The complex co-evolutionary systems approach (CCeSA) provides a well-suited framework for analysing agricultural systems, serving as a bridge between biophysical and socioeconomic sciences, allowing for the explanation of phenomena, and for the use of metaphors for thinking and action. By studying agricultural systems as self-generated, hierarchical, complex co-evolutionary farming systems (CCeFSs), one can investigate the interconnections between the elements that constitute CCeFSs, along with the relationships between CCeFSs and other systems, as a fundamental step to understanding sustainability as an emergent property of the system. CCeFSs are defined as human activity systems emerging from the purposes, gestalt, mental models, history and weltanschauung of the farm manager, and from his dynamic co-evolution with the environment while managing the resources at his hand to achieve his own multiple, conflicting, dynamic, semi-structured and constrained purposes. A sustainable CCeFS is described as one that exhibits both enough fitness to achieve its multiple, dynamic, constrained, semi-structured, and often incommensurable and conflicting purposes while performing above threshold values for failure, and enough flexibility to dynamically co-evolve with its changing biophysical and socioeconomic environment for a given future period. Fitness and flexibility are essential features of sustainable CCeFSs because they describe the systems' dynamic capacity to explore and exploit its dynamic phase space while co-evolving with it. This implies that a sustainable CCeFS is conceived as a set of dynamic, co-evolutionary processes, contrasting with the standard view of sustainability as an equilibrium or steady state. Achieving sustainable CCeFSs is a semi-structured, constrained, multi-objective, and dynamic optimisation management problem with an intractable search phase space, that can be solved within the CCeSA with the help of a multi-objective co-evolutionary optimisation tool. Carnico-ICSPEA2, a Co-Evolutionary Navigator (CoEvoNav) used as a CCeSA's tool for harnessing the complexity of the CCeFS of interest and its environment towards sustainability, is introduced. The software was designed by its end-user - the farm manager and author of this thesis - as an aid for the analysis and optimisation of the "San Francisco" ranch, a beef cattle enterprise running on temperate pastures and fodder crops in the central plateau of Mexico. By combining a non-linear simulator and a multi-objective evolutionary algorithm with a deterministic and stochastic framework, the CoEvoNav imitates the co-evolutionary pattern of the CCeFS of interest. As such, the software was used by the farm manager to "navigate" through his CCeFS's co-evolutionary phase space towards achieving sustainability at farm level. The ultimate goal was to enhance the farm manager's decision-making process and co-evolutionary skills, through an increased understanding of his system, the co-evolutionary process between his mental models, the CCeFS, and the CoEvoNav, and the continuous discovery of new, improved sets of heuristics. An overview of the methodological, theoretical and philosophical framework of the thesis is introduced. Also, a survey of the Mexican economy, its agricultural sector, and a statistical review of the Mexican beef industry are presented. Concepts such as modern agriculture, the reductionist approach to agricultural research, models, the system's environment, sustainability, conventional and sustainable agriculture, complexity, evolution, simulators, and multi-objective optimization tools are extensively reviewed. Issues concerning the impossibility of predicting the long-term, detailed future behaviour of CCeFSs, along with the use of simulators as decision support tools in the quest for sustainable CCeFSs, are discussed. The rationale behind the simulator used for this study, along with that of the multi-objective evolutionary tools used as the makeup of Carnico-ICSPEA2, are explained. A description of the "San Francisco" ranch, its key on-farm sustainability indicators in the form of objective functions, constraints, and decision variables, and the semi-structured, multi-objective, dynamic, constrained management problem posed by the farm manager's planned introduction of a herd of bulls for fattening as a way to increase the fitness of his CCeFS via a better management of the system's feed surpluses and the acquisition of a new pick-up truck are described as a case study. The tested scenario and the experimental design for the simulations are presented as well. Results from using the CoEvoNav as the farm manager's extended phenotype to solve his multi-objective optimisation problem are described, along with the implications for the management and sustainability of the CCeFS. Finally, the approach and tools developed are evaluated, and the progress made in relation to methodological, theoretical, philosophical and conceptual notions is reviewed along with some future topics for research.