Many of these developments certainly depend directly upon physics in one form or another. Moreover, the basic rules of chemistry, as understood today, are also fundamentally physical ones (in principle if not in practice) — mainly coming from the rules of quantum mechanics. Biology is a good deal further from being reducible to physical laws, but we have no reason to believe (consciousness apart) that biological behaviour is not, at root, purely dependent upon physical actions that we now basically understand. Accordingly, biology seems also to be ultimately controlled by mathematics.
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To be clear, biological systems and chemical systems do not reduce to physical systems, since if they did, they would just be physical systems. Instead, physical systems are the foundation from which chemical and then biological systems emerge. A chemical system is both chemical and physical, a biological system is biological, chemical and physical. Physics models the physical level of chemical and biological systems.
In this view, biological behaviours are not "dependent" on physical actions. Instead, biological and physical are two levels of description of biological phenomena.
Moreover, mathematical models of phenomena do not "control" phenomena, biological or otherwise, any more than a map controls the territory it models.
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