Darwinian theory, like classic physics, is an incomplete oversimplification of the most complex aspects of the reality. According to the complementarity principle of Taoism and quantum physics, a Lotka-Volterra oscillation between catabolic-entropic and anabolic-syntropic processes might generate the emergence of collective behaviours and fractal structures near the critical points in many physical and biological systems. The proposed mechanism, named metabolic hypercycle, explains many evolutionary dynamics with two alternate and complementary phases at the levels of molecules, cells, organisms, and populations. In the catabolic-entropic phase, the genetic apparatus and the Darwinian processes allow the reproduction and conservation of biological systems. In the anabolic-syntropic phase, the epigenetic apparatus and the Lamarckian anti-Darwinian processes produce innovative adaptations to variable environment. Many experimental evidences, such as for example the distribution of retroelements and DNA mutations in complex genomes, suggest the existence of mechanisms based on epigenetic signals, reverse transcription, and micro-recombination, that promote DNA changes and horizontal transfer of genetic information between organisms and cells, in particular between somatic and germline cells. In complex animals, the acquired immunity regulates the selective proliferation of the cells with adaptive mutations during the physiological responses to stresses. The same immunotrophic process allows the maternal selection of embryos with adaptive mutations. Moreover, the fetal-maternal incompatibility counteracts the negative aspects of Darwinian natural selection and maintains the metabolic biodiversity of animal populations. In conclusion, the increased knowledge of relationships among metabolism, epigenetic systems, genome plasticity, and acquired immunity, supports the idea that these processes could provide a form of Lamarckian adaptive evolution in response to environmental stresses. A better understanding of the biology will increase our ability to design medical and biotechnological applications. Some of these innovative applications are discussed in the paper.