The most efficient way of quantifying changes in crop yield within the range of tested plant population densities is the application of relevant yield-density equations. A simple comparison of means just will reveal the best density among the tested densities. However, application of yield-density equations will estimate crop yield at any density within the range of minimum and maximum densities that are investigated. My experience shows that the reciprocal equations are the best, if at least three densities are tested.   

In case of  crops particularly fruit crops, plant population density investigations and yield-density equations go together. High density system of planting accommodates more population than wider spacing. The choice of the system of planting in the orchard depends on topography, crop, variety, plant density, production technology to be followed.

I agree with the earlier writers. The repetitive nature of density investigations necessitates the need for quantifying the relationships between density and yield (total biomass and/or seed yields). Several equations were developed to quantify the relations between density and yield; but it was later widely accepted that reciprocal yield-density equations are more meaningful and sensible in explaining the relationship between yield and density . Some of the earlier equations used in establishing the relationship between density and yield are well documented (Yahuza, 2011; Willey and Heath, 1969).

Ordinarily, as density is increased, yield will also increase until a point is reached where yield either plateaus or declines; where yield plateaus reciprocal asymptotic equations will explain yield more satisfactorily than other equations, and where yield declines reciprocal parabolic yield-density equations are more applicable (Yahuza,2012; Willey and Heath, 1969). Consequently, it is now well established that in circumstances where the relationship between yields and density deviated from linearity, equations based on reciprocal relations between yield per plant and density are better at quantifying yields than other equations; these equations can be categorized as either reciprocal asymptotic or reciprocal parabolic. See Yahuza (2011) for further details.

Stay with non-linear regression of a relevant yield density equation. Many of them are algebraically equivalent so I tend to go with the simplest, which is a Michaelis Menten equation in most cases. Avoid means comparisons at all cost. These will give you incorrect conclusions.