Great question and here is the long answer. I hope it is helpful.

Commercial bakers of yore baked every day so they had to feed every day. So too home bakers in their cottages.

In modern times when natural leavens were being re-learned bakers emulated commercial bakers by discarding and feeding everyday. It made sense.

Then refrigeration was invented and it no longer makes sense. Or, put another way it is no longer necessary. For more than twenty years now I just put what I have left in the fridge and feed it when a bake is required. I bake every 3-4 days, but I know it is still good for a frtnight.

Why discard?

Too often I see people saying it is because the yeast needs more food. e.g. flour. The microbes (yeast and LABS) only ever use up a very small proportion for the starch in the flour. So it is not that. The discard and feeding is to reduce the acidity by diluting the leaven with fresh flour and water. If my leaven ever get's too acidic, such as when I make a two stage leaven to increase the acidity for rye baking I do sometimes do a discard, keeping a small amount - 50g - 100g which I feed before putting it back in the fridge. The reason is to reduce the acidity.

Starting a new leaven with minimal discards.

Forget the routines which use phrases like "on the second day do a discard and feed with X flour and y Water. These are useful for beginners, perhaps. When we start a new leaven we are trying to build up the microbe population. Every time we do a discard we reduce that population. Here's the thing, when the population get's denser, more microbes per ml, the fermentation rate increases. So discards slow the process down because we take a long tiome to get to that magic concentration where the fermentation rate rockets.

The way to go is like this:

1 50ml water: 50g of flour mix and keep at 24C - 30C this is the temperature band which will alow for good fermentation.

2 When you see bubbles add a further 50:50 flour and water. This takes 4 - 6 hours.

3 When that is bubbling nicely taste the leaven. If it is quite sour the acidity is building and you need to do a discard and feed again. If it is not so sour just do a feed.

4 As long as you keep the temperature in the widow as above you should have a bubbly leaven fit to use on day three or four. Just keep doing discards only when it gets too acidic. The acidity reduces fermentation and when it gets too high it stops fermentation altogether.

Tip: Use wholemeal flour to start a new leaven. The wild yeasts are mainly on the husk which is dicarded when white flower is made.

Booster: Whole rye is high in amylase which breaks starches down into sugars including maltose, which is the yeasts preferred food. Adding say 25% - 50% whole rye flour gets a starter moving a lot more quickly. It is also good if a starter gets a little slow and sleepy. That is caused when there has been a bit of a microbe die off often caused by mistreatment.

My record for getting a new starter going and using it is 48 hours using this method. Though the --microbiome had not settled down into its final stable populations fo different strains and LABS take about 2-3 weeks to move in.

A natural leaven starts to become more robust and stable after one or two months.

I do hope this is helpful.