Expression of algal population dynamics is at the base of Models of HABs. Increasing evidences from experiments suggest specific physiology of causative species is necessary for exceptional events of HABs, to incorporate parameters of physiology and life-history in HAB models draws an extensive attention in modelists. This contribution aims to detect determination of these parameters by modeling. Nutrient uptake is expressed in Droop\'s equation, simulations indicate that carrying capacity for algal cell number is determined by minimal cell quota for cell division and concentration of limiting nutrients. Nitrate concentration in sea water recorded in literature all are sufficient to support a cell number over HAB criteria. Therefore, the key question confronting from an world-widely increasing HABs is not what triggers HABs but what changes classical diatom blooms into Dinoflagellate Blooms. As exceptional events, HABs usually last a relatively short period, one or two weeks. Only a high cell division rate is insufficient for the short period blooms, simulation results that are sensitive to temperature dependence of algal growth rate suggest that causative species of HABs should have an unique temperature dependence in physiology. At the end of HABs, nutrient concentration is not exhausted, why algae stop growing seems to be the most curious question related to disappearance of HAB. Simulation results do not support grazing pressure assumption, but nonlinear death rate of density dependence as a cause. Virus or bacteria seem to be a possible access. In a mono-specific bloom, annual pattern of population size is usually characterized by a single peak. When cyst formation and germination are considered, simulations show population dynamics are characterized by two peaks at least, one occurs in spring and another in autumn. Two cyst forms: quiescent and dormant lead to different annual cycles of population dynamics.