Morels are mycorhizal fungi, that is, they live symbiotically on the roots of some species of trees. Apples, elms, poplars and ashes are all noted in the literature for being indicator species to locate potential morel hot spots and dead or dying trees of these species tend to produce prodigious crops of morels under the right conditions. That said however, morels don't require these trees to produce mushrooms. Morels have been found in pots of chrysanthemums, in parking lots, golf courses and other odd corners too numerous to mention with none of the above named species anywhere in sight, so these odd little fungi - while they may partner with or favor particular species - are not completely dependent on them. As nearly all researchers have noted, "Morels are where you find them." Still all morels I've encountered have always occurred in patches and are usually clearly associated with one of the above-named tree species.
Mycelium grows underground for an indeterminate length of time - perhaps months or even several years - before it stores enough food to produce its fruiting body - the actual morel. (Individual stands of mycelia can apparently measure their life spans in centuries.) This mushroom mycelium lives underground year round and - assuming the year is a good one and the organism is mature - produces small "buttons" of fleshy, compact mycelia just below the soil at strategic points along its length during late summer or early fall. These buttons (usually) remain dormant throughout the fall and winter and come spring with its rising temperatures and increased rainfall some of them swell and grow into the fruiting bodies that we call morels. Occasionally fruiting is triggered in the fall and at least a few of these buttons can develop (under the right circumstances - which are unknown) into mature mushrooms. This, however is a fairly rare occurrence. Morels appear when the ground temperature four inches below the surface reaches 55 degrees Fahrenheit and ceases when the ground temperature reaches 62 degrees.