TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Catalyst: The acid catalyst is selected from hydrofluoric acid, sulfuric acid, and fluorosulfonic acid.    TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Method: The step of partially hydrogenating the bioisoprene composition involves contacting the bioisoprene composition with hydrogen gas and a catalyst for catalyzing partial hydrogenation of isoprene. The step of alkylating the isoamylene with an isoparaffin involves contacting the isoamylene with the isoparaffin in the presence of an acid catalyst. The method (M1) involves: (a1) contacting a bioisoprene composition with an acid catalyst to produce at least one mixed olefin product of 5-50C olefins, where the mixed olefin products comprise higher molecular weight olefin products including 16-50C olefins and lower molecular weight olefin products including 5-15C olefins; (b1) converting the higher molecular weight olefin products of 16-50C olefins to lower molecular weight olefin products of 5-15C olefins; and (c1) hydrogenating the lower molecular weight olefin products including 5-15C olefins to produce saturated hydrocarbon including 5-15C alkanes fuel constituents; where a substantial portion of the isoprene in the bioisoprene composition is chemically converted to at least one non-isoprene compound. The step (b1) of converting the higher molecular weight olefin products including 16-50C olefins to lower molecular weight olefin products including 5-15C olefins involves thermal cracking, steam cracking or metathesis. Preferred Composition: The bioisoprene composition comprises or contains isoprene ( greater than or equal to 2 mg, or greater than or equal to 99.94 wt.% compared to the total weight of all 5C hydrocarbons in the composition). Preferred Components: The chemical capable of partially hydrogenating isoprene in the bioisoprene composition to produce an isoamylene comprises a hydrogen gas and a catalyst for catalyzing partial hydrogenation of isoprene. The isoparaffin for alkylating the isoamylene is propane, isobutane or isopentane. Preferred Catalyst: The olefin or isoprene metathesis catalyst or catalyst for catalyzing metathesis of isoamylene comprises or involves at least a metal complex (preferably rhenium complex, ruthenium complex, rhodium complex, osmium complex, tungsten complex, molybdenum complex, or titanium complex). The catalyst for catalyzing partial hydrogenation of isoprene comprises a palladium catalyst. The acid catalyst is perhaloalkylsufonic acid. The catalyst for hydrogenating at least one olefin product to form at least one alkane fuel constituent comprises a catalyst selected from palladium catalysts, nickel catalysts, cobalt catalysts, ruthenium catalysts, and rhodium catalysts. The system further comprises an acid catalyst for alkylating isoamylene. Preferred System: The fermentation system is a continuous fermentation system such as continuous fermentation, or continuous with recycle processes fermentation; batch fermentation, fed-batch fermentation. In the system at least 99% of the bioisoprene composition is in gaseous phase. Preferred Product: The olefin product comprises a higher ( greater than or equal to 5C) olefin and/or a lower ( less than or equal to 5C) olefin (preferably at least one olefin product from isoprene metathesis comprises ethylene, isobutylene, or olefins including cyclic olefins and containing 6, 8 and 12 carbon atoms (e.g. dimethylhexatrienes)). The olefin product from isoamylene metathesis comprises at least one olefin selected from ethylene and olefins containing 6, 8 and 12 carbon atoms (e.g. dimethylhexenes). EXAMPLE - Continuous oligomerization of isoprene from a bioisoprene composition with a solid acid catalyst was carried out as follows. Isoprene (from bioisoprene composition) monomer was continuously converted into 10C dimers and 15C trimers in dimerization reactor containing Amberlyst 15 (RTM: ion exchange resin). The feed stream of bioisoprene composition included isoprene monomer and optionally 5C derivatives of isoprene and a co-solvent. The process was conducted at 20-200 degrees C and pressures of 0.5-200 bars. The products of dimerization step were fractionated in a first fractionation column to separate unreacted isoprene from higher (greater than 5C) oligomers. The 5C fraction was returned to the dimerization reactor and heavy (greater than 5C) fraction was introduced into second fractionation column in which desired 10C/15C fraction was collected from the overhead stream. The bottom fraction consisting of greater than 15C oligomers was fed into a heavy recycle reactor containing metathesis catalyst such as the Grubbs 2nd generation catalyst. The metathesis catalyst converted portion of higher oligomer fraction into lighter components by olefin cross-metathesis reactions that were subsequently fed into fractionation column. Overall, the process resulted in conversion of isoprene monomer into 10C dimer and 15C trimer precursors for fuel constituents derived from biologically produced isoprene, which were then subjected to partial hydrogenation. The partial hydrogenation was carried out over 5% Pd/C catalyst on Midi-Cube (RTM: hydrogenation instrument) at 40 degrees C and 5 bar hydrogen pressure. Substrate flow rate was 10 ml/minute and hydrogen was delivered at 125 ml/minute (5 mmol/minute). The resulting partially saturated compounds were suitable as fuel compositions and as fuel blend stocks.