NOVELTY - Oleaginous microalgal cell, optionally comprising 23S rRNA having at least 65% nucleotide sequence identity to SEQ ID NO: 76 (a 573 base pair sequence fully defined in the specification) and an exogenous sucrose invertase gene so that the cell can grow on sucrose as a sole carbon source, and obligately heterotrophic, is new.    USE - The cell is useful for producing oil, which is useful for producing food, fuel or chemical product including frying oil, lubricating oil, cleaning solvent, surfactant, foam, lubricant, or an oleic acid dimer (all claimed).    ADVANTAGE - The cell produces oil with enhanced oxidative and thermal stability.    DETAILED DESCRIPTION - Oleaginous microalgal cell, optionally comprising 23S ribosomal RNA having at least 65% nucleotide sequence identity to SEQ ID NO: 76 (a 573 base pair sequence fully defined in the specification) and an exogenous sucrose invertase gene so that the cell can grow on sucrose as a sole carbon source, and obligately heterotrophic, is new, where the cell comprises an exogenous gene encoding an active lysophosphatidic acid acyltransferase-beta (LPAAT) enzyme and produces an oil comprising triglycerides, and the oil is, by virtue of the LPAAT activity comprising (a) enriched in triglycerides with midchain fatty acids, or (b) enriched in triglycerides of the saturated-unsaturated-saturated type. INDEPENDENT CLAIMS are included for:    (1) producing an oil comprising providing or cultivating the cell and extracting the oil, where the cell is cultivated heterotrophically;    (2) the oil comprising triglycerides produced by the method;    (3) a food, fuel or chemical product produced using the oil;    (4) a natural oil or refined, bleached and deodorized (RBD) oil produced from a natural oil, comprising 3.5% or less saturated fatty acids, and optionally comprising greater than 50% of oleic acid and/or greater than 1% of palmitoleic acid;    (5) a recombinant oleaginous cell, optionally comprising 23S rRNA having at least 65% nucleotide sequence identity to SEQ ID NO: 76 and optionally obligately heterotrophic, where the cell comprises an exogenous gene encoding an active ketoacyl-CoA synthase enzyme;    (6) a chemical produced from the oil;    (7) a recombinant oleaginous cell comprising recombinant nucleic acids operable to suppress the activity of a delta 12 fatty acid desaturase gene product so that the cell produces an oil with a triacylglycerol profile having less than 5% linoleic acid;    (8) a method comprising (a) providing a recombinant oleaginous cell, optionally comprising 23 S rRNA having at least 65% nucleotide sequence identity to SEQ ID NO: 76, optionally obligately heterotrophic, where the cell comprises recombinant nucleic acids operable to modify the amount of a fatty acid made by the cell in response to a change in an environmental condition, (b) cultivating the cell under a first environmental condition that is permissive to synthesis of the fatty acid so as to allow for cell division and increase the number of cells, (c) cultivating the cell under a second environmental condition that, due to the recombinant nucleic acids, reduces the synthesis of the fatty acid and thus the amount of that fatty acid in an oil produced by the cell, and (d) extracting the oil from the cell;    (9) a product produced from the oil; and    (10) a construct, vector, chromosome or host cell comprising nucleic acids encoding a protein having at least 90% identity to SEQ ID NOs: 77-79 (one of 3 (327-385) amino acid sequences all fully defined in the specification).