The factors to which models respond vary among models and evolve as modelers attempt to make them more comprehensive and universally applicable. In contrast, some researchers who want to apply them do not have all needed inputs, or they may want to embed a crop model into economic or other models for analyzing responses across scales. Some researchers have used more comprehensive crop models to create reduced form crop models that have much fewer input requirements, run fast, and produce responses needed for specific applications . For example, Chikowo et al. used the APSIM cropping system model to generate parameters and variables needed to operate a much simpler field scale crop model . The reduced form summary model responds to nitrogen and phosphorus levels for different soil characteristics and management inputs. Dzotsi et al. used a similar approach, showing that reduced maize, peanut, and cotton models parameterized from the DSSAT CSM model accurately reproduced DSSAT results across time and space. Reduced form crop models allow researchers to produce situation specific summary models that approximate the responses of a more comprehensive model for use in broader scale analyses that may involve socioeconomic, livestock, and environmental sustainability components. Reduced-form crop models can be interpreted as the “production function” that is the foundation of economic production models , and can be linked to economic models to create “hybrid” models for policy analysis and impact assessment . Keating et al. demonstrated a similar process of summary model development, building from the foundation of a comprehensive set of crop soil and management system simulations. They developed a summary model from thousands of APSIM simulations with three key parameters that captured 88% of the variation in space and time of key water balance variables.A central element driving production, profitability, and efficiency in livestock systems is animal performance. Hence, the most commonly used livestock models are those that predict animal meat and milk productivity. Precursors to performance models have existed since the 1940s when the first feed requirements for livestock were developed . Since then,grow lights many have been built and refined regularly across the US and Europe . Nutrient requirements models are the workhorse of the feed industry for ration formulation and for recommending changes in feed management to farm advisors. These models are often based on a mixture of statistical regressions derived from experimental data plus mechanistic principles of the energetics and protein metabolism of mammals.
They also need an estimate of feed intake, perhaps the most important parameter. While these models are good for calculating feed requirements, dynamic models of digestion are more accurate at predicting the nutrient supply to animals under a wide range of conditions from the high-yielding dairy cow to the smallholder goat , because they predict intake more accurately, and they can deal with more complex diets and their interactions. Some models also predict methane production by ruminants and manure quantity and quality, which are important for estimating GHG emissions and the role of livestock in nutrient cycles. These models are typically used to answer ‘what if’ questions around the impacts of different feeding practices or changes of animal types on animal performance . Herd dynamics models follow herd evolution over time in terms of animal numbers and herd structure. Herd dynamics models usually start by splitting a herd into cohorts of different ages or weight, and sex. These cohorts are specified with different mortality, reproductive,selling and replacement rates. Adult females produce offspring at specified reproductive rates, which grow or die, become part of the next cohort, and get sold, and the cycle continues. The best of these models include interactions between animal nutrition and reproduction to drive reproductive and mortality parameters stochastically. This feature is important as feed availability or supplementation strategies have significant impacts on herd reproduction and performance. Some applications of herd dynamics models include estimating optimal stocking rates and carrying capacities, assessing the impacts of reproductive technologies and/or reductions in mortality, and predicting removal of biomass from crop or pasture systems. These models are also widely used by livestock epidemiologists for estimating impacts of diseases on herd mortality and morbidity. They have also been used with dynamic programming for optimizing replacement decisions in commercial dairy herds , or in linear programming applications for studying optimal sales policies, herd sizes, etc. Biological simulation models are sometimes used as input output coefficient generators for linear programming models to aid in the selection of management strategies in livestock systems .These models represent whole livestock farms and their key components . The complexity of some livestock systems justifies the need to build whole-system models using simulation and optimization techniques to represent different components and their interactions . For example, grazing management strategies cannot be defined without also considering herd and nutritional management, since herd dynamics or feed supplementation practices determine the grazing intensity, use of forage, and subsequently animal performance.
Thus, simulations of the biology of livestock enterprises include flexible models representing pasture growth, structure and quality; individual animal performance to test nutritional strategies; and population dynamics describing management practices at herd or flock level , which subsequently determine animal numbers and their age or physiological state classes .Biologists have been building mathematical models to describe the population dynamics of agricultural weeds, pests and diseases for more than a hundred years. Recent progress in modeling these components is discussed by Donatelli et al. ; here we focus more on broad concepts and general state of progress. The diversity of modeling approaches that constitute the current state of science can be categorized in different ways. The first and most obvious is by production type and threat. Thus there are models that describe the dynamics of weeds, diseases and pests that are threats to arable crops, the diseases of livestock, and the diseases of fish used in aquaculture. While threats such as pests and diseases have been recognized since pre-history, the complexities of the microbial communities on the crop surface and in the soil around plants, and in the gut and rumen, are only just becoming more fully understood. Models of the mixture of beneficial and pathogenic organisms that these systems contain have not yet been developed. A broad distinction can be made between mechanistic and non-process-based pest and disease models. The former include explicit biology while the latter use a purely statistical approach. The choice of modeling approach depends greatly on the intended application. For example, a farm manager may want to know when to apply a prophylactic insecticide against a common insect pest. For this purpose, future insect population density may be best predicted by a statistical model containing independent biological variables such as crop stage, and dependent weather variables such as temperature and rainfall. In some cases, information about the pest itself may be included in the model, for example from pheromone or other traps monitored by the farmer or in the case of mobile insects from publicly-operated monitoring networks. A different statistical application is the use of climate-matching models to predict future pest problems. The current distribution of an organism is modeled using a set of predictors including climate. The distribution of the organism after climate change is then estimated by mapping the “climate envelope” using scenarios developed from global climate models. There is now a broad literature on the strengths and weaknesses of this approach, particularly challenging the assumption that organisms are able to move easily to track climate. Important recent advances in statistical models of pest dynamics have included the application of modern spline and neural net estimation techniques, and in the use of personal computers and mobile devices. Mechanistic models incorporate at least some information about the biology of the crop and pest species concerned. The models may be highly abstract – summarizing, for example, a pest population by a single state variable such as density – or, alternatively, highly complex with individual pests each represented by numerous attributes. The simplest models sacrifice realism for mathematical tractability and general insights, while models of intermediate complexity include more biological detail but are constructed in such a way that simpler analytical models can be recovered as limiting cases to help interpretation. Pest and disease models also vary in the degree to which they explicitly incorporate stochastic processes and in whether they treat a population as homogeneous or spatially variable. An important area is the coupling of pest and disease models with crop models . Donatelli et al. review issues involved and existing major projects that have attempted to bridge this gap.
They also propose a road map to improve pest and disease modeling focusing on improving the data resources available for parameterization and validation, bettering the coupling of crop to antagonist models,led grow lights and creating a community of researchers that can collaborate to share expertise and produce community tools.Mechanistic models can be used to predict near-future pest and disease threats in similar ways to statistical models. As was discussed with crop models, they may be more successful than statistical models if biological insights can substitute for missing data or if they can aid prediction by suggesting a model structure that simple statistical fitting would miss. Consider, for example, the response of an insect to daily temperature. Higher temperatures may elevate growth and reproduction, and thus result in more pests, a pattern that could be derived with sufficient weather and population data. Alternatively, the physiological response of the insect could be modeled, which might improve the model’s predictive power or allow insect dynamics to be predicted in data-poor systems . Several schools of physiological modeling exist. However, we are not aware of any formal comparison of different process and statistical approaches to the same problem. An area where biological insights have proven fruitful has been in disease spread through commercial livestock populations. An understanding of how animals interact, and more importantly how they are moved around, can provide critical advice to policy-makers. Current state-of-the-art livestock models incorporate data on movements of animals between individual farms coupled with modern Bayesian parameter estimation. However, the type of data needed for such approaches is prohibitively expensive to obtain or politically unacceptable for many countries to collect . Modeling has also proved valuable in assessing possible pest risks and in guiding general policy development. The basic epidemiological number is the number of secondary cases of a disease that are expected to happen when a primary case occurs in a susceptible population. Calculation of R0 for prevalent human diseases has proved useful in prioritizing investment in control strategies and vaccine development. Today, sophisticated mathematical tools are available for calculating R0 for complex structured populations, for spatially extended populations, and in the presence of stochastic effects . Probably the most sophisticated applications of population genetics to weed, pest and disease issues in agriculture are models of the evolution of resistance to pesticides, and of the dynamics of plant diseases. Evolutionary models can be broadly categorized as genetic or phenotypic. Although phenotypic models have been explored in agriculture , the vast majority of evolutionary models have been genetic. Based on theoretical analyses, areas of fields have been set aside unsprayed or not planted with modified crops that express an insecticide in order to slow the rate of spread of resistance . The genetic basis of plant-pathogen interactions have been resolved for a number of major systems, which has allowed detailed analysis of strain dynamics and how disease spread may be slowed by judicious use of a range of different crop varieties. State-of-the-art work in genetic models of weeds, pests and diseases includes using the avalanche of data that modern high-throughput DNA measurement technologies are providing, and modeling how novel genetic interventions may be used to suppress pest populations. Some of the most sophisticated pest monitoring software now includes specific economic variables with parameters such as commodity prices that can be updated dynamically. The farmer may make different decisions about pest management depending on current market conditions. More generally, a goal of many people working to increase the sustainability of agriculture is to reduce chemical inputs by practicing “integrated pest management”. The models required to support such work are challenging to construct, but some of the most advanced incorporate economic elements as well as various biological processes.Linear economic optimization models of farm systems, developed in the 1950–60s, provide a basis for prescriptive farm management advice .