There are three main reasons for stepping up:
- having too much medium and too little yeast increases the risk of contamination considerably.
- a large quantity of medium causes the first few generations of yeast to bud rapidly, resulting in lots of scar tissue which functions poorly as a membrane.
- It allows the strength of the wort to start out low and gradually increase. The lower strength wort (1.025-1.030) helps reduce osmotic stresses on the yeast, resulting in a more vital population.
When making a starter, there is always some level of contamination (bacteria, wild yeast). If the number of yeast cells is low, the ratio of contaminants to brewers yeast will be higher, possibly to a point where you cultivate significant quantities of these. By keeping the starter in proportion to the amount pitched, the level of contaminants is lower and so you get fewer contaminants in the produced wort.
The second point is about how yeast reacts according to the volume of the medium. With a small population of yeast and a large quantity of medium, the initial generations bud rapidly and continually. Cell bud many times, creating lots of budding "scars" on the cell wall. These scars prevent efficient transfer of nutrients and waste products in an out of the cell, leading to a lower quality population. By using a suitable volume (not too large) the yeast bud less often and have a healthier cell membrane as a result. In other words, the aim is to get the yeast to bud at a healthy rate, but not to go into overdrive.
Another reason to "step up" is if you want to increase the number of cells without using a larger vessel. E.g. a 2 liter starter may have 200 billion cells. Decanting the spent wort and pitching another liter may take this up to 300 billion cells, effectively giving a 3 liter starter in a 2 liter vessel. (In practice, it's not linear because the yeast/volume ratio is much higher, causing propagation rates to slow, but you can bump up the count to some degree by decanting and adding fresh wort.) I don't consider this stepping up in the usual sense.
Yeast propagation and maintainance describes stepping up and why it is benecifial.
During yeast propagation it is important to keep the yeast growing
exponentially. Diluting the yeast out too far
will slow down their growth and give bacteria a chance to overtake the
culture. Since bacteria can grow as much as 6 times faster than yeast
(the average doubling time for a bacterium is 20 minutes!), it is
important to keep yeast growing rapidly. If more than 1 or 2 liters
of starter are required, it is best to do more than one step-up. In
most cases it is best to do a 500 ml intermediate starter and after
1-2 days step this up to as much as 1-2 gallons. In each case the
yeast should reach saturation in 24-48 hours. Figure 4 outlines the
two different propagation strategies.
The same page states ideal step up ratios between 4-10 fold for the final generations of yeast. Stepping up in larger volumes reduces attenuation as the efficiency of maltose and maltriose metabolization is reduced, leading to sweeter finishes. So, stepping up from a 10ml slant, a 50 fold increase is ok, since these are only the initial generations, and also represent only a small percentage of the final yeast population, but as the starter volume approaches the final volume desired, step ups should be smaller.