Temperature and light are key determinants of microalgal specific growth rates (μ) and hence also influence aquatic ecosystem dynamics. Despite this importance there is no clear consensus on the functions that should be used to model the effects of these environmental variables on within- and across-species microalgal growth rates. Therefore examining the biological basis and statistical fits of existing functions, and deriving new ones, comprise the main objective of this thesis. Using quantile regression, and information theory I have compared existing functions and derived new ones that describe microalgal maximum specific growth rates (μmax) in response to temperature, photon-flux density (PFD), daylength, and PFD, and daylength combined. The main findings are outlined in (i) to (v), below, (i) A comparison of the μmax temperature function derived here to the function of Eppley (1972), suggested that the Eppley curve intercept is too low and that models that incorporate the Eppley function may underestimate primary production by ~ 30%. (ii) My non-linear general model of microalgal growth in response to daylength will be useful in comparative studies to normalise growth rates to a standard daylength.