Ecological theory recognizes the importance of the variety of species
for maintaining the functioning of ecosystems and their derived
services. We assert that when studying the effects of shifts in
biodiversity levels using mathematical models, their dynamics must be
sensitive to the variety of species traits but not to raw species
numbers, a property that we call scale--invariance. We present a testing
procedure for verifying scale--invariance of ecological network models
---with or without trait adaptation--- expressed as ODEs. Furthermore,
we applied our test to several influential models used for evaluating
biodiversity effects on ecosystem functioning. In most of the surveyed
studies the equations failed our test. This raises doubts about the
validity of previous results and calls for revisiting the theory derived
from these studies. Our results foster the creation of artifact--free
models, a necessary step towards building a more robust theory of
biodiversity--driven ecosystem functioning.