We interpret the potential of natural capital productivity in a spatial ecological social economic system (ESES) as the stock of free energy. According to the definition of entropy flow in an open system, the «negative entropy» inflow occurs into the Earth’s biosphere, with the sustainability of the negentropic budget maintaining the living matter mass conservation law posited by Volodymyr Vernadsky. Introduction of spatial heterogeneity into the free energy definition reveals the non-additive property of its volume across spatial subsystems of the biosphere. This further emphasizes the conceptual shortcomings of stakeholder-centric and property-based sustainability decision-making models. Instead, trajectories of system’s dynamics on different scales should become the subject of preventive decision-making and risk management by economic agents and regional stakeholders, acting in a multi-layered communication and coordination network with horizontal as well as hierarchical information and resource flows. The case of the Carpathian region is used to illustrate the substantive necessity and institutional prerequisites of a new spatial model for sustainable development. 

natural capital, spatial ecological social economic systems, free energy, negentropy, preventive governance for sustainability 

An application of econometric methods for balance assessment of natural and historic-cultural recreational factors’ influence in recreational potential grade formation, as well as for completeness assessment of taking natural recreational resources into account in grading, is proposed. Regression analysis of natural and historic-cultural recreational resource indicators’ relations to the final grade value is applied. A panel linear regression model was built across the identified resort and recreation zones of Zakarpatska region. The value of the territorial recreational potential grade, proposed by Molnar, O. and Marchenko, O., was chosen as the dependent variable. As independent variables, the number of mineral water springs, used in the recreation zone, was chosen for balneological resources, the percent of the territorial forestation for forest resources, the qualitative availability estimation of various water resource categories, presented as a quantitative variable ranged from 0 to 3, for water resources. Estimation of linear regression parameters was performed using LibreOffice 4.2.4.2. The estimated model coefficients are significant as a whole by Fischer’s criterion with p<=0.01; the forestation and water resource indicator coefficients are insignificant with 0.9 confidence level. This means that estimation results have not allowed detection of forestation and water resources’ recreational significance impact upon the final grade value. Based on the source data, we have calculated the adjusted grade value with exclusion of certain recreational potential components, namely the number of mineral water springs that can potentially be used in the zone, as well as the percentage of forested area suitable for recreation. After the repeated estimation of our regression model parameters, the water resources availability impact significance indicator has lowered from p=0.146 to p=0.049; the corresponding value for the forestation percentage has lowered from p=0.312 to p=0.024, both values indicating significance of impacts with 0.95 confidence level. For additional grading methodology testing purposes, we have updated the grade for resort in Zakarpatska region and recreation zones for the year 2012. Desrcibing the results of the repeated regression estimation for the updated grade value, the consistently lower significance of forestation and water resources’ impact (p<=0.01, while other impacts’ significance and model significance as a whole is estimated at p<=0.001), as well as balance of natural and historic-cultural recreational potential components’ impact, are worth noting. For statistical reasons, exclusion of correlated indicators describing a particular natural resources group from the source data list is therefore justified for grading, despite the possibility for them to reflect certain essential recreational potential components. More generally, an improvement of the whole natural recreational resource indicators list can be suggested. Based on the analysis results, identification of forest and water recreational resource indicators requires primary attention. 

territorial recreational potential, grading, forest recreational resources, water recreational resources, Trans-Carpathian region, panel linear regression model