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Nature-inspired algorithms have been developed with biological mimicking. Machine learning algorithms from artificial neurons and artificial neural networks have been developed to mimic the human brain with synthetic neurons. This research can be traced back to the 1940s and has been expanded to agri-food problem solving in the last three decades. Now, the research and applications have entered the stage of deep learning with more layers and neurons that have complex connections to extract deep features of the target. In this paper, the developments of artificial neural networks and deep learning algorithms are presented and discussed in conjunction with their biological connections for agri-food applications. The related independent studies previously conducted by the author are summarized with the newly conducted being presented. At the same time, the algorithms motivated by recent bionics studies are compared and discussed for their potentials for agri-food production. [ABSTRACT FROM AUTHOR]