What specific environmental condition for complex biology is jeopardized by extreme eccentricity in Earth's orbit?
Liquid water availability and a stable climate over billions of years.
For life, especially complex life that requires long evolutionary timescales, orbital stability is arguably the most paramount factor relating to planetary dynamics. When Earth's orbit becomes extremely eccentric due to strong gravitational perturbations (like those potentially caused by a missing Jupiter), the planet experiences massive variations in its distance from the Sun. This variation translates directly into extreme climate fluctuations, swinging between periods where solar energy absorption triggers runaway greenhouse effects, and periods resulting in deep freezes. The inability to maintain liquid water on the surface for extended periods due to these cycles makes the sustained development and proliferation of complex biology nearly impossible.
