  Sigmoid growth models are often used to study population dynamics. The size
of a population at equilibrium commonly depends explicitly on the availability
of resources, such as an energy or nutrient source, which is not explicit in
standard sigmoid growth models. A simple generalised extension of sigmoid
growth models is introduced that can explicitly account for this
resource-dependence, demonstrated by three examples of this family of models of
increasing mathematical complexity. Each model is calibrated and compared to
observed data for algae under sea-ice in Antarctic coastal waters. It was found
that through careful construction, models satisfying the proposed framework can
estimate key properties of a sea-ice break-out controlled tipping point for the
algae, which cannot be estimated using standard sigmoid growth models. The
proposed broader family of energy-dependent sigmoid growth models likely has
usage in many population growth contexts where resources limit population size.
