Analysis Optimizing agricultural land-use portfolios with scarce data— A non-stochastic model Thomas Knoke a, ⁎, Carola Paul a , Fabian Härtl a , Luz Maria Castro a,b , Baltazar Calvas a,c , Patrick Hildebrandt c a Institute of Forest Management, TUM School of Life Sciences Weihenstephan, Department of Ecology and Ecosystem Management, Technische Universität München (TUM), Freising, Germany b Departamento de Economía, Universidad Técnica Particular de Loja, Loja, Ecuador c Institute of Silviculture, TUM School of Life Sciences Weihenstephan, Department of Ecology and Ecosystem Management, Technische Universität München (TUM), Freising, Germany abstract article info Article history: Received 16 April 2015 Received in revised form 22 September 2015 Accepted 29 October 2015 Available online 13 November 2015 Keywords: Robust optimization Risk Portfolio theory Land use Diversification Shannon's index The theory of portfolio selection has often been applied to help improve economic decisions about the environ- ment. Applying this theory requires information on the covariance of uncertain returns between all combinations of the economic options and also assumes that returns are normally distributed. As it is usually difficult to fulfill all data requirements and assumptions, this paper proposes a variant of robust portfolio optimization as an alter- native that needs less pre-information. The approach considers future uncertainties in a non-stochastic fashion through possible deviations from the nominal return of land-use alternatives. Maximizing the economic return of the land-use portfolio is conditional on meeting an inclusive set of constraints. These demand that a pre- defined return threshold is achieved by the robust solution for each uncertainty scenario considered. Based on data for eight agricultural crops common in the Ecuadorian lowlands, a comparison with portfolios generated by classical stochastic mean-variance optimization shows greater land-use diversification (through increased Shannon indices), but only moderate expected economic loss of non-stochastic robust land-use portfolios. We conclude that non-stochastic derivation of land-use portfolios is a good alternative to the classical stochastic model, in situations where information on economic input parameters is scarce. © 2015 Elsevier B.V. All rights reserved. 1. Introduction Modern financial theory is still largely based on the famous results that follow from Markowitz's (1952, 2010) theory of portfolio selection. The theory of portfolio selection is used to analyze and improve decision making in natural resources and the environment, for issues such as bio- diversity conservation, forestry, grassland and fisheries management, and land allocation. Examples include analyzing common agricultural policy, conservation payments, irrigation, flood management, and opti- mization. For instance, Figge (2004) applied portfolio theory to develop a concept for valuing the benefits of biodiversity. In a marine case study on biological conservation, Halpern et al. (2011) adopted portfolio se- lection theory to analyze the impact of spatial variance in returns from natural resources on the equitable delivery of value to individuals and communities. Koellner and Schmitz (2006) contributed an application of the portfolio theory in grassland science using the reward-to- variability ratio for optimization (cf. Sharpe, 1994). There are also vari- ous applications of the portfolio theory in forest science; Hildebrandt and Knoke (2011) provide an overview on forest investment decisions under uncertainty, including applications of portfolio theory. There are many other applications of portfolio selection theory in fishery science. For example, Griffiths et al. (2014) recently concluded that portfolio theory provides a straightforward method for characteriz- ing the resilience of salmon ecosystems and their services. Moore et al. (2010) also used economic portfolio theory to simulate the impact of synchronization of salmon populations on the risk-adjusted perfor- mance of fish portfolios. Sanchirico et al. (2008) employed a portfolio framework to consider variance and covariance in gross fishing reve- nues when setting total allowable catch for individual species. Another example is the work of Edwards et al. (2004), who systematically com- bined various fish stocks into a portfolio that balances expected aggre- gate returns against risks. In an earlier study, Larkin et al. (2003) maximized unit returns for various pre-defined risk levels to show that the actual composition of fish resources is not part of the efficient portfolios (that is, portfolios that achieve maximum economic return for pre-defined risk levels). This paper deals with the important problem of allocating scarce land to various land-use options, which has also been supported by portfolio theory in various studies. Land allocation is among the world's most pressing environmental issues, as confirmed by Wise et al. (2009). They conclude that allocating scarce land resources to competing ends, for instance, to balance climate protection and food production, will re- main a major challenge of the 21st century. The allocation of land has long been studied in land-use economics, beginning with von Thünen's Ecological Economics 120 (2015) 250–259 ⁎ Corresponding author at: TUM School of Life Sciences Weihenstephan, Technische Universität München, Hans-Carl-von-Carlowitz-Platz 2, 85354 Freising, Germany. E-mail address: knoke@forst.wzw.tum.de (T. Knoke). http://dx.doi.org/10.1016/j.ecolecon.2015.10.021 0921-8009/© 2015 Elsevier B.V. All rights reserved. Contents lists available at ScienceDirect Ecological Economics journal homepage: www.elsevier.com/locate/ecolecon