Is there a way to optimise the spread of explanatory variables in experimental design? I am designing an experiment to test density effects of interacting species.  The real example is quite complicated to explain, so I'll give a simplified example - I want to test whether the density of herbivores effects plant growth.  
I am planning on using regression to test for any effect of density on growth.  I have enough plants for 12 treatments and I'm wondering how best to design the spread of density treatments.  Would it be better to have evenly spaced treatments e.g. herbivore densities of 0, 10, 20, 30, 40, 50 etc.  Or should I space them widely over a greater scale e.g. 0, 10, 20, 40, 80, 160 etc ?
This is the first experiment on this system, so I have no idea about the natural variation in productivity between plants, or how they will likely respond to the treatments, or if there is a threshold at which they start to respond.  
Ideally, I would like this experiment to test an interesting hypothesis suitable for publication (ie. does growth decline as herbivore density increases?), but also provide information about the shape of the relationship that will help inform future experiments (ie. how many herbivores do we need to use to show an effect in subsequent studies?). 
I wondered if there was guidance on the spread of explanatory variables in regression or experimental design?  Or if it just comes down to judgement/guesswork.  
 A: When designing such an experiment, it's important to think about the expected shape of the response. This is probably best approached by studying the underlying theory and by considering your specific goals. But here are a few possibilities that are commonly considered in ecology: 


*

*If you expect a linear (unlikely) or symmetric unimodal response, even spacing across a gradient
of densities should work well. 

*If you expect an asymmetric unimodal response, you might want more measurements around the hump (if you are interested in characterising the asymmetry) or around the extremes (if you are more interested in responses to extreme conditions).

*If you expect a saturating response (common in ecology), it may be useful to have more measurements at low densities than at high ones. This is because there will be little variation at high densities, and focussing your efforts at low densities will allow you to characterise the functional form better. But what constitutes 'low' and 'high' requires domain knowledge to answer. 


As you can see, there are rules of thumb that may be helpful but specific suggestions are difficult to offer. They will depend strongly on the specifics of your system. This is partly why it is frequently recommended to try a small pilot experiment to evaluate the possibilities before embarking on the full-blown project.
