If success depends on measured distribution of effort, efficient fuel assimilation and expenditure, and on the certainty that pressing the pedal five hours into it will cause the engine to respond with something better than a cough, then it's the capacity of the tank rather than the size or appearance of the engine that matters. Long endurance efforts universally require one to carry his/her engine so power-to-weight ratio is equally important: increase power and endurance without gaining size or compromising oxygen efficiency."
The above excerpt is from the Gym Jones site. It was written in regards to cycling, but could just as easily be applied to alpine climbing.
An alpine objective usually involves an approach of low-level endurance, start and stop efforts when climbing a route - at times with brief maximum efforts - and again low-level endurance energy expenditure during the descent. This is usually done carrying weight. In some situations, you have to additionally deal with less than normal sleep and eating habits and amounts.
If this is what you are training for, how do you do it?
you need to 1) create a large gas tank, 2) use body fat stores as fuel, 3) maximize strength-to-weight ratio in body composition (in other words be as strong and powerful as possible at the lowest weight).
Sport -specific skill training should be separated from physical training such as endurance, strength, power, etc.
If we look at rock climbing as an element of the alpine mix we can divide training for this into skill focused or physical focused. (There is of course some overlap, but the point is the intent or priority of the training)
Rock climbing skill list (partial):
finding & utilizing rests
precise use of feet
using momentum generated from legs
turning & flagging
Rock climbing physical list (partial):
continuous up/down climbing for <30 minutes
interval training, 1:1 ratio of lap climbing with rest period
maximum effort on route with full recovery between repetitions
linking 4-6 moves at maximum effort
speed climbing intervals
An alpinist should be focused on skills that will make him/her more efficient and faster. Physical training should be made up mostly of endurance-level efforts.
Again, looking just at rock climbing, an alpinist should improve their ability in rope handling, placing protection and on-sight climbing to cite just three skill elements. Physically focused training for rock should rely heavily on continuous up/down climbing of up to 60 minutes, interval training at around 80% maximum effort (12-15 laps) and speed climbing intervals.
The above is only really scratching the surface of one facet that makes up an alpinist. There are also the abilities in ice, snow, mixed terrain, skiing, etc. Additionally, just off the top of my head, the areas nutrition, mental strength and equipment are critically important.
This is what makes alpinism a totally engaging life-long pursuit. And perhaps why some of us have a chip on our shoulders about specialists active in only one of the various disciplines that make up the complete alpine picture.