Assessing policy options for agricultural livestock development: A case study of Mexico’s sheep sector

The demand for sheep meat in the populous central region around Mexico City has grown rapidly in recent years. To assess the impacts of potential “regional development” policy options, a dynamic model of Mexico’s sheep sector with regional and producer group disaggregation is developed that incorporates interactions between herd dynamics, feed dynamics, market inventories of sheep meat and prices for sheep meat and animals. The model is used to assess the outcomes for commercial and tras patio (backyard, small-scale) Mexican sheep producers and sheep meat consumers of three growth assumptions and two intervention alternatives: a variable cost subsidy or the implementation of a stylized health intervention. Model simulations indicate that the dynamics of growth dominate the policy responses; the principal beneficiaries of producer subsidy and animal health interventions are Mexican sheep meat consumers. Commercial sheep producers will experience increases in cumulative net margin, but tras patio producers will be made worse off than they would have been in the absence of interventions. The Mexican sheep system thus exhibits two characteristics of dynamically complex systems: *Corresponding author: David Parsons, School of Land and Food, University of Tasmania, Private Bag 98, Hobart, Tasmania 7001, Australia; Department of Agricultural Research for Northern Sweden, Swedish University of Agricultural Sciences, Umeå 90183, Sweden E-mails: dparsons@utas.edu.au, david.parsons@slu.se Reviewing editor: Pedro González-Redondo, University of Seville, Spain Additional information is available at the end of the article ABOUT THE AUTHORS David Parsons and Charles F. Nicholson share a common interest in understanding systems and how they function, through modelling. In particular, they study livestock systems and the interactions between the biophysical, social, and economic components. Nicholson is an agricultural systems modeller who focuses on the economics and supply chain components of livestock systems, and is currently editor for the journal Agricultural Systems. PUBLIC INTEREST STATEMENT Global demand for livestock is increasing, particularly in the developing world. This offers opportunities for farmers, but also challenges for policy makers, as they attempt to balance competing interests between farmers, consumers, and the environment. Increasing demand for sheep meat in Mexico has generated a production response from farmers, and government institutions attempting to provide “regional development” strategies. However, financial assistance is mostly directed towards commercial producers, and technology improvements generally only reach large producers. Simulation models can be useful to assess impacts of potential regional development policy options on Mexico’s sheep sector and their implications for commercial and smallholder sheep producers and consumers. The principal beneficiaries of producer subsidy and animal health interventions are Mexican sheep meat consumers, with very little benefit to producers. Smallholders may actually become worse off than they would have been in the absence of interventions. These results suggest broader implications for interventions in agriculture-based livelihood systems and the need for ex-ante assessment of proposed policies. Received: 01 December 2016 Accepted: 26 March 2017 First Published: 31 March 2017 © 2017 The Author(s). This open access article is distributed under a Creative Commons Attribution (CC-BY) 4.0 license. Page 2 of 20 David Parsons

ABOUT THE AUTHORS David Parsons and Charles F. Nicholson share a common interest in understanding systems and how they function, through modelling. In particular, they study livestock systems and the interactions between the biophysical, social, and economic components. Nicholson is an agricultural systems modeller who focuses on the economics and supply chain components of livestock systems, and is currently editor for the journal Agricultural Systems.

PUBLIC INTEREST STATEMENT
Global demand for livestock is increasing, particularly in the developing world. This offers opportunities for farmers, but also challenges for policy makers, as they attempt to balance competing interests between farmers, consumers, and the environment. Increasing demand for sheep meat in Mexico has generated a production response from farmers, and government institutions attempting to provide "regional development" strategies. However, financial assistance is mostly directed towards commercial producers, and technology improvements generally only reach large producers. Simulation models can be useful to assess impacts of potential regional development policy options on Mexico's sheep sector and their implications for commercial and smallholder sheep producers and consumers. The principal beneficiaries of producer subsidy and animal health interventions are Mexican sheep meat consumers, with very little benefit to producers. Smallholders may actually become worse off than they would have been in the absence of interventions. These results suggest broader implications for interventions in agriculture-based livelihood systems and the need for ex-ante assessment of proposed policies.

Introduction
Global demand for livestock products has increased rapidly and is expected to continue to do so during the next two decades; the global value livestock products will exceed that of crops by 2020. This so-called "Livestock Revolution" (Delgado, Rosegrant, Steinfeld, Ehui, & Courbois, 1999) challenges policy makers in many countries to re-examine their objectives and formulate appropriate policies to achieve them. Most analyses of growing livestock product demand have used global partial equilibrium market models to explore broader implications, such as impacts on grain markets (e.g. Bruinsma, 2003; Organisation for Economic Co-operation & Development, 2006;Rosegrant, Ringler, Msangi, Cline, & Sulser, 2005). Country-and regional-level dynamic models that focus on livestock can complement these global analyses by assessing a more specific set of market and technology policy options. Of particular concern is market transformations will influence the ability of smallholder livestock producers to participate in, and benefit from, rapid demand growth. Tedeschi, Nicholson, and Rich (2011), Lellis Vieira (2011), Parsons, Nicholson, Blake, Ketterings, Ramírez-Aviles, Fox et al. (2011) and  argued that system dynamics (SD) models of livestock systems can be useful to policy makers examining this and other regional issues.
An example of the policy challenges in responding to the Livestock Revolution can be observed in Mexico. The demand for sheep meat occurs primarily but not exclusively in the populous central region around Mexico City, and demand patterns changed rapidly during the decade from 1995 to (Food & Agriculture Organization, 2013. Total domestic availability of sheep meet (a proxy for domestic consumption calculated as production + imports−exports) grew by more than 130% between 1996 and the peak value in 2004, primarily due to increased imports of sheep meat-which grew by more than 300%. The share of domestic sheep meat consumption provided by imports reached more than 50% during 2000 to 2004. Although Mexican production grew more than 50% from 1996 to 2004, the rapid growth in demand and the rapid growth in imports suggested to policy makers that measures to promote domestic production (i.e. import substitution) had merit. Structural changes in Yucatecan agriculture became apparent due to this growth in domestic demand for sheep met. Parsons et al. (2006) reported that sheep production had become a much more important source of household cash income in Yucatán state between 1989 and 2004. This rapid demand growth prompted federal and state governments in sheep-producing regions to provide a variety of investment and feed subsidies as "regional development" strategies. In response to the perceived opportunity for sheep production to substitute for imports and contribute to the region's economic growth, the state government of Yucatán granted subsidies to sheep producers, particularly in the form of subsidized loans, cost-sharing grants or input cost subsidies. This financial assistance was almost always directed to larger-scale, commercial producers, and both lowered the investment cost for entry into larger-scale sheep production and reduced operating costs. In part, this financial assistance derives from a philosophical legacy in Mexico of the desirability of self-sufficiency in agricultural production. Although more than 60% of sheep meat consumed in Mexico was imported (mostly from New Zealand) in 2000, policy makers in Mexico saw an opportunity to capitalize on consumer preferences for fresh rather than frozen sheep meat, increasing earnings in the agricultural sector and reducing import dependency with a single set of policies. By 2013 (the most recent year reported by FAO), imports of sheep meat had fallen to 20% of their 2004 levels and domestic sheep meat production had grown by 30% (Food & Agriculture Organization, 2013). However, overall availability of sheep meat in 2013 was 30% lower than what it was in 2004, and dollar-denominated prices were 17% higher.
These subsequent developments suggest that the efforts of the government to support domestic sheep production were at least partially successful, but sheep meat consumers faced lower availability and higher prices.
The dynamic changes described above-particularly during the period 1995 to 2005-provide the context for our case study of livestock development interventions. During the early 2000s, researchers at a number of Gulf region universities and the Instituto Nacional de Investigaciones Forestales, Agrícolas y Pecuarias (INIFAP; Mexico's national agricultural research service, similar to the USDA's ARS) began working on technologies and practices to improve the productivity of the systems (e.g. reduce mortality, increase feed production and quality). Given the paucity of agricultural economists working for INIFAP, ex ante impact assessments are infrequently conducted for technologies under development, either at the level of the individual production unit or at the market level. Thus, little is known about the potential market impacts of successful development and implementation of these technologies. Moreover, relatively little is known to date about the characteristics of demand growth in Mexico City, although one study examined marketing channels for sheep meat (Fell, 2005; personal communication regarding MSc thesis on sheep marketing channels in central Mexico). Most policy makers in state governments in Mexico seemed to be operating under the assumption that rapid demand growth would continue indefinitely, and that sheep meat prices would remain at levels profitable for producers regardless of the actions that producers take in response to the current levels of profitability.
In a more general sense, in agriculture and international development contexts there are often significant delays in the development and implementation of technologies and policies, and agriculture-based livelihood systems are in constant and sometimes rapid evolution. In order to make technologies and policies better match the future state of these systems, it is necessary to better understand the likely evolution of agricultural systems. The goal of these efforts should be to improve understanding about which technologies and policies will be relevant for the state of future systems so that research can begin on them now. In essence, researchers, policy makers and donors need an improved understanding of general behavioural tendencies for target systems five to ten years hence. Although this idea is widely accepted, assessment of systems evolution appears to have been addressed infrequently and largely in an ad hoc manner in international agricultural research. Nicholson (2007) noted that analyses of systems evolution will be more useful if they allow simultaneous treatment of both underlying drivers of the dynamics of agricultural livelihood systems and the impacts of technological and policy options.
Thus, the objectives of this paper are twofold. The first objective is to assess the likely dynamic impacts of technological change and state government support policies on the profitability of Yucatecan sheep production for different types of producers. One technology (a stylized health intervention that reduces animal mortality) and one policy option (stylized variable cost subsidies) are assessed under three different assumptions about future demand growth. The second objective is to provide one case study of how analyses of systems evolution can incorporate specific policy and technology options. To achieve these objectives, a dynamic model of sheep markets in Mexico is developed and parameterized. Sterman (2000) and Costanza, Wainger, Folke, and Mäler (1993) argue that most coupled humannatural systems have the characteristic of dynamic complexity, that is, they can demonstrate unanticipated changes in behavioural modes as a result of the interaction of factors endogenous to the system (even in the absence of significant external shocks). As a result, short-term and long-term effects of interventions may differ, and the outcomes of policy interventions are often offset to a substantial degree or result in the converse of what was intended. Batty and Torrens (2005) carry this discussion further, suggesting that "Complex systems generate a dynamic which enables their elements to transform in ways that are surprising, through adaptation, mutation, transformation and so on…the hallmark of this kind of complexity is novelty and surprise which cannot be anticipated through any prior characterization. All that can be said is that such systems have the potential for generating new behaviours".

Model specification
To address the potential for dynamically complex behaviour in Mexico's sheep industry, an integrated dynamic model of sheep markets, sheep flock dynamics and feed resources is appropriate. This model represents a stock-flow-feedback structure that captures the potential for nonlinear (or counterintuitive) responses to current policy instruments. The model represents sheep and sheep meat markets in Mexico, but also includes trade linkages because of the importance of imported sheep meat in Mexican consumption. The production sector is represented by two different regions (Yucatán and Other). Although Yucatán only produces a small proportion of Mexico's sheep meat, it is represented separately to illustrate impacts on a region with a large proportion of small producers, relatively distant from main consumption centers. Each region has two different types of producers: commercial or tras patio (Parsons et al., 2006). Commercial producers tend to be larger scale, have better access to capital, have good market access and are often owned by individuals for whom agriculture is not the principal economic activity. Tras patio, or backyard, producers are smaller scale, often have a limited investment in sheep production other than animals, (that is, they do not typically invest in housing or equipment) have poorer market access and are owned by individuals who earn a significant portion of household cash income from agriculture. The differences in producer characteristics are assumed to influence the costs of production and prices received for live animals. Consistent with available evidence, demand for sheep meat is centred on a single market in Mexico City. As in the commodity models developed by Meadows (1970) and Sterman (2000), inventories of sheep meat are assumed to influence the price of sheep meat, which in turn influences both sales (quantity demanded) and sheep meat imports. An overview of the various model sectors and assumptions follows, and a diagrammatic representation of the model (as a stock-flow structure) is shown in Figure 1. A more detailed and mathematical representation of the model structure is in Appendix A.

Animal numbers
This component of the model structure is an adaptation of that in the Meadows (1970) model of the US hog sector. The model specifies two types of animals: breeding sheep (BS) and young stock (YS). BS produce YS with delays for gestation and maturation, and with mortality losses. It is assumed that YS are either sold when "mature" or enter into the BS flock. The maximum rate at which YS can enter the BS flock is one-half of the maturation rate to account for only females entering the BS flock. The reproduction rate of the BS flock depends on the lambing interval, the lambs per lambing, and the fraction of mortality. The model assumes that the lambing interval and mortality depend on relative feed availability (i.e. nutrients consumed), and allows for separate effects of technological interventions to decrease mortality or the lambing interval.
The number of BS depends on two flows: entrants into the BS flock (the replacement rate) and culls of BS. The rate of entrants depends on a replacement rate and an adjustment for differences between the current BS and a desired number of BS. Mean time in BS is increased if the number of desired BS is greater than the current BS. Maintenance or expansion of the BS takes precedence over YS sales. Of those maturing, all males are sold, but only those females not desired for the BS are sold.
The key behavioural assumption for sheep producers relates to the determination of the desired level of BS, which in turn determines desired replacement animals, adjustments to the current level of BS, the culling rate and the number of YS sold. The desired BS is based on an anchoring and adjustment heuristic that Sterman (2000) argues is commonly used in capacity-related decisions and that has been applied in other livestock policy analysis models (e.g. McRoberts, Nicholson, Blake, Tucker, & Diaz Padilla, 2013;Nicholson & Stephenson, 2014). The desired BS depends on the current BS and the expected long-term net margin of sheep production relative to a reference value of net margin. Notes: Stocks (state variables) are represented by rectangles, and have inflows and outflows (rate variables) represented by pipes with valves. Other named variables are either not determined by the behaviour of the system itself but influence the system, or represent parts of the system for which a value can be calculated through behaviour of the system. Mathematical linkages between variables (and their direction of influence) are indicated with solid arrows.

Feed resources
The model includes a single aggregated "local" feed resource, which assumes that most of the feed resources used in sheep production are forage or browse and are available locally (i.e. not traded among regions or producers). This is not quite accurate, because commercial sheep producers in particular buy feeds, but it may be adequate for the purposes of this model because the majority of feed resources available are those grazed by the animals, particularly for tras patio producers. The quantity of feed available is increased by feed production and decreased by feed consumption. Total feed production depends on the land area, feed production per land area and relative (regional) rainfall. Feed consumption depends on the number of animals, a base level of per-month feed consumption and the availability of feed per animal, with consumption increasing nonlinearly with increases in feed availability. Seasonal differences in feed quality and interactions between quality and quantity are ignored. The availability of feed per animal is used to modify the reproductive performance of the sheep flock, with monotonically decreasing functions specified for both the time required for YS to mature and the lambing interval.

Sheep market
A single aggregated sheep market (i.e. in Mexico City) consists of an inventory of sheep meat (i.e. distinct from sheep numbers), which is assumed to influence price-setting for sheep meat and therefore sheep meat sales. Although income and population growth will be the key drivers of sheep meat demand, the model does not include these directly. Rather, it includes structure to create exogenous growth in demand to test the impact of various demand growth patterns on the sheep production and marketing system. The assumed own-price demand elasticity is −0.5 based on estimates for other livestock products in Mexico (Stout & Abler, 2004). The sheep meat price is assumed to translate into a producer sheep price by subtracting the per kg meat marketing costs and multiplying by the number of kg meat per animal (the carcass yield, which is set equal to 55% of the mature BS weight of 40 kg and 65% of the mean YS weight of 25 kg). Meat marketing costs are assumed to vary by region and producer type (to reflect the potential relative disadvantage to Yucatecan producers and smaller tras patio producers). This implies that the net price received by producers, and the aggregated net margin, will differ by region and producer type. Producer revenues are calculated as animal sales time animal prices. Producer costs include fixed costs (close to 40% of total costs based on observations made during field visits in 2004 and 2005) and variable costs (just over 60% of total costs). The latter are based on costs per BS, assuming that the majority of variable costs are for the breeding flock.

Technology adoption and subsidy policies
As noted above, the model includes two regions (Yucatán and "Other") and two (aggregated) types of producers (commercial and tras patio). Commercial producers are assumed to receive all state government subsidies and to be the only adopters of new technologies. The proportion of commercial producers that use a technology is time-dependent and is assumed to demonstrate sigmoidal growth to full adoption over three years. Thus, this assumes that the technology-particularly with subsidies-is regarded as highly desirable by commercial producers and accessible to them. The adoption of a stylized health intervention by commercial producers is assumed to reduce the mortality of YS, for which mortality rates average about 20% per year. An investment subsidy percentage variable allows the variable costs of sheep production to be reduced for commercial producers, to simulate the effects of cost subsidies provided by state governments.

Mathematical formulation and solution
Mathematically, the model is formulated in Vensim® (a detailed discussion of the structure is included in the Appendix). Vensim® is a simulation modelling software package developed by Ventana Systems, Inc. (http://vensim.com) that features iconic representation and a graphical user interface. It is used to develop models that are systems of differential equations solved by numerical integration. Vensim® software also provides a visual interface representing feedback structure, explicit stock-flow (state-rate) structure, and quantitative decision rules characterizing the system. The model includes four key state (stock) variables (BS, YS, feed resources and sheep meat inventories).
The inclusion of inventories that mediate between current sheep meat production and current sales implies the possibility for dynamic disequilibrium in Mexican sheep meat markets. The model time unit of observation is one month, and the calculation time step is 0.125 months. Alternative values of the time step were used to evaluate the degree of integration error. The value of 0.125 was determined to be adequate as a compromise between computational requirements and the likely degree of computational error due to the assumption of dS/dt is constant for the interval Δt, as assumed for Euler integration. The model is initialized in dynamic equilibrium for time t = 0 representing data from 2005, and technology or policy changes are assumed to be initiated at time t = 12 months. The model is simulated for a total of 120 months using the Euler method of numerical integration. Runge-Kutta integration (4th-order) was also employed as a part of model evaluation and simulated outcomes were not notably different from Euler integration. The model was evaluated following the procedures outlined in Sterman (2000) for dynamic simulation models, and various sensitivity and extreme conditions tests have been conducted but are not reported herein.

Policy options analyzed
Nine alternative scenarios are analyzed with the dynamic model (Table 1). These scenarios are (1) a base case that assumes no changes in YS mortality over time due to technology adoption and no variable cost subsidy, (2) a scenario in which YS mortality is reduced from 20% to 10% per year due to a stylized health intervention (assumed to be developed by Mexican university and INIFAP researchers) for commercial producers in both regions, and (3) a scenario in which governments provide variable cost subsidies that lower by 20% the unit costs of sheep production for commercial producers in both regions. Each of these scenarios is assessed under three different demand growth scenarios: No growth (which serves as a dynamic equilibrium baseline in the absence of technological change or subsidies), growth of 6% per year throughout the simulation and 6% growth over four years, slowing to 2.5% growth over the remaining years of the simulation. This latter scenario is designed to test the importance of the assumption on the part of state-level policy makers concerning continuous rapid growth in the Mexico City market. The key outcomes of interest to policy makers from these simulations are sheep meat prices, net margins for each type of producer in both regions, total consumer expenditures on sheep meat and government expenditures on variable cost subsidies.

Results
The results are presented using two approaches. First, a graphical representation of key variables over the model time horizon is provided for selected variables. The graphical approach facilitates discussion of the dynamic effects of the interventions because their short-term and long-term effects often differ. Second, as a means of summarizing the overall policy or technology effects over a ten-year period, tabular summaries of relevant variables are reported and compared to a baseline dynamic equilibrium without growth. Although the scenarios with no demand growth are not realistic, they provide insights that are relevant for latter consideration of the two scenarios with growth. As noted above, the key variables of likely interest to policy makers and agricultural researchers are the sheep meat price, net margins for different types of sheep producers in the two regions, and government expenditures on variable cost subsidies.

No growth scenarios
The effects of the subsidy policy and the intervention to reduce mortality have differing initial effects on Mexican sheep markets. The subsidy reduces commercial producers' costs of production, increasing net margin. As a result of this immediate increase in profitability, commercial producers seek to expand sheep numbers (that is, the desired number of BS increases). In the short-term, this results in an inverse supply response, because a larger number of female YS are retained for inclusion in the breeding flock ( Figure 2). The sheep meat price increases for a period of about 18 months as commercial producers adjust their BS holdings, but as the gap between desired and current BS holdings is closed and more YS are being produced, prices fall below the level observed in the dynamic equilibrium simulation (Figure 3). The subsidy policy also results in oscillatory behaviour of prices over a period of about seven years. Initially, commercial producers experience a rapid increase in net margin ( Figure 4), but this is eroded by increasing costs (associated with larger BS holdings) and eventual decrease in animal prices due to increased meat inventories. Net margins for commercial producers are increased overall, but not by as much as the amount of the subsidy. Tras patio producers, in contrast, benefit from the policy in the short-term when sheep prices are above the dynamic equilibrium baseline level, but ultimately see net margins eroded by increased supplies resulting primarily from commercial producers ( Figure 5).
The impact of the technology to reduce YS mortality, in contrast to the subsidy, produces a gradual increase in YS supplied to the market ( Figure 3) and a gradual reduction in sheep meat prices (Figure 2), albeit with low amplitude oscillations. These patterns of behaviour are driven in part by the gradual process of adoption assumed for use of the technology by commercial producers, and by the less direct effect of the intervention on net margin and desired BS. Adoption of the technology increases net margin for commercial producers over time (Figure 4), but also demonstrates oscillatory behaviour. Oscillations arise from a system structure that includes at least one negative    feedback loop with a significant delay process. In this case, the negative feedback loop involves the response of sheep numbers to higher margins, and the delays are those associated with acquisition of additional BS (i.e. the maturation delay). Ultimately, the net margins become similar to those under a subsidy: commercial producers see increases in net margin and tras patio producers, a reduction. The ultimate outcomes with regard to sheep meat prices derive in part from the assumption of inelastic demand. The subsidy and mortality reductions both increase the supply of animals, and markets respond by reducing prices (which must fall to a larger degree due to inelastic demand). However, it is worth noting that the initial and subsequent outcomes often differ, the ultimate outcomes differ by type of producer (and presumably the impact on tras patio producers would be considered undesirable) and that this system demonstrates considerable policy resistance: the integrated market system responds in a way that offsets the magnitude and sometimes the intended direction of the interventions.
The cumulative outcomes for each of the health intervention and the subsidy policy under no demand growth are lower mean sheep meat prices, reductions in consumer expenditures (but increased sheep meat consumption), increased cumulative net margin for commercial producers and reduced cumulative net margin for tras patio producers (Table 2; first three data columns). Changes in the overall cumulative net margin in the Yucatán are small (less than 0.5% for the subsidy policy and 1.1% for the health intervention), but the direction of change differs for these two interventions. The increase in cumulative net margin for both types of producers in Yucatán due to the cost subsidy constitutes only about 2% of the government expenditures (the increase in cumulative net margin for commercial producers is only 13% of subsidy expenditures), indicating the extent to which policy resistance processes undermine intended outcomes. The principal beneficiaries of both of the interventions are Mexican sheep meat consumers, for whom the change in cumulative expenditures amounts to about $35 to $50 million US dollars over ten years. Thus, the interventions have the (perhaps unintended) consequence of benefiting higher-income sheep meat consumers and larger (and wealthier) commercial sheep producers at the expense of tras patio producers (and the government in the case of the subsidies).

Constant growth scenarios
In the context of constant growth in sheep meat demand, prices for sheep meat increase continuously over model simulation time regardless of the type of intervention assumed ( Figure 6). This rate of increase is not constant over time, however, and differs depending on the intervention. Analogous to the behaviour observed in the no growth case, price initially increases most rapidly under the subsidy policy, but after two years remains lower than the price for the scenario without any intervention. The increase in prices is the least rapid and of the smallest magnitude for the intervention to reduce YS mortality. The increases in prices may be misinterpreted (or misrepresented) by policy makers as resulting from their policy actions rather than from the underlying dynamics of demand growth and lags in production response. Despite the appearance of robust growth in sheep production and prices, sheep meat and animal prices are in fact lower than they would have been in the absence of the interventions, again consistent with outcomes observed for no growth case.
The impacts of the interventions on sheep producer net margin mirror those of the no growth case. Commercial sheep producers see an initial dramatic increase in net margin upon introduction of the subsidies (Figure 7), a period when net margin with the subsidy is roughly equal to that without subsidies, and then a period of increasing difference due to the subsidy. In this case, the effects of growth over the long term dominate the initial response of commercial producers to the subsidy, and net margins continue to rise over the 10-year period. Net margins are initially larger than they would have been without interventions for tras patio producers due to relative reduction in YS sales by commercial producers and the associated more rapid price increase (Figure 8). By two years after the introduction of the interventions, however, net margins are smaller for tras patio producers because the decrease in prices is not compensated by either a corresponding reduction in variable costs or increased sales.
In cumulative terms, constant demand growth without other interventions results in a 37% increase in the mean sheep meat price over the model simulation time, a 46% increase in the cumulative value of sheep meat sales (due to both price and quantity increases) and a 116% increase in regional net margin for Yucatán sheep producers ( Table 2). The impacts of the interventions generally are to decrease each of these values by a small amount. Commercial sheep producers in Yucatán benefit from interventions in the context of demand growth and tras patio producers are made Table 2. Simulated outcomes of alternative policy options (baseline, subsidy, and reduced mortality) under three demand growth scenarios (no growth, constant growth, and slowing growth) Notes: All monetary values are in pesos. The symbol "$" is used to denote this in Mexico. ($1 USD in March 2017 = 19 Mexican pesos). 1 Dynamic equilibrium, which implies no changes in animal numbers over time and is useful as a baseline from which changes can be evaluated. 2 Mean value over 120-month simulation. 3 Cumulative value over 120-month simulation.

Outcome
No growth Constant growth Slowing growth

Slowing growth scenarios
If demand growth were to slow to less than half its current annual rate after four years of model simulation time, the results are qualitatively similar to those with constant growth, but somewhat attenuated. Because the graphical results in particular are qualitatively similar to those for constant growth, only tabular results are presented for these scenarios. Demand growth that slows over time still results in markedly increased sheep meat prices, consumer expenditures on meat sales, and sheep producer net margins ( Table 2). The impacts of the interventions on prices and the value of sheep meat sales in the context of slowing growth are qualitatively similar to the constant growth case, but the magnitude of the impacts is somewhat reduced. This suggests that the magnitude of the policy impacts depends to a certain extent on the rate of demand growth relative to the ability of the sheep production sector to respond given the inherent biological delays and the assumed producer decision-making structure. Slowing growth does not alter the outcome that the principal beneficiaries of interventions in the sheep production sector are higher-income consumers, that commercial sheep producers benefit from the policy and that tras patio producers experience reductions in net margin. Nor does the growth rate change modify the limited effectiveness of the subsidy expenditures for increasing producer net margin. In fact, slowing growth reduces the proportion of subsidy expenditures realized by commercial producers as net margin.

Discussion
The foregoing analyses suggest that rapid growth in the demand for sheep meat in Mexico would have generated increased earnings for both commercial and tras patio sheep producers during the decade beginning in 2005. Our analysis suggests that growth in demand would dominate the effects of policies designed to assist the sheep sector, whether through direct production subsidies or research to support technological interventions that reduce animal mortality. The policies, in fact, have the impact of primarily benefiting Mexican sheep meat consumers, many of whom tend to be higherincome urban residents, and inevitably reduce net margins (relative to no interventions) for smaller, resource-poor tras patio producers. Thus, as a strategy for rural development, the policies have decidedly mixed results and the effectiveness of government expenditures-in terms of benefits for producers-is quite limited. The Mexican sheep system thus exhibits two characteristics of dynamically complex systems: unintended consequences (e.g. reduced cumulative net margins for all sheep producers in some cases as a result of policy) and policy resistance-the ability of the endogenous response of the system to various incentives to limit the ability of policy to achieve specified objectives.
Although the principal results of the modelling effort discussed above are specific to the case of sheep production in Mexico and the specific interventions analyzed, there are also a number of broader implications. The first concerns the usefulness of an approach to modelling systems evolution that addresses both policy and technology options as a part of the process. In this case, the system evolution is driven externally by exogenous demand growth (i.e. the drivers of that demand growth change are not modelled), but also internally by the stock-flow-feedback structure and behavioural responses assumed to characterize the system. The principal results of this modelling effort are specific to the Mexican sheep case and are not meant to be a prediction of the future. Rather, our intention was to assess a range of outcomes given specific livestock sector development policy scenarios (only some of which were actually implemented), but not prescriptive of how the information should be used . Although it is easy to imagine extensions of this model to better represent the drivers of change and the evolution of production technologies, the above analyses illustrate in a relatively simple and stylized case the practicability of system evolution analyses that include policy and technology factors.
Second, this application of a dynamic model highlights the usefulness of what has sometimes been termed the "complex systems" approach to analysis of agricultural systems. As mentioned in the introduction, some authors believe that most social, economic, biological and other natural systems can be usefully conceived of as dynamically complex (Allen & Strathern, 2005;Rosser, 1999;Sterman, 2000). Thus, these systems can generate a variety of behavioural modes and outcomes that differ in the short and long term. The concepts and conclusions underlying this general school of thought are not frequently applied in models of agricultural systems, but they may prove useful for predicting future systems evolution with policy and technological interventions. According to this school of thought, unexpected future developments may arise due to the nonlinear characteristics of the system, past behaviours (and therefore statistical relationships or correlations) may not be a good guide to the future, and simplification through aggregation may ignore essential elements of system structure and undesirable elimination of potential behavioural modes. This perspective on modelling extends also to model evaluation, suggesting that neither parsimony nor independent verification is always possible when the production system of interest may display dynamically complex behaviour. The use of a systems approach that emphasizes the development of both conceptual and empirical causal models often will be most appropriate for these systems.
Finally, this process of undertaking this research has underscored the benefits of interdisciplinary collaboration to assess technology and policy options. A simplified version of this model has been used as a pedagogical tool for high-level agricultural researchers in INIFAP. Because they had not previously been exposed in any detail to economic concepts, they did not realize the importance that a parameter such as the demand elasticity could play in the determination of outcomes related to their principal mission of developing technologies to benefit agricultural producers in Mexico. Conversely, however, there is often a benefit to economic analyses of more detailed representation of the stock-flow-feedback dynamics found in all agricultural production and market systems. Applied biological scientists working collaboratively with economists to develop more appropriate systemsoriented models often can provide both better policy answers and more robust learning processes.
Feed resources available are the integral of feed production, losses (feed not consumed that becomes senescent and decays) and feed consumed by animals. This is the differential equation representation of (16).
Feed produced per unit land is a decreasing nonlinear function of current forage or browse biomass relative to the maximum possible biomass and current month rainfall.
Losses of feed are a constant proportion of current forage or browse biomass.
Feed consumption equals feed consumed by BS and by YS, where consumption by each of those animal types is equal to the number of current animals times the amount of feed consumed per animal per month.
Feed consumed per animal per month is a function of the relative availability of feed, which is in turn a function of the current forage or browse biomass and the numbers of BS and YS.

Inventory and price dynamics
Sheep meat inventories are increased by the slaughter rate and imports and decreased by sales.
Sheep meat imports are an increasing function of Mexican sheep meat prices, formulated as a reference level of imports times current sheep meat price relative to a reference meat price value with an import demand elasticity ε > 0. Note that there are few trade barriers for sheep meat entering Mexico.
Sheep meat sales are a decreasing function of Mexican sheep meat prices, formulated as a timedependent reference level of sales times current sheep meat price relative to a reference meat price value with own-price demand elasticity η < 0. Growth in demand for policy scenarios is effected through increases in the value of "reference" sales over time.
Sheep meat prices are determined in response to a smoothed value of inventory coverage (inventories at time t divided by sales at time t, which has units of the number of months for which (14 inventories are sufficient to cover the current rate of sales). Prices are a nonlinear decreasing function of inventory coverage.
Prices per BS animal received by sheep producers are equal to the sheep meat price less meat marketing costs (which differ by producer type and region) adjusted by the yield in kg per animal.
Prices per YS animal received by sheep producers are equal to the sheep meat price less meat marketing costs (which differ by producer type and region) adjusted by the yield in kg per animal.

Producer decision dynamics
The desired (aggregated by producer group and region) level of breeding stock is equal to the current number of BS times a nonlinear increasing function of expected long-run net margin (an exponential smooth of past net margin values) relative to a reference net margin value. The functional form is constant elasticity, with an elasticity of BS* with respect to long-run net margin of ξ > 0. Note that this uses an anchoring and adjustment heuristic that Sterman (2000) argues is commonly used in capacity decisions.
The mean time an animal is retained in the BS stock is a nonlinear increasing function of the ratio of desired to current breeding stock.
The number of animals to be replaced is a first-order expression involving the number of desired BS animals and the mean time animals are retained as BS (MTBS).
Adjustments are animals added to the BS in response to changes in the desired level of BS holdings. They are expressed as a first-order expression of the difference between current and desired levels of BS holdings, modified by a parameter representing the time required to adjust BS holdings (BSAT).
Animals are culled at a fractional rate of animals currently held as BS. This fractional rate equals (1/MTBS).
Sales of YS by the sheep producer are limited by the maturation rate. Animals not needed for replacements or adjustments due to changes in the desired breeding stock are assumed to be sold.