During the past 60 years, changes in the agricultural industry have led to a global agrifood system dominated by large, capital-intensive farms [1–3]. These farms are increasingly specialized in terms of the crops they produce, and hence are dependent on inputs from other sectors of the economy [4–6]. This change in agriculture has been driven by the search for increased economic efficiency, economies of scale, and reduced marginal costs of production. However, the homogenization of agriculture may have an unintended drawback, and some evidence suggests that these more specialized farms are also less resilient [7–12] and that they experience increased income volatility [13–15]. Hence, there may be trade-offs between agricultural returns and the resilience of those returns in modern farming systems.
We present the results of an empirical study that used data on forecasted annual average agricultural gross margins (GMs) between 1966 and 2010 and data on land-use diversity (derived from census data and satellite imagery) to examine the relationships between landscape units with different levels of agricultural diversity and the amount and volatility of the expected GMs from agriculture that each different landscape unit provided. We examined this relationship at a range of different spatial scales to address two core research questions. We investigated first, whether more specialized landscapes (that is, those with lower land-use diversity) have higher average GMs, and second, whether more specialized landscapes have more volatile returns. In addition, we examined the role of spatial scaling of land-use patterns in real landscapes on these two relationships. Together, these analyses indicate the extent to which, and at what scales, there may be a trade-off between expected GMs and the volatility and resilience of those expected GMs.
Resilience and agricultural systems
The central theoretical concept in this paper is that of ‘resilience’, derived from systems dynamics thinking, which the literature broadly describes as the tendency of a system to return to its original state following a disturbance. Resilience therefore has a number of properties: the ease with which a system can be disturbed (resistance), the way in which a system returns to its pre-disturbance state (that is, its speed and trajectory), and the propensity for a system to move to an alternative stable state following disturbance [16, 17]. Resilience is often interpreted as a measure of either the size of the perturbation required to flip a system into a new dynamically stable state (regime shifts or system identity shifts) [18, 19] or the capacity of a system to maintain its current equilibrium state in the face of perturbations .
Operationalizing resilience in many empirical situations is complex, thus system behavior typically either needs a systems model or experimental perturbation to assess the way in which the system responds. Both of these factors are difficult to simulate for large-scale, complex systems. In some extreme examples, a regime shift can be identified by very significant changes. Notable examples include the Dust Bowl period of the 1930s in North America, when a prolonged drought rendered millions of hectares of farmland unproductive, and displaced hundreds of thousands of people from their homes ; the Ethiopian Famine in the 1980s, when a relatively minor drought triggered a catastrophic famine [22–24]; or the Irish Potato Famine, when the failure of a single crop caused a permanent depopulation of western Ireland [25, 26]. Although extremely important, studying such tragedies lends itself to a qualitative case study-based research approach, and are difficult to analyze quantitatively, for a sample of other case studies see [27, 28].
Attempts to quantify resilience in the absence of clear regime shifts are hampered by the multi-dimensional nature of the concept, particularly given that the different properties of resilience may be quantified in incommensurable units. As most systems are continually disturbed and fluctuate around a quasi-equilibrium state , examining resilience as the relationship between the size of disturbance and the effect of that disturbance [29–31] is perhaps more generally useful. For most applications to agricultural systems not subject to catastrophic change, this element of resilience can be articulated as the stability of agricultural returns in the presence of different exogenous shocks . Agricultural returns are inherently volatile, and change in response to a range of exogenous (for example, disease outbreaks, climate, currency exchange rates, market forces, rapidly changing subsidy systems) and endogenous (for example, crop choice) factors [33, 34], with the returns from different agricultural sectors being sensitive to different exogenous drivers of change .
One of the key themes deriving from the resilience literature is the hypothesis that agricultural landscapes that are more heterogeneous may also be more resilient in terms of the stability of agricultural returns, as such diverse landscapes should reduce risk (defined in terms of the expected variance in returns [28, 36–41]). However, there is potentially an inherent trade-off, in that a diversified strategy reduces volatility at the cost of reduced expected mean returns. The concept of ‘bet-hedging’ captures this dichotomy; in highly variable systems, strategies that trade off the variance against mean returns can often be superior [42–44]. Hence, in this study, we were interested in determining whether land-use diversity influences the volatility and resilience of the expected GMs in agricultural landscapes.
Land-use diversification has the potential to reduce resilience (expected volatility of GM per unit of expected GM) because the returns generated from an individual land use are dependent on a relatively narrow range of weather conditions and the vagaries of commodity price. Both weather conditions and commodity markets have become increasingly erratic [45, 46], causing concerns that farm returns have become less resilient . For example, between 1990 and 2007, the average annual net income of a UK farming enterprise (excluding horticulture) was approximately £23,000; however, this averaged figure hides the significant volatility in these returns over this time period, with the average return ranging from approximately £45,000 in 2002 to just £8,700 in 2000 .
In this research, we quantified the volatility of agricultural returns in terms of the expected standard deviation (SD) of GMs and economic resilience (or rather one important aspect of economic resilience) as the coefficient of variation (CV) in expected GM. CV is a normalized measure of dispersion of a probability distribution, which is defined as the ratio of the SD to the mean. In this case, we used the ratio of the expected (mean) GMs to the expected SD of the expected GMs as our measure of resilience. We based this on the assumption that agricultural land-use portfolios (the choice of agricultural land-use investments within a landscape) that provide a lower expected variance to returns ratio would be more resilient. It should be noted that we did not address the resilience of individual farmers, which would require detailed knowledge of the assets, capacities and access to formal and informal institutional support of individual farmers; rather, we sought to investigate the potential role of land-use diversification on the volatility and resilience of returns from agriculture.
We examined this question at a range of different spatial scales (from 25 to 3600 hectares) to investigate the degree to which spatial extent would influence the results.
Modern portfolio theory (MPT) provides analytical tools for investigating the relationships between land-use choices, expected GMs, and the expected variance in those GMs on a landscape scale. MPT was developed in the field of finance in the 1950s, to quantify the optimum level of diversification that would balance risks (the expected variance in returns) and the expected mean return of a given investment portfolio . The key concept in portfolio management is that income streams are additive, whereas risks may partially cancel each other out [49, 50]. The logic is that diversification in a portfolio can reduce the risk (or the expected variance) of the portfolio’s returns to perturbations, as long as not all possible investments respond in the same way to the same shocks; that is, provided there is not perfect covariance over time in the returns from different agricultural activities. This concept can be applied to agricultural systems by considering the different land-use choices as the individual elements of a portfolio. Therefore, the key to reducing expected variance in returns is for a farmer to select a diversity of land uses that will respond differently to market, institutional, or environmental perturbations. For example, when this concept is applied to an agricultural system of wheat and oats, it is clear that the inputs needed to produce both of these crops are roughly the same (because the crops are of a similar type, namely cereals), and thus the costs of these inputs are likely to increase or decrease by the same amount (this is called a systematic risk). However, the market price of these crops is inversely correlated; wheat prices often increase at the same time as the price of oats decreases (this is called a unique risk) . Thus, by investing in both wheat and oats, the farmer can diversify away the unique risks associated with market-price volatility.
The application of MPT to natural rather than financial assets has, to date, been limited. It has been suggested that the principles of MPT could be transferable to the field of biodiversity conservation , and MPT has previously been used to quantify the risk and return profiles of individual farmers in Northern Ireland  and to the genetic diversity within cereal crops [53, 54]. It has also been suggested that MPT is an appropriate tool for assessing vulnerability of food systems through the diversification of crop production and the basket of food entitlements . However, the application of MPT to agricultural landscape patterns represents a novel approach to operationalizing agricultural ecosystem resilience.
In this study, we used published data for land use and expected average agricultural GM data in conjunction with MPT to analyze the relationships between land-use diversity, expected mean returns for agriculture, and the expected variance and resilience of those returns in three UK lowland agricultural regions. This analysis differs from previous applications of MPT to agricultural land-use investments  in that it used real land-use patterns to assess the relationships between expected returns and expected variance of returns for actual land-use portfolios.