Analo­gies are of­ten drawn be­tween nat­u­ral se­lec­tion and gra­di­ent de­scent (and other train­ing pro­ce­dures for para­met­ric al­gorithms). It is im­por­tant to un­der­stand to what ex­tent these are use­ful and ap­pli­ca­ble analo­gies. Here, un­der some mod­est (but ul­ti­mately ap­prox­i­mat­ing) sim­plify­ing as­sump­tions, nat­u­ral se­lec­tion is found to be math­e­mat­i­cally equiv­a­lent to an im­ple­men­ta­tion of stochas­tic gra­di­ent de­scent.