, and related and related fields often fields distinguish often dis- betweentinguish between quantities quantities representing representing stocks from stocks those from of those the flows. of theThey flows. differ They concerning differ con- thecerning measurement the measurement units. A units. stock isA measuredstock is measured at one specific at one pointspecific of point time andof time represents and rep- a quantityresents a existingquantity then, existing and then, based and on thebased past on accumulation. the past accumulation. A flow variable A flow is variable measured is overmeasured an interval over an of interval time. Therefore, of time. Therefore, a flow is measureda flow is measured per unit ofper time unit (suchof time as (such a year). as Flowa year). is roughlyFlow is roughly analogous analogous to rate orto speedrate or in speed this sense,in this meaningsense, meaning that level that function level func- (V) maytion (V) be calculated may be calculated in a one-time in a period, one-time while period, two-time while periods two-time are neededperiodsto are calculate needed the to ratecalculate function the rate (Growth). function (Growth). Based onon thethe structurestructure shown shown in in Figure Figure2, 2, the the number number of visitorsof visitors (V) (V) is represented is represented by aby level a level variable. variable. This This means means that allthat changes all changes in visitors’ in visitors numbers’ numbers over time over are time accumulated are accu- inmulated this variable. in this variable. The annual The change annual inchange V is observed in V is observed through through the variable the variable Growth. Growth.

Figure 2. Basic concept of calculation.calculation.

5. Results 5.1. The TALC Model Veriﬁcation 5.1. The TALC Model Verification The number of visitors V is observed in the period from 2007 to 2019 and collected The number of visitors V is observed in the period from 2007 to 2019 and collected at at the level of the 27 Local Administrative Units (LAUs), belonging to ﬁve EU countries, the level of the 27 Local Administrative Units (LAUs), belonging to five EU countries, being the partners in the HORIZON 2020 SmartCulTour project this research leans on, i.e., being the partners in the HORIZON 2020 SmartCulTour project this research leans on, i.e., Belgium, Spain, Croatia, Italy, and Netherlands (Table1). The LAUs belong to the areas Belgium, Spain, Croatia, Italy, and Netherlands (Table 1). The LAUs belong to the areas delineated as Living Labs (LL), indicating territories where different (tourism) stakeholders delineated as Living Labs (LL), indicating territories where different (tourism) stakeholders can co-operate, co-create and co-manage tourism development. The Living Labs represent specific destinations that differ significantly in terms of the space they cover, administrative units they belong to (municipality, province, city and metropolitan area) and size. The data from Table 1 are used not just as an input for a quantitative model but also to conduct a simulation using the Powersim studio nine software package.

Table 1. Data on arrivals along the LAUs and LLs in the period from 2007–2019. Source: [51].

can co-operate, co-create and co-manage tourism development. The Living Labs represent speciﬁc destinations that differ signiﬁcantly in terms of the space they cover, administrative units they belong to (municipality, province, city and metropolitan area) and size. The data from Table1 are used not just as an input for a quantitative model but also to conduct a simulation using the Powersim studio nine software package.

Table 1. Data on arrivals along the LAUs and LLs in the period from 2007–2019. Source: [51].

2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 BE 23-TOTAL 40,727 51,614 47,882 46,696 49,077 55,170 56,907 75,382 74,473 71,756 80,759 88,008 96,358 Bornem 12,020 12,105 11,889 12,146 12,543 12,325 12,003 13,315 13,700 13,356 13,876 13,601 15,660 Pu.-Si.-Am. 2638 2996 3354 3713 4071 4429 4787 5442 5395 6144 5276 6570 7418 Aalst 18,759 28,618 25,143 23,230 25,405 29,688 31,119 48,224 47,814 44,537 52,851 58,623 62,628 Berlare 2838 2839 2487 2797 2606 3151 2482 2100 2862 2732 2921 3109 4020 Dendermonde 4472 5056 5009 4810 4452 5577 6516 6301 4702 4987 5835 6105 6632 ES 24-TOTAL 267,090 297,506 261,463 280,208 271,409 247,693 276,771 288,902 329,622 381,897 387,165 407,220 400,611 Ainsa 3439 6356 9273 12,190 15,107 18,024 19,426 26,888 25,260 29,692 32,609 55,503 35,258 Benasque 70,753 68,201 63,243 72,698 67,585 49,759 56,079 57,041 59,285 71,142 81,818 78,271 79,695 Huesca 77,565 92,458 71,568 69,988 66,990 65,409 72,650 78,374 90,168 92,857 90,091 90,091 90,168 Jaca 115,333 130,491 117,379 125,332 121,727 114,501 128,616 126,599 154,909 188,206 182,647 183,355 195,490 HR 03-TOTAL 294,370 327,557 306,968 301,086 405,275 400,456 503,400 568,271 706,592 794,964 1,019,852 1,204,130 1,305,993 Dugopolje 3000 4000 9000 10,282 29,676 32,258 61,193 46,726 53,960 25,927 51,299 49,159 45,779 Kaštela 28,501 29,987 26,893 25,509 54,880 32,670 41,016 42,406 50,191 60,364 83,605 100,530 114,990 Klis 100 100 100 100 100 300 300 300 500 877 1909 2931 4085 Sinj 8689 9645 7649 7179 7694 7110 9035 10,691 10,266 9633 11,317 13,116 11,620 Solin 2500 4000 5500 7530 14,590 11,118 6915 10,422 14,449 15,693 22,139 32,042 41,322 Split 185,718 211,299 176,185 203,539 252,287 265,630 318,057 381,227 487,474 583,041 720,325 859,224 941,185 Trogir 65,862 68,526 81,641 46,947 46,048 51,370 66,884 76,499 89,752 99,429 129,258 147,128 147,012 IT H3-TOTAL 183,858 183,119 168,631 173,731 192,618 198,268 217,598 218,073 236,852 242,609 286,103 293,648 303,550 Caldogno 1833 2029 1742 1651 1838 2121 1131 842 842 842 842 842 842 Gr. delle Abb. 1769 3146 5642 3663 8396 9622 11,115 11,038 11,748 12,458 13,168 13,878 14,588 Lonigo 7403 8013 7154 7136 6718 6949 6913 7130 7717 8304 8891 9478 10,065 Montagnana 6121 6369 4636 4681 4667 3700 4055 4514 3248 1982 716 0 0 Vicenza 166,732 163,562 149,457 156,600 170,999 175,876 194,384 194,549 213,297 219,023 262,486 270,000 279,871 NL 33-TOTAL 471,342 557,097 642,852 728,607 814,361 922,282 953,188 1,065,836 1,148,228 1,243,377 1,354,261 1,469,674 1,445,218 Barendrecht 12,801 14,187 15,573 16,959 18,345 19,260 20,924 22,601 24,012 25,013 28,755 28,106 27,980 Delft 26,527 29,515 32,503 35,490 38,478 40,290 44,185 48,050 50,688 52,455 60,653 59,572 59,501 Dordrecht 33,779 36,944 40,109 43,274 46,439 48,165 52,419 56,548 59,602 61,432 70,246 68,517 68,513 Ridderkerk 12,350 13,638 14,927 16,215 17,503 18,430 19,986 21,473 22,625 23,494 27,160 26,702 26,529 Rotterdam 373,226 448,964 524,702 600,440 676,179 778,000 796,000 896,000 969,000 1,058,000 1,141,000 1,261,000 1,237,000 Zwijndrecht 12,659 13,848 15,038 16,228 17,418 18,137 19,674 21,165 22,302 22,982 26,447 25,777 25,695

To present Excel sheet data (Table1), the following function is used in a business simulation software Powersim: GRAPHCURVE (X, X1, DX, Y(N)). The GRAPHCURVE function returns tabulated values (referred to as grid points or fixed points) for given input values. If the input value does not correspond to any of the tabulated values, GRAPHCURVE computes a value based on interpolation and/or extrapolation. X is the desired input value that GRAPH finds a matching output value. X1 is the first point of the graph, and DX is the increment between the fixpoints on the curve. Y is an array containing N fix points. If X lies between the fixpoints on the tabulated graph, the output value of GRAPHCURVE is calculated by third-order polynomial interpolation. A third-order polynomial is constructed based on all fixpoints and solved for the given input value, consequently giving a smooth function. If X is less than X1 or larger than X1 + (N − 1) × DX (thus lying beyond the range of the given fixpoints), the output value is computed by linear extrapolation. GRAPHCURVE uses linear asymptotes constructed as lines connecting two outermost fixpoints (www.powersim.com, accessed on 15 December 2020). Figure3 describes the behavior of a GRAPHCURVE function for each Living Lab (based on its correspondent LAUs’ visitor arrivals (Table1). Based on the GRAPHCURVE function, we calculated the annual average of the arrivals growth rates. Since we have been observing the multi-year lifecycle of a specific tourist area, we omitted seasonality analysis. The GRAPHCURVE function can also be used to validate the TALC system dynamics’ model. Sustainability 2021, 13, 4803 9 of 22 Sustainability 2021, 13, x FOR PEER REVIEW 9 of 22

1,500,000

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LL-TOTALS

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08 09 10 11 12 13 14 15 16 17 18 19 BE 23-TOTAL ES 24-TOTAL HR 03 -TOTAL IT H3-TOTAL NL 33-TOTAL Non-commercial use only! FigureFigure 3.3. BehaviorBehavior ofof aa GRAPHCURVEGRAPHCURVE functionfunction forfor allall LivingLiving Labs.Labs.

AsAs seenseen inin FigureFigure3 ,3, in in the the observed observed period period (2007–2019) (2007–2019) the the number number of of visitors visitors at at each each LivingLiving LabLab recordedrecorded aa wavywavy growth.growth. EachEach ofof thethe waves,waves, i.e.,i.e., thethe sigmoidsigmoid S-shapeS-shape ofof thethe curvecurve atat a a speciﬁc specific multi-year multi-year interval, interval, can can be be viewed viewed as aas distinct a distinct mini mini TALC. TALC. These These are theare destination’sthe destination short-term’s short-term ‘ups ‘ups and and downs’, downs which’, which cumulatively cumulatively contribute contribute to the to the shape shape of itsof long-termits long-term life life cycle. cycle. Precisely, Precisely, based based on on the the cumulative cumulative effects, effects, a a speciﬁc specific trend trend of of the the entireentire LivingLiving LabLab (destination)(destination) developmentdevelopment cancan bebe predicted predicted (as (as shown shown in in Figure Figure3 ).3). InIn hishis seminal paper paper Butler Butler [15] [15 ]dealt dealt with with six six TALC TALC stages stages while while some some other other authors authors[52–55 [52] were–55] weresuggesting suggesting destination destination can canpass pass less lessthan than six sixstages. stages. Here, Here, we we propos proposee an ananalytical analytical procedure procedure for for determining determining the the limits limits of of different different TALC TALC stages, assumingassuming therethere areare threethree stages,stages, i.e.,i.e., • TheThe supply-dominancesupply-dominance stage;stage; • TheThe demand-dominancedemand-dominance stage;stage; • TheThe restructuringrestructuring stage.stage.

5.2.5.2. GenericGeneric StructuresStructures ofof thethe TALCTALC Model Model Behavior Behavior TheThe changechange ofof anan objectobject speedspeed dependsdepends onon itsits accelerationacceleration andand thethe timetime neededneeded toto achieve it. The larger is the difference between the current and the desired values, the achieve it. The larger is the difference between the current and the desired values, the stronger is the effort to equalize them. If we deal with the inert (sluggish) system, a small stronger is the effort to equalize them. If we deal with the inert (sluggish) system, a small change can easily become bigger and ultimately lead to unwanted consequences (the change can easily become bigger and ultimately lead to unwanted consequences (the but- butterfly effect). However, the type and intensity of the adverse impacts depend on a terfly effect). However, the type and intensity of the adverse impacts depend on a system’s system’s ability and resilience. Given this, we first have to elaborate generic structures that ability and resilience. Given this, we first have to elaborate generic structures that charac- characterize specific patterns of behavior, such as (+)FBL delineating exponential growth, terize specific patterns of behavior, such as (+)FBL delineating exponential growth, i.e., i.e., ability and (−)FBL delineating logarithmic growth. (−)FBL explains the observed ability and (−)FBL delineating logarithmic growth. (−)FBL explains the observed variable variable tendency to reach a maximum, which leads to overall system resilience. tendency to reach a maximum, which leads to overall system resilience. By combining these two generic structures, we reach the limits of growth, being an By combining these two generic structures, we reach the limits of growth, being an archetype of system dynamics whose behavior corresponds to the TALC curve behavior. Properarchetype knowledge of system of dynamics the supply whose and behavior demand corresponds subsystems to can the help TALC to curve formalize behavior. this approach.Proper knowledge By understanding of the supply how and they demand behave, subsystems we can simulate can help the destinationto formalize system’s this ap- responsesproach. By while understanding searching forhow a newthey statebehave, of stability. we can simulate the destination system’s responses while searching for a new state of stability. Sustainability 2021, 13, 4803 10 of 22 Sustainability 2021, 13, x FOR PEER REVIEW 10 of 22 Sustainability 2021, 13, x FOR PEER REVIEW 10 of 22

LookingLooking atat thethe structuralstructural diagramdiagram inin FigureFigure1 ,1, we we can can see see that that two two feedback feedback circuits circuits Looking at the structural diagram in Figure 1, we can see that two feedback circuits existexist inin the TALC TALC logistic logistic curve, curve, i.e. i.e.,, positive positive (+)FBL1 (+)FBL1 and and negative negative (−)FBL2, (−)FBL2, showing showing char- exist in the TALC logistic curve, i.e., positive (+)FBL1 and negative (−)FBL2, showing char- characteristicacteristic (generic) (generic) patterns patterns of behavior, of behavior, as shown as shown in Figures in Figures 4 and4 and 5. 5. acteristic (generic) patterns of behavior, as shown in Figures 4 and 5.

1,500,000 1,500,000

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0 0 08 09 10 11 12 13 14 15 16 17 18 19 08 09 10 11 12 13 14 15 16 17 18 19 V (tourist) M (tourist) LAU-data[HR 03 -TOTAL] V (tourist) M (tourist) LAU-data[HR 03 -TOTAL] Non-commercial use only! Non-commercial use only!

FigureFigure 4.4.Exponential Exponential growth.growth. Figure 4. Exponential growth.

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08 09 10 11 12 13 14 15 16 17 18 19 08 09 10 11 12 13 14 15 16 17 18 19 V (tourist) M (tourist) LAU-data[HR 03 -TOTAL] V (tourist) M (tourist) LAU-data[HR 03 -TOTAL] Non-commercial use only! Non-commercial use only!

Figure 5. Goal seeking. FigureFigure 5.5. GoalGoal seeking.seeking. In both, Figures 4 and 5, the growth rate (k) is constant, and the blue curve indicates InIn both,both, FiguresFigures4 4 and and5 ,5, the the growth growth rate rate (k) (k) is is constant, constant, and and the the blue blue curve curve indicates indicates the official data on visitors for the Croatian Living Lab, consisting of seven LAUs (ex- thethe officialofficial data data on on visitors visitors for for the the Croatian Croatian Living Living Lab, consistingLab, consisting of seven of LAUsseven (expressedLAUs (expressed as HR-03-Total). aspressed HR-03-Total). as HR-03-Total). (+)FBL1 describes the structure of the exponential growth pattern (Figure 4) similar (+)FBL1(+)FBL1 describesdescribes thethe structurestructure ofof thethe exponentialexponential growthgrowth patternpattern (Figure(Figure4 )4) similar similar to a compound interest account, where the principal is accrued based on the interest rate. toto aa compoundcompound interestinterest account,account, wherewhere thethe principalprincipal isis accruedaccrued basedbased onon thethe interestinterest rate.rate. Then, in the next stage, the interest rate is added to the principal, with the procedure re- Then,Then, inin the next stage, stage, the the interest interest rate rate is is added added to to the the principal, principal, with with the the procedure procedure re- peated for each subsequent period. Thus, as regards the (+)FBL1, there are no limits of repeatedpeated for for each each subsequent subsequent period. period. Thus, Thus, as as regards regards the (+)FBL1, there are nono limitslimits ofof growth, but instead, growth depends on the penetration coefficient k and the initial state growth,growth, butbut instead, instead, growth growth depends depends on on the the penetration penetration coefficient coefficient k andk and the the initial initial state state of of the number of visitors V(t1). theof the number number of visitorsof visitors V(t1). V(t1). The number of visitors V(t) can grow continuously towards infinity because there are TheThe numbernumber ofof visitorsvisitors V(t)V(t) cancan growgrow continuouslycontinuously towardstowards infinityinfinity becausebecause therethere areare no boundaries/limits to slow the growth. This explained, it can be concluded that (+)FBL1 nono boundaries/limitsboundaries/limits to slow the growth. ThisThis explained,explained, itit cancan bebe concludedconcluded thatthat(+)FBL1 (+)FBL1 describes an unlimited demand market, i.e., a situation with no competitors or any other describesdescribes anan unlimitedunlimited demanddemand market,market, i.e.,i.e., aa situationsituation withwith nono competitorscompetitors oror anyany otherother external influence. In such a case, demand would grow exponentially with the coefficient externalexternal influence.influence. InIn suchsuch aa case,case, demanddemand wouldwould growgrow exponentiallyexponentially withwith thethe coefficientcoefficient k,k, accordingaccording toto thethe structurestructure (+)FBL1. (+)FBL1. k, according to the structure (+)FBL1. However,However, thethe limitslimits ofof growthgrowth existexist andand areare conditionedconditioned byby supply,supply, i.e.,i.e., greatergreater de-de- However, the limits of growth exist and are conditioned by supply, i.e., greater de- mandmand cannotcannot bebe reachedreached outout unlessunless enabledenabled byby supply,supply, which which means means that that the the maximum maximum mand cannot be reached out unless enabled by supply, which means that the maximum expectedexpected number number of of visitors visitors (M) (M) equals equals total total supply. supply. Being Being constant, constant, supply supply may may represent repre- expected number of visitors (M) equals total supply. Being constant, supply may repre- asent constraint a constraint on expected on expected demand demand with a with constant a constant penetration penetration coefficient coefficient k. With k. this With regard, this sent a constraint on expected demand with a constant penetration coefficient k. With this Sustainability 2021, 13, 4803 11 of 22

Sustainability 2021, 13, x FOR PEER REVIEW 11 of 22 the dynamics of the maximum expected number of visitors (M) is determined by (−)FBL2 structure that has a pattern of goal seeker (Figure5). The patternregard, of behavior the dynamics between of the the maximum two elaborated expected number structures of visitors (+)FBL1 (M) andis determined (−)FBL2 by (−) is shown in Figure6.

(b) Graphs of the first and second order (a) The TALC curve behavior pattern derivative of the TALC curve

FigureFigure 6. Pattern 6. Pattern of behavior of behavior and graphs and of the graphs first and of thesecond first order and derivative second of order the TALC derivative logistic curve. of the TALC logistic curve. We see that the behavior pattern of the TALC logistic curve has a sigmoidal shape. In this case, k and M are constant. The growth rate acceleration occurs until the threshold We see thatpoint, the behavioraffecting various pattern pressures of the TALCin a destination. logistic curveIn that point, has a called sigmoidal the inflexion shape. point, In this case, k andthe M TALC are constant. curve changes The from growth a convex rate to acceleration a concave shape. occurs until the threshold point, affecting variousWith pressuresthis regards inthe a point destination. of inflexion In may that be point, equated called with the the inflexiondestination point,’s carry- the TALC curveing changes capacity, from defined a convex as the maximum to a concave number shape. of people who can visit a tourist destina- With this regardstion at the the same point time, of inflexion without causing may be unacceptable equated with disturbances the destination’s of the physical, carrying eco- capacity, definednomic as the and maximum socio-cultural number environment of people and reduction who can in visit visitor a touristsatisfaction destination [44]. at Following the UNWTO’s [16] carrying capacity definition, both supply and demand the same time,subsystems without causing have their unacceptable growth thresholds. disturbances Hence, the of physical, the physical, economic economic and socio-cul- and socio-cultural environmenttural environment and (i.e., reduction assets), inimpose visitor thesatisfaction supply subsystem [44]. boundaries. On the other Followinghand, the UNWTO’s the demand [subsystem16] carrying threshold capacity is over definition, if visitor satisfaction both supply is reduced, and demand indicating subsystems havethe their gap between growth their thresholds. expectations Hence, and thewhat physical, promised. economic After some and time, socio-cultural a failure to de- environment (i.e.,liver assets), the promised impose offer the will supply affect subsystem a decrease boundaries.in arrivals to a On destination the other for hand, the sake the of demand subsystemother competitive threshold isdestinations. over if visitor Opposite satisfaction to this, improvements is reduced, in indicating any said environment the gap can increase the destination’s carrying capacity, eventually attracting visitors from com- between their expectations and what promised. After some time, a failure to deliver the petitive destinations. promised offer willAs affect soon a as decrease a destination in arrivals reaches to its a carrying destination capacities, for the suppliers sake of start other to compete compet- by itive destinations.lowering Opposite prices, to cutting this, improvements costs, finally resulting in any in said an environmentoverall quality candecline. increase Eventually, the destination’s carryingdemand capacity,overpowers eventually supply. However, attracting absolute visitors numbers from of competitive arrivals are growing destinations. but with As soon asdiminishing a destination growth reaches rates. itsFurther carrying growth capacities, increases additional suppliers pressures start to until compete reaching by a lowering prices,saturation cutting threshold costs, finally after which, resulting as presumed in an overall by the qualityTALC approach, decline. in Eventually, the last stage demand overpowersdifferent supply. scenarios However, may occur, absolute depending numbers on a destination of arrivals’s resilience. are growing but with Reaching the point of inflexion provides a signal that unacceptable changes have diminishing growthbeen occurring rates. Further in a destination. growth Moreover, increases the additional flow of the pressuresbest-fit straight until line reaching describing a saturation thresholdthe acceleration/deceleration after which, as presumed of the arrivals by thegrowth TALC rate approach,during the observed in the last period stage will different scenariosenable may management occur, depending of the entire on destination a destination’s system. resilience. Reaching the pointIn line with of inflexion the above, provides we have decided a signal to use that the unacceptable number of arrivals, changes as suggested have been occurringby in the a destination. UNWTO [16], Moreover, as an indicator the of flow the ofdynamics the best-fit of carrying straight capacities line describing and the flow the acceleration/decelerationfunction V(t) to determine of the arrivals the TALC growth stages. rate during the observed period will To determine the saturation point, i.e., the maximum of the function V(t), it is neces- enable management of the entire destination system. sary to equate its first-order derivative V′(t) with zero. The inflexion point of the function In line withV(t) the is above,reached weby equating have decided its second- toorder use the derivative number V″ of(t) arrivals,with zero. asThe suggested value of the by the UNWTOargument [16], as t anwill indicator represent the of thetime dynamicspoint at which of V(t) carrying reaches capacities an inflexion and point. the The flow same function V(t) to determine the TALC stages. To determine the saturation point, i.e., the maximum of the function V(t), it is necessary to equate its first-order derivative V0(t) with zero. The inflexion point of the function V(t) is reached by equating its second-order derivative V”(t) with zero. The value of the argument t will represent the time point at which V(t) reaches an inflexion point. The same is on the graph of the function V(t) and its first-order derivative Growth (t) and the second-order Sustainability 2021, 13, x FOR PEER REVIEW 12 of 22

Sustainability 2021, 13, 4803 12 of 22 is on the graph of the function V(t) and its first-order derivative Growth (t) and the second- order derivative Deriv2(t) (Figure 1). The simulated TALC curve has an inflexion point, i.e., Deriv2 (t) = 0 in 2010, while the moment of saturation Growth(t)à0 is expected in 2021. derivativePrecisely, Deriv2(t) the two (Figure points1 ).of Thetime simulatedcan be considered TALC curve as limits has of an the inflexion three TALC point, stages. i.e., Deriv2 (t) = 0 in 2010, while the moment of saturation Growth(t)à0 is expected in 2021. In the first stage, there is supply-dominance, with supply-driven innovations pushing the Precisely, the two points of time can be considered as limits of the three TALC stages. destination’s attractiveness, eventually affecting further demand growth. In this period, In the first stage, there is supply-dominance, with supply-driven innovations pushing the supply-driven development positively affects destination, especially in terms of socio-eco- destination’s attractiveness, eventually affecting further demand growth. In this period, nomic and cultural impacts. This period of growth lasts until the first point of time (t-point supply-driven development positively affects destination, especially in terms of socio- of inflexion). economic and cultural impacts. This period of growth lasts until the first point of time In the second stage, suppliers fiercely compete for the limited amount of resources to (t-point of inflexion). attract visitors. The visitors benefit from this competition and growingly visit a destina- In the second stage, suppliers fiercely compete for the limited amount of resources to tion, thus indicating the demand dominance stage. Along with the growth of arrivals, attract visitors. The visitors benefit from this competition and growingly visit a destination, many pressures are generated, indicating a destination’s maturity. Each effort to increase thus indicating the demand dominance stage. Along with the growth of arrivals, many pressuresvisitors in are this generated, stage ends indicating up with aan destination’s increase in maturity.the consumption Each effort of resources. to increase Such visitors an inapproach this stage questions ends up the with very an increasesurvival inof thea destination consumption as a ofsystem. resources. This Suchstage an begins approach with questionsthe inflexion the verypoint survival and ends of up a destination with the saturation as a system. point, This indicating stage begins the with maximum the inflexion num- pointber of andvisitors. ends up with the saturation point, indicating the maximum number of visitors. As soon as as the the saturation saturation point point is isachieved, achieved, the the third third stage stage can can start, start, aiming aiming at a atdes- a destination’stination’s restructuring, restructuring, which which may may initiat initiatee its its new new development development cycle cycle together with itsits gravitating areaarea oror aa completecomplete decline.decline. Following the above explanation, it is necessary to approximate TALC asas accuratelyaccurately as possiblepossible withwith realreal data.data. As presented in Figure6 6,, thethe approximateapproximate visitorvisitor curvecurve V(t)V(t) only roughly determines the the trend. trend. The The reason reason is isthat that the the k-coefficient k-coefficient of ofpenetration penetration to- togethergether with with the the M M-maximum-maximum expected expected number number of of visitors visitors is is constant. Following Figure4 4,, coefficientcoefficient kk determinesdetermines thethe demanddemand itselfitself andand itsits growthgrowth rate.rate. Therefore,Therefore, basedbased onon thethe ideaidea of an an unlimited unlimited market, market, we we can can assume assume that that it synthesizes it synthesizes all allelements elements affecting affecting de- demand,mand, thus thus indicating indicating behavior behavior according according to to the the exponential exponential growth pattern. pattern. Demand Demand constraintsconstraints areare caused,caused, among among other other things, things, by by the the attractiveness attractiveness of supply—Mof supply— (proxiedM (proxied by theby the maximum maximum expected expected number number of arrivals). of arrivals). Simply Simply said, said, a new a new product product in a in destination a destina- cantionincrease can increase M. This M. scenarioThis scenario is presented is presented in the in graph the graph of the HR-03of the TotalHR-03 visitors’ Total visitors arrival’ functionarrival function in Figure in 6Figure. Each 6. short-time Each short TALC-time endsTALC with ends a with shift a of shift the Mof the limit, M eventuallylimit, even- initiatingtually initiating a new short-timea new short TALC.-time TALC. InIn lineline withwith the the above, above, we we can can say say that that M synthesizesM synthesizes all elementsall elements of supply. of supply. If M doesIf M notdoes grow, not grow, the function the function of arrivals of arrivals will eventually will eventually behave behave according according to the target to the search target pattern,search pattern, as in Figure as in 4Figu. However,re 4. However, if the new if the supply new supply is created is created to fight to market fight market saturation, satu- theration, growth the growth of the variable of the variable M will behave M will followingbehave following the TALC the curve. TALC An curve. extreme An caseextreme of a structurecase of a whenstructure practically when practically all supply wasall supply defined was at the defined beginning at the of beginning the observed of the period ob- isserved presented period by is graph presented V(t) forby thegraph Living V(t) Labfor the NL-33, Living as shownLab NL in-33, Figure as shown3. in Figure 3. Given thethe above,above, wewe cancan looklook atat kk andand MM asas time-dependenttime-dependent variables.variables. Thus,Thus, insteadinstead of presentingpresenting thethe TALCTALC structurestructure likelike inin FigureFigure1 ,1, we we can can show show it it in in Figure Figure7. 7.

Figure 7.7. Casual loop diagram of the TALCTALC modelmodel inin thethe contextcontext ofof supply-demandsupply-demand dynamics.dynamics.

Dependence of the number of visitors V on variables k and M can be explained by the scenario analysis presented on Figure8. Sustainability 2021, 13, x FOR PEER REVIEW 13 of 22

Sustainability 2021, 13, 4803 13 of 22 Dependence of the number of visitors V on variables k and M can be explained by the scenario analysis presented on Figure 8.

_HRV_Behaviour of V depending of k _HRV_Behaviour of V depending of M 2,000,000 2,000,000

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08 09 10 11 12 13 14 15 16 17 18 19 08 09 10 11 12 13 14 15 16 17 18 19 Non-commercial use only! Non-commercial use only! (a) Behavior of V depending on k (b) Behavior of V depending on M

Figure 8. DependenceFigure 8. of Dependence the number of of the visitors number V of on visitors variables V on k variables and M. k and M.

As presentedAs on presented the left side on the of left Figure side8 of, an Figure increase 8, an ofincrease the penetration of the penetration coefficient coefficient k k (with a constant(with M) a constant affects M)the affects demand the growth demand rate. growth It does rate. not It does increase not increase the supply. the supply. Namely, lowerNamely, positioned lower graphs positioned have graphs lower have values lower of coefficient values of coefficient k and react k and more react slowly more slowly to supply use. While tending to reach the offer, the top positioned graph slows down the to supply use. While tending to reach the offer, the top positioned graph slows down growth of arrivals. On the right side of Figure 8, the situation with M is the opposite. the growth of arrivals. On the right side of Figure8, the situation with M is the opposite. Higher values of M (with a constant k) allow for an increase in the number of arrivals. Higher values of M (with a constant k) allow for an increase in the number of arrivals. Since M is easily reached with a given k, the number of arrivals with a small M (the lowest Since M is easilypositioned reached graph) with ahas given a sigmoid k, the numbershape. However, of arrivals a high with value a small of M M takes (the longer lowest to reach positioned graph)the supply has a sigmoidas the number shape. of However,visitors grows a high exponentially. value of M takes longer to reach the supply as the numberAfter the of TALC visitors curve grows crosses exponentially. the inflexion point with different pressures evidenced, After theit TALC is necessary curve crossesto consider the introducing inflexion point cultural with or different other innovative pressures destination evidenced, products it is necessary(to to increase consider M). introducing In the previous cultural subsection or other, we innovativehave shown destinationhow to extend products the observation (to increase M).of Indynamics the previous to a deeper subsection, level than we the have TALC shown logistic how curve. to extend The dynami the observationzation of k(t) as a of dynamics torepresentative a deeper level of demand, than the and TALC M(t) logisticas a representative curve. The of dynamizationsupply, will enable of k(t) the obser- as a representativevation ofof demand,the relationship and M(t) between as a supply representative and demand of supply, over time will through enable V(t), the which observation ofcharacterises the relationship the life between cycle of supply the destination. and demand over time through V(t), which characterises the life cycle of the destination. 5.3. The TALC System Dynamics Model in Powersim Studio 5.3. The TALC SystemTo develop Dynamics a quantitative Model in Powersim model following Studio the previously described structure (Fig- To developure a 8), quantitative the Powersim model simulation following modeling the previously software described package was structure used. Powersim(Figure8) as, well the Powersimas simulation system dynamics modeling recognizes software four package basic types was of used. parameters: Powersim as well as system dynamics recognizes State variables four basic—which types accumulate of parameters: change. It takes one moment to read them. These variables remember values and are denoted by the rectangle symbol (in Figure 9, • State variables—which accumulate change. It takes one moment to read them. These these are k, M, SumSTDError and V-simulation Data). variables remember values and are denoted by the rectangle symbol (in Figure9, these  Rate variables—which indicate change, i.e., speed (first-order derivative). It takes are k, M, SumSTDErrortwo time moments and V-simulation to calculate Data). their values. They are marked with a picture of the • Rate variables—whichvalve and flow. indicate A bubble change, at the i.e., beginning speed (first-order or end indicates derivative). the source It takesand abyss of two time momentsthe stream. to calculate Input or theiroutput values. presents They a parameter are marked for state with variab a pictureles. In Figure of the 9, these valve and flow.are A Growth bubble k, at Growth the beginning M, Growth or end V, STDError. indicates the source and abyss of the stream. Input Auxiliary or output variables presents— awhich parameter are used for state to clarify variables. calculations In Figure and9, these flow are within the Growth k, Growthmodel. M, Linking Growth them V, STDError.to/from rate variables enables a partial calculus. Constants are • Auxiliary variables—whichpermanent identifiers are used th toroughout clarify calculations the simulation and period. flow within They the are model. denoted by a Linking themrhombus to/from (in rate Figure variables 9, k-rate, enables M-rate, a partial M0, id calculus.-LAU-whose Constants value in are the perma- model is se- nent identifierslected throughout based on the the simulation radio-button period. and the They variable). are denoted by a rhombus (in Figure9, k-rate, M-rate, M0, id-LAU-whose value in the model is selected based on the radio-button and the variable). Sustainability 2021, 13, x FORSustainability PEER REVIEW2021, 13, 4803 14 of 22 14 of 22

FigureFigure 9. Flow 9. Flow diagram diagram of ofthe the HR HR 03 03-LL-LL TALC TALC modelmodel simulation simulation presented presente byd Powersimby Powersim symbols. symbols.

As previously described,As previously in Figure described, 3, we in have Figure shown3, we havegraphs shown of approximated graphs of approximated visitor visitor arrival functions for each Living Lab, based on time-series data from 2007 to 2019 (Table1). arrival functions for each Living Lab, based on time-series data from 2007 to 2019 (Table In the next step, based on the simulation model shown in Figure9 (which is leaning on 1). In the next step,the based structure on the described simulation in Figure model7), we shown describe in Figure graphs of9 (which the visitor is leaning arrivals’ on trends. The the structure describedinput variables in Figure are 7), k-rate, we describe M-rate, graphs and M0. of By the using visitor the arrivals optimization’ trends. tool The in Powersim, input variables arethe k optimal-rate, M values-rate, ofand the M0. above By input using variables the optimization were determined tool in to Powersim, minimize the sum of the optimal valuesstandard of the above deviations input at varia each timebles were point, determined i.e., the minimum to minimize (SumSTDError). the sum of Simply put, standard deviationsthe at optimization each time taskpoint, is toi.e. determine, the minimum the optimal (SumSTDError). values of the Simply input variables put, the so that the optimization taskgraph is to ofdetermine the simulated the numberoptimal of values arrivals of deviates the input as little variables as possible so that from the the graph of graph of the simulatedthe approximate number of function arrivals based deviates on the as actual little time as possible series data from collected the graph at the of level of five Living Labs (Table1). the approximate function based on the actual time series data collected at the level of five Living Labs (Table5.4. 1). Scenario Analysis Based on the TALC System Dynamics Model The results for each of the Living Labs/destinations are presented in Figures 10–14, 5.4. Scenario Analysiseach Based one consisting on the TALC of the System two parts. Dynamics The first Model part delineates the TALC curve based on the The results fornumber each ofof visitor the Living arrivals Labs and/destinati the secondons one are describes presented the propertiesin Figures of 10 the–14, TALC curve each one consisting(1st of and the 2nd two order parts. derivative), The first indicating part delineates what stage the of TALC its life cyclecurve LL/destination based on is in. the number of visitorHence, arrivals the and first the part second in each ofone the describes following the figures properties (from Figures of the 10 TALCa–14a) contains the following graphs: curve (1st and 2nd order derivative), indicating what stage of its life cycle LL/destination • is in. V-simulation data (red graph)—representing the number of arrivals per year, representing the trend of the observed period; Hence, the first part in each of the following figures (from Figures 10a–14a) contains the following graphs:  V-simulation data (red graph)—representing the number of arrivals per year, representing the trend of the observed period;  V-Official Data (light green graph)—representing the number of arrivals per year, based on the interpolated data;  Maximum expected number of visitors (M) (blue graph) equals total supply. Sustainability 2021, 13, 4803 15 of 22

• V-Ofﬁcial Data (light green graph)—representing the number of arrivals per year,

Sustainability 2021, 13, x FORbased PEER on REVIEW the interpolated data; 15 of 22 • Maximum expected number of visitors (M) (blue graph) equals total supply. The second part in each of the following figures (from Figures 10b–14b contains the following graphs:The second part in each of the following figures (from Figures 10b–14b) contains the • Growthfollowing of V (dark graphs: green graph)—the first-order derivative of the V-simulation function;  Growth of V (dark green graph)—the first-order derivative of the V-simulation func- • Derivative2 (redtion; graph)—the second-order derivative of the V-simulation function; • Derivative2 signDerivative2 (blue graph)—a (red graph) sign—the of second the second-order-order derivative derivative of the V indicating-simulation mo-function; ment when aDerivative2 destination sign passes (blue from graph) one— stagea sign toof another;the second-order derivative indicating mo- • t-asix (light greenment when graph)—drawn a destination to passes enable from monitoring one stage of to theanother first; and second-order derivative functionst-asix (light flow. green graph)—drawn to enable monitoring of the first and second-order derivative functions flow. The simulated visitor arrival curves (V-simulation data) have a sigmoidal shape corresponding toThe the theoreticalsimulated visitor TALC arrival curve. curves Observed (V-simulation differences data) across have Living a sigmoidal Labs shape can corresponding to the theoretical TALC curve. Observed differences across Living Labs can be explained by different dynamics of their supply (offer) development proxied by the be explained by different dynamics of their supply (offer) development proxied by the maximum expected number of visitors (M). maximum expected number of visitors (M). Given the above,Given the the models above, the are models presented are presented as follows as in follows Figure in 10 Figure: 10:

(a) TALC—supply curve of B-23 (b) Properties of B-23 TALC curve

Figure 10. TALC—supplyFigure 10. curve TALC and—supply properties curve of and B-23. properties of B-23.

Due to the supplyDue to expansion, the supplyat expansion, the end of at the the observed end of the period observed (2019), period the (2019), Living the Lab Living B- Lab 23 (BELGIUM/Prov.B-23 (BELGIUM Oost-Vlaanderen/the/Prov. Oost-Vlaanderen Scheldeland/the region/Denderleeuw, Scheldeland region/Denderleeuw, Willebroek) Wil- has hosted approximatelylebroek) has hosted 40,000 approximately more visitors 40,000 than at more its beginning visitors than (in 2007)at its beginning (Figure 10 (ina). 2007) (Figure 10a). It has passed through the first (growth) stage, or the supply dominance stage It has passed through the ﬁrst (growth) stage, or the supply dominance stage in 2017 in 2017 and reached its carrying capacity threshold, after which has entered the second (of and reached its carrying capacity threshold, after which has entered the second (of the the three elaborated) TALC stage, i.e., the demand dominance stage. As shown in Figure three elaborated)10a, the TALC supply stage, (M) i.e., curve the has demand a slight dominance S-shape indicating stage. Asthe shownLL’s involvement in Figure 10witha, tour- the supply (M)ism. curve Figure has 10b a slight shows S-shape that the indicating maximum the acceleration LL’s involvement of the visitors with tourism.’ growth rates Figure 10b shows(Deriv2) that was the maximumachieved inacceleration 2014, with the of themaximum visitors’ number growth of rates arrivals (Deriv2) reached was in 2017 achieved in 2014,(Deri withv2 = 0), the after maximum which it number began to of decline. arrivals Parallel reached to in this, 2017 the (Deriv2 curve =representing 0), after the which it begannumber to decline. of visitors Parallel (V) became to this, concave, the curve tending representing to reach the the threshold number indicating of visitors the max- (V) became concave,imum number tending of visitors. to reach the threshold indicating the maximum number of visitors. In 2019, the LL -ES24 (SPAIN/Aragón/Huesca/Ainsa, Barbastro, Benasque, Graus, In 2019,Huesca, the LL -ES24Jaca, Sariñena) (SPAIN/Arag has increasedón/Huesca/Ainsa, the number of Barbastro, visitors by Benasque, approximately Graus, 120,000 Huesca, Jaca,compared Sariñena) to has2007 increased (Figure 11a). the The number fastest ofacceleration visitors by of the approximately growth rate was 120,000 achieved in compared to2014, 2007 after(Figure which 11a). it Thebegan fastest to decline acceleration (Figure 11b).of the It growth has reached rate was its carrying achieved capacity in 2014, afterthreshold which it (associated began to decline with the (Figure given supply 11b). Itstructure) has reached in 2016 its and carrying has entered capacity the second threshold (associatedlifecycle stage, with thei.e., giventhe demand supply dominance structure) stage. in 2016 and has entered the second lifecycle stage, i.e., the demand dominance stage. Sustainability 2021, 13, 4803 16 of 22 Sustainability 2021, 13Sustainability, x FOR PEER 2021 REVIEW, 13, x FOR PEER REVIEW 16 of 22 16 of 22

(a) TALC—supply curve of ES-24 (b) Properties of ES-24 TALC curve (a) TALC—supply curve of ES-24 (b) Properties of ES-24 TALC curve Figure 11. TALC—supplyFigure 11. T curveALC— andsupply properties curve and of ES-24. properties of ES-24. Figure 11. TALC—supply curve and properties of ES-24. In the observedIn period, the observed the number period, of visitorsthe number in the of LL visitors IT-H3 in (ITALY/Veneto/Vicenza/ the LL IT-H3 (ITALY/Veneto/Vi- In the observed period, the number of visitors in the LL IT-H3 (ITALY/Veneto/Vi- Vicenza, Caldogno,cenza Pojana/Vicenza, Maggiore, Caldogno, Grumolo Pojana delleMaggiore, Abbadesse, Grumolo Lonigo, delle Montagnana)Abbadesse, Lonigo, has Monta- cenza/Vicenza, Caldogno, Pojana Maggiore, Grumolo delle Abbadesse, Lonigo, Monta- increased by approximatelygnana) has increased 120,000 visitors by approximately (Figure 12 a). 120,000 However, visitors it has (Figure grown 12a). ata However, lower it has gnana) has increasedgrown atby a approximatelylower rate than 120,000in Belgium visitors and (FigureSpain. Hence, 12a). However,maximum itacceleration has of the rategrown than at ina lower Belgium rate andthan Spain. in Belgium Hence, and maximum Spain. Hence, acceleration maximum of acceleration the growth rateof the was achieved in 2015,growth and rate the was maximum achieved number in 2015, of and visitors the maximum was reached number in 2018, of visitors indicating was reached in growth rate was2018, achieved indicating in 2015, the point and thewhen ma LLximum has entered number into of thevisitors second was TALC reached stage, in with a dimin- the point when LL has entered into the second TALC stage, with a diminishing number of 2018, indicatingishing the point number when of LLvisitors has entered along the into remaining the second period TALC (Figure stage, 12b).with a dimin- visitorsishing number along the of visitors remaining along period the remaining (Figure 12 periodb). (Figure 12b).

(a) TALC—supply curve of IT-H3 (b) Properties of IT-H3 TALC curve (a) TALC—supply curve of IT-H3 (b) Properties of IT-H3 TALC curve FigureFigure 12. TALC—supply curve curve and and properties properties of of IT-H3 IT-H3. . Figure 12. TALC—supply curve and properties of IT-H3. AtAt the end of the observed period period (in (in 2019), 2019), the the LL LL NL-33 NL-33 (NETHERLANDS/Zuid- (NETHERLANDS/Zuid- Holland/theHolland/the Rotterdam RotterdamAt the Metropolitan Metropolitan end of the observed Region/R Region/Rotterdam, periodotterdam, (in 2019),Delft, Delft, Dordrecht,the Dordrecht, LL NL- 33Molenlanden, (NETHERLANDS Molenlanden, /Zuid- Barendrecht,Barendrecht, Ridderkerk,Ridderkerk,Holland/the Zwijndrecht) Rotterdam Metropolitan has realisedrealised Region approximately/Rotterdam, 970,000 Delft, more Dordrecht, tourists Molenlanden, as Barendrecht, Ridderkerk, Zwijndrecht) has realised approximately 970,000 more tourists comparedas compared to 2007.to 2007. It reachedIt reached the the end end of of the th seconde second TALC TALC stage stage yet yet in in 2015, 2015, primarily primarily due as compared to 2007. It reached the end of the second TALC stage yet in 2015, primarily todue the to role the role of the of citythe city of Rotterdam of Rotterdam (as (as presented presented in in Table Table1 and 1 and Figure Figure 13 13a).a). Currently, Currently, the due to the role of the city of Rotterdam (as presented in Table 1 and Figure 13a). Currently, accelerationthe acceleration growth growth rate rate tends tends to zero, to zero, which wh meansich means that that the numberthe number of visitors of visitors will will bethe the acceleration growth rate tends to zero, which means that the number of visitors will samebe the each same year. each The year. second-order The second-order derivative deriv graphative (Deriv2)graph (Deriv2) indicates indicates that the that acceleration the acceleration of thebe visitors’ the same growth each year.rate has The ch secondanged- orderits direction derivative and graphis not declining (Deriv2) indicatessteeply that the ac- of the visitors’celeration growth rate of the has visitors changed’ growth its direction rate has and changed is not its declining direction steeplyand is not anymore. declining steeply Bothanymore. the ﬁrst Both and the thefirst second-order and the second-order derivative derivative graphs graphs tend to tend zero, to which zero, which means means that the that the destinationanymore. (LL) Bothapproaches the first theand third the second stage -oforder its lifecycle derivative (Figure graphs 13b). tend This to zero, par- which means destination (LL)that approaches the destination the third(LL) approaches stage of its the lifecycle third stage (Figure of its 13 lifecycleb). This (Figure particular 13b). This particular Living Lab differs from the others concerning its supply (M) remains almost con- Living Lab differsticular from Living the others Lab differs concerning from the its others supply concerning (M) remains its almostsupply constant(M) remains along almost constant along the observed years, indicating that NL-33 Living Lab (destination) has not sig- the observed years,stant along indicating the observed that NL-33 years, Living indicating Lab that (destination) NL-33 Living has Lab not (destination) signiﬁcantly has not significantly improved its supply. improved its supply.nificantly improved its supply. Sustainability 2021, 13, 4803 17 of 22 Sustainability 2021, 13, x FOR PEER REVIEW 17 of 22

Sustainability 2021, 13, x FOR PEER REVIEW 17 of 22

(a) TALC—supply curve of NL-33 (b) Properties of NL-33 TALC curve

Figure 13. TALC—supplyFigure 13. TALC curve— andsupply properties curve and of properties NL-33. of NL-33.

The LL HR-03The (CROATIA/Jadranska LL HR-03 (CROATIA Hrvatska/City/Jadranska Hrvatska of Split/City metropolitan of Split metropolitan area/Split, area/Split, Trogir, Dugopolje,Trogir, Solin, Dugopolje, Klis, Kaštela, Solin, Klis, Sinj) Kaštela, consists Sinj) of consists seven municipalities, of seven municipalities, out of which out of which four coastal onesfour (twocoastal inscribed ones (two on inscribed the World on Heritagethe World List) Heritage currently List) currently record significant record significant tourist flows. The three rural municipalities have recently got involved more intensively tourist flows. The three rural municipalities have recently got involved more intensively with the tourism business. However, despite the newcomers, the whole of the Split met- with(a the) TALC tourism—supply business. curve of However,NL-33 despite(b) the Properties newcomers, of NL-33 the TALC whole curve of the Split ropolitan LL has reached its carrying capacity in 2017 and is currently in its second lifecy- metropolitan LL has reached its carrying capacity in 2017 and is currently in its second cleFigure stage 13. (the TALC demand—supply dominance curve and stage)properties (Figure of NL-33. 14a). The sudden take-off in terms of the lifecycle stagenumber (the demand of visitors dominance (V) resulting stage) from (Figure the enhancement 14a). The sudden of its supply take-off attractiveness in terms (M) of the numberhappened of visitorsThe LL in theHR-03 (V) period resulting (CROATIA/Jadranska from 2013 from to the 2016, enhancement when Hrvatska/City it also reaches of of its Split supplythe metropolitanmaximum attractive- acceleration area/Split, ness (M) happenedofTrogir, the invisitor Dugopolje, the period growth Solin, from rate Klis, (Deriv2) 2013 Kaštela, to 2016, (Figure Sinj) when consists 14b). it The also of seven maximum reaches municipalities, the number maximum of out visitors of which is acceleration ofachievedfour the coastal visitor in 2017, ones growth meaning(tworate inscribed that (Deriv2) it onwas the (Figure just World one 14- yearHeritageb). distance The List) maximum between currently numberreaching record significant ofthe maxi- visitors is achievedmumtourist acceleration inflows. 2017, The meaning ofthree the ruralvisitor that municipalities itgrowth was justrate one-yearandhave the recently maximum distance got involved number between moreof reach-visitors intensively (arri- ing the maximumvals).with accelerationthe tourism business. of the visitor However, growth despite rate the and newcomers, the maximum the whole number of the ofSplit met- visitors (arrivals).ropolitan LL has reached its carrying capacity in 2017 and is currently in its second lifecy- By decliningcle stage along (the the demand second dominance stage of its stage) lifecycle, (Figure the 14a). visitor The number sudden take-off growth in tends terms of the number of visitors (V) resulting from the enhancement of its supply attractiveness (M) to reach its predefined supply M. The LL HR-03 has the steepest decline of the growth happened in the period from 2013 to 2016, when it also reaches the maximum acceleration rate compared to other LLs, which means the fastest deceleration of the number of visitors. of the visitor growth rate (Deriv2) (Figure 14b). The maximum number of visitors Worth noting is that HR-03 LL has accomplished the most significant advancement of its is achi supply in the observed period, delineated by more than a million arrivals.

(a) TALC—supply curve of HR-03 (b) Properties of HR-03 TALC curve Figure 14. TALC—supply curve and properties of HR-03.

By declining along the second stage of its lifecycle, the visitor number growth tends to reach its predefined supply M. The LL HR-03 has the steepest decline of the growth rate compared to other LLs, which means the fastest deceleration of the number of visitors. Worth noting is that HR-03 LL has accomplished the most significant advancement of its supply in the observed period, delineated by more than a million arrivals. (a) TALC—supply curve of HR-03 (b) Properties of HR-03 TALC curve

Figure 14. TALC—supply6. DiscussionFigure curve14. TALCand and Conclusive— propertiessupply curve Remarks of and HR-03. properties of HR-03. Apart from the theoretical contributions, the model developed in this research has By declining along the second stage of its lifecycle, the visitor number growth tends been tested and verified on five specific cases. The analysis revealed that all observed Liv- 6. Discussion andto reach Conclusive its predefined Remarks supply M. The LL HR-03 has the steepest decline of the growth ing Labs (destinations) reached the second lifecycle stage (demand-dominance stage), Apart fromrate the compared theoretical to other contributions, LLs, which means the model the fastest developed deceleration in this of the research number has of visitors. with the LL NL 33-Netherlands entered as early as in 2015, and LL ITH3-Italy in 2018 Worth noting is that HR-03 LL has accomplished the most significant advancement of its been tested and(Table verified 2). on five specific cases. The analysis revealed that all observed Living Labs (destinations)supply in the reachedobserved the period, second delineated lifecycle by stage more (demand-dominancethan a million arrivals. stage), with the LL NL 33-Netherlands entered as early as in 2015, and LL ITH3-Italy in 2018 (Table2). 6. Discussion and Conclusive Remarks Apart from the theoretical contributions, the model developed in this research has been tested and verified on five specific cases. The analysis revealed that all observed Liv- ing Labs (destinations) reached the second lifecycle stage (demand-dominance stage), with the LL NL 33-Netherlands entered as early as in 2015, and LL ITH3-Italy in 2018 (Table 2). Sustainability 2021, 13, 4803 18 of 22

Table 2. The comparative presentation of the LLs’ lifecycle stages.

The Year When the The Year When the Maximum Growth Rate of Maximum Acceleration of Living Lab the Visitor Growth Rate Was Arrivals Is Reached Lifecycle Stage Reached (Carrying Capacities Threshold) BE-23; BELGIUM, Prov. The second lifecycle stage-the Oost-Vlaanderen and 2014 2017 Antwerpen, the Scheldeland demand dominance stage region The second lifecycle stage- the ES 24: SPAIN, Aragón, Huesca 2014 2016 demand dominance stage HR-03; CROATIA, City of The second lifecycle stage- the 2016 2017 Split metropolitan area demand dominance stage The second lifecycle stage- the IT H3; ITALY, Veneto, Vicenza 2015 2018 demand dominance stage NL 33; NETHERLANDS, Zuid-Holland, The Rotterdam 2015 2015 The end of the second Metropolitan Region lifecycle stage

Considering data availability and Butler’s [15] original idea, in this model the number of visitors V is taken as the reference point, with the logistic curve explaining the destination’s development over time. The visitor growth rate acceleration occurs until the threshold point when various pressures in a destination become evident. At that point, called the inflexion point, a destination reaches its carrying capacity and enters into the so-called demand-dominance stage (corresponding to the Butler’s consolidation stage), with the TALC curve changing from a convex to a concave shape. The steeper is the decline of the growth rate, the faster is deceleration/fall of the number of visitors, as in the LL HR-03- CROATIA. However, when interpreting the specific TALC curve behavior, it has to be borne in mind that each of the observed destinations consists of several municipalities, each one differing from another in terms of quantity and quality of resources and overall development framework. These specificities potentially affect their position on a life cycle curve and the duration of a stage they reached. Moreover, comparing peripheral/rural municipalities with the urban ones regarding tourism intensity, it becomes evident that their smallness, remoteness and overall fragility may affect reaching the carrying capacity threshold sooner than urban destinations and with fewer tourists. Given the above, we may conclude that the elaborated TALC system dynamics model cannot explain the causes affecting either demand or supply behavior. However, understanding the socio-economic framework and the trends in an observed period can help us understand the reasons behind their behavior. The period we have chosen to observe (2007 to 2019) is specific as it encompasses the year before the global economic crisis (2007), together with the immediate recovery and the post-recovery period. Many authors [34,56–58] discussed the role of tourism in the period after the crisis, considering it as a means by which the capitalist system as a whole sustains itself. With this regards, they conclude that tourism was used as one of the most common responses to the 2008 global economic crisis, which is why many governments strongly stimulated it to enhance economic recovery [57]. It certainly contributed to the expansion of demand worldwide. Apart from this, the rise of low-budget airlines, social media and Internet platforms and improved living standards in highly populated countries have also led to the enormous expansion of tourism demand, leading to overtourism, especially in cities rich with cultural heritage. This trend is also evident in some of the towns belonging to the analysed Living Labs, such as Rotterdam, Split, Vicenza, and Trogir, which recorded significant demand growth in a short period. Due to them, their corresponding LLs entered the demand-dominance stage before the COVID-19 pandemic crisis. Sustainability 2021, 13, 4803 19 of 22

As explained, the demand-dominance stage begins with the inflexion point ending up with the saturation point (Butler’s stagnation stage), indicating the maximum number of visitors that a destination can withstand. As soon as the saturation point is achieved, the third stage starts, when a destination’s managers have to decide which of the following strategies they should apply: • To reduce the number of arrivals; • To remain in the steady-state (the same number of arrivals each year), or • To initiate a new lifecycle by introducing innovative and sustainable tourism products to enhance offer (M) and to rejuvenate destination. The destination rejuvenation strategies and policies have been researched by many authors, such as Faulkner [59], Faulkner and Tideswell [60], Hovinen [61], Albaladejo and Martinez [62], Ferreira and Hunter [63], Malcolm-Davies [64], and many others, proving the rule of the thumb that ‘the same policy does not fit all. Our findings have both theoretical and empirical implications. From the theoretical standpoint, system thinking contributed to understanding the complexity and structure of a tourist destination as a system. Moreover, the system dynamics applied to modeling tourist destination life cycle (TALC) contributed to understanding its behavior and the ways information feedback governs using feedback loops, delays and stocks and flows. Worth noting is that this research added to the existing body of knowledge on the chaos and complexity concepts in researching tourism and tourist destination, which, as indicated by Olmedo and Mateos [4] and Sedarati et al. [7], is still in its initial phase. We also tried to introduce some novelty into the usual TALC modeling performed so far. To this end, we investigated the dynamics of the variables usually taken as constants, representing quite a challenging approach rarely applied, as in Lundtorp and Wanhill [65]. Unlike the original TALC model [15], suggesting six lifecycle stages, this research offered a model with three lifecycle stages, i.e., the supply-dominance stage, the demand-dominance stage, and the restructuring stage. The supply-dominance corresponds to the three stages of Butler’s model, i.e., exploration, involvement, and development stages, while the demand-dominance corresponds to Butler’s consolidation stage. Finally, the demand-dominance stage ends up with a saturation point, after which the third stage begins, e.g., the restructuring or Butler’s rejuvenation stage. The TALC system dynamics model was performed in several phases. First, by using empirical data on visitors in five LLs from 2007 to 2019, we have shown graphs of approximated visitor arrivals functions for each Living Lab. In the next step, following a causal loop diagram of the TALC model structure, describing the interaction among the variables, the simulation model was developed using the Powersim simulation modeling software. It aimed to determine the optimal values of the input variables. Then we simulated the function of arrivals, using the graph slightly deviating from the approximated one, based on the actual time-series data on arrivals. Finally, scenario analysis based on the TALC system dynamics model, consisting of the two parts, was performed for each Living Lab. The first part delineates the TALC curve based on the number of visitor arrivals, while the second describes the properties of the TALC curve (1st and 2nd order derivative), indicating the stage of a destination/LL life cycle. From the empirical standpoint, the above-elaborated model may be used by destination managers as a warning tool, indicating two crucial moments of a destination development cycle, i.e., the moment when it reaches its carrying capacities and the moment of saturation, after which an innovative cycle ought to begin. Using this tool, managers may timely apply appropriate strategies and policies to enhance the destination’s sustainability and prevent its decline. Of course, this model, as any, has gaps. The main gap is associated with its inability to indicate threshold and saturation points before the accumulated problems cause stagnation and decline. Furthermore, the model is based on just one variable, i.e., the number of visitors to a destination. Additionally, it delineates only three lifecycle stages, which, Sustainability 2021, 13, 4803 20 of 22

of course, simpliﬁed its construction. However, by introducing more, a destination’s development path can be better understood and managed. Given the above, future research may go in several directions. First, based on the elaborated methodological considerations and obtained results, it may focus on introducing the third-order derivative into the TALC model, implying the moment in which the second-order derivative reaches its maximum. However, it has to be carefully considered given the inertia of a large destination system on one side and the fast changes in small destination systems on the other side, hence questioning its applicability. Namely, large systems react slowly to changes, especially to small changes characterized by the third-order derivative. On the other hand, small systems are too volatile, which brings their credibility into question. In other words, the changes of the third-order derivative characteristics can be temporary and can lead to wrong decisions. Nevertheless, investigating its applicability can enable splitting the three TALC stages into more. In addition, by investigating speciﬁc destinations, we may learn what particular policies should be introduced to either increase, adjust, or reduce the supply, thus ending with the adjusted M (maximum expected number of visitors). Furthermore, by introducing new variables on the supply side, a detailed simulation macro-model may be developed and used as a prognostic tool for tourist destinations, eventually supporting better decision-making.

Author Contributions: Conceptualization, M.H. and L.P.; methodology, M.H. and L.P.; software, M.H.; validation, M.H. and L.P.; formal analysis, M.H.; investigation, M.H. and L.P.; resources, M.H.; data curation, M.H.; writing—original draft preparation, M.H. and L.P.; writing—review and editing, L.P. and M.H.; visualization, M.H.; supervision, L.P.; project administration, L.P.; funding acquisition, L.P. All authors have read and agreed to the published version of the manuscript. Funding: This article is based on research done in the context of the SmartCulTour project that has received funding from the European Union’s Horizon 2020 Research and Innovation Programme under grant agreement no. 870708. The authors of the article are solely responsible for the information, denominations and opinions contained in it, which do not necessarily express the point of view of all the project partners and do not commit them. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable. Conﬂicts of Interest: The authors declare no conﬂict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

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