The answer to this question is an event called Endoreduplication. It is a very fancy term for a simple phenomenon. The cells instead of multiplying and increasing in number, they simply increase in size. This provides two benefits the organ (in this case flower) can still grow inspite of not having meristimatic tissue, and still retain the shape and organization. And how do the cells undergo endoreduplication? They simply duplicate their genome or the DNA but do not divide into sister cells. Because they have double the DNA they need to expand and increase in mass and volume. The following picture illustrates the process of Endoreduplication.
As can be seen from the following image Endoreduplication yields increase in size without changing the shape as against growth by mitosis.
This brings in a new variable into play. Polyploidy. Usually cells have two identical copies of their DNA. It is to ensure that the cell has one extra copy in case one of the copy goes bad and cannot function due to a mutation. It is like keeping two sets of pens, an extra one in case the other does not work . So usually cells are diploid (2n). But now after endoreduplication the cells are tetraploid (4n) i.e. the cells have 4 copies of the same DNA. It has its own benefits, I will be writing about polyploidy later.
So does this happen in all orchids or even in other plants. And the answer is yes. It does occur in all orchids studied so far. It might not be as dramatic as observed in Vandaeceous flowers though. It also happens in other plants, an exciting example is that from an apple variety reported here by Peter Hirst from the Purdue University.
Cells in the fruits of Grand Gala apples on the right, undergo endoreduplication, which causes them to grow larger than the regular Gala apples, on the left.
There are many benefits of endoreduplication. Firstly as I mentioned previously it allows an organ to enlarge in size even when it has lost the capacity for multiplication. It also does not need reorganization and patterning of the tissue. Another important thing is that endoreduplication is much more energy efficient. It involves much less protein synthesis and energy expenditure on the part of the cells. And lastly the resulting cells are polyploidy which has many benefits, about which I will talk in another article. I hope you like this article and understand and are in awe of the multitude ways the orchids delight us.