The catering industry, a key player in the global food service market, is one that defies the constraints of a stagnant environment. It is a vibrant cosmos that keeps reinventing itself, much like a culinary chameleon, to keep pace with changing customer preferences, technological advancements, and socio-economic dynamics. As we move into the future, a robust analysis of the trends and predictions shaping this landscape is critical for industry stakeholders to stay ahead.

A notable shift in the industry is the rising importance of sustainability, both in terms of sources and practices. The World Resources Institute's 'Shift Wheel' model provides an insightful explanation of this trend. The model postulates that catering companies can reduce their environmental impact by limiting demand for resource-intensive food, improving supply chain efficiency, and harnessing the power of innovation. This shift towards eco-friendly practices is driven by increasingly conscious consumers, stringent regulations, and the moral obligation of businesses to minimize their ecological footprint.

The use of technology is another significant trend shaping the industry's future. Cloud Kitchen, a term coined by the tech industry, refers to a setup devoid of any dining area, focusing solely on delivery through digital platforms. The mathematical model of Queuing Theory offers a fascinating perspective on this trend. By applying principles like the Poisson process and Markov chains, one can optimize the order processing time in a cloud kitchen, thereby maximizing efficiency and profits. The COVID-19 pandemic has further underscored the relevance of this model, with companies like Zomato and DoorDash reporting exponential growth in demand for home deliveries.

Along similar lines, implementation of AI and machine learning in catering services is gaining traction. A concept rooted in computer science, machine learning is a type of artificial intelligence that provides systems the ability to improve automatically through experience and without being explicitly programmed. It can be used to predict customer preferences, optimize menu offerings, and automate routine tasks, thereby enhancing operational efficiency and customer satisfaction. This trend is corroborated by studies from McKinsey and Company, highlighting the growing investment in AI by foodservice businesses.

Moving to the socio-economic factors influencing the industry, the concept of 'gig economy' is worth examining. An economic environment characterized by temporary, flexible jobs, the gig economy is increasingly adopted by catering companies to meet fluctuating demand and minimize fixed labour costs. However, this practice is fraught with legal and ethical implications, as highlighted in a Harvard Business Review article. As the gig economy matures, companies must tread a fine line between operational efficiency and social responsibility.

Another critical aspect defining the future of catering companies is the evolving dietary preferences of consumers. The advent of 'flexitarianism', a semi-vegetarian diet focusing on plant-based meals with occasional meat consumption, is a testament to this trend. This shift is an outcome of increasing health consciousness and ethical considerations, and is supported by research in the field of nutritional science. Catering companies will need to adapt their offerings to cater to this demographic, integrating diverse dietary requirements into their service model.

Looking ahead, one might speculate that the future of catering companies is likely to be defined by a triumvirate of sustainability, technology, and evolving consumer preferences. The companies that can seamlessly blend these elements into their business model will be the ones leading the pack. In this dynamic landscape, Darwin's theory of natural selection seems apt - it is not the strongest or the most intelligent who will survive but those who can best manage change.

In conclusion, the future of the catering industry is an exciting confluence of challenges and opportunities. It beckons those who are willing to innovate, adapt, and evolve in response to shifting paradigms. One thing is certain; the table is set for some fascinating times ahead. The question is - who will rise to the occasion and who will be left picking up the crumbs?