There are hundreds of scientific articles on the effects of plant population on yield for every crop plant you can imagine. The investigator is interested to learn where maximum yield is obtained at a specific number of equally spaced plants per acre. Keep in mind, however, that the ideal plant population for corn will be different than for soybean.
For the gardener, we are also concerned with maximizing yield and strive to give each plant an opportunity to produce a bountiful crop of high-quality fruit. Unfortunately, and especially for the novice gardener, there is a tendency to over-seed which inadvertently allows young seedlings to crowd one another.
Seedlings that are crowded by neighboring plants have to compete for sunlight, soil nutrients and soil moisture. As well, their roots become entangled thus complicating the task of thinning. If the thinning process doesn’t take place promptly, you run the risk of damaging young roots while pulling plants from the ground. The early stages of plant development are critical to future plant development and fruit production, hence, giving each plant an opportunity to thrive, soon after emerging from the soil, is important.
My approach to seeding most vegetables is to plant a number of seed equal to the final number of plants desired in the garden. To be clear, if the final recommended number of bush bean plants is 4 plant per foot of row, I’ll plant 8 – 10 seed per foot of row. Of course, this assumes good quality seed with a germination rate of at least 80%. This approach requires minimal thinning without disturbing the roots of neighboring plants. Remember, the objective is to establish an optimum and vigorous plant stand which is typically a precursor to good yield results.
There is a lot more which can be said about this topic however I feel that this can wait for another day.