  The simple and partial Mantel tests are routinely used in many areas of
evolutionary biology to assess the significance of the association between two
or more matrices of distances relative to the same pairs of individuals or
demes. Partial Mantel tests rather than simple Mantel tests are widely used to
assess the relationship between two variables displaying some form of
structure.
  We show that contrarily to a widely shared belief, partial Mantel tests are
not valid in this case, and their bias remains close to that of the simple
Mantel test.
  We confirm that strong biases are expected under a sampling design and
spatial correlation parameter drawn from an actual study.
  The Mantel tests should not be used in case auto-correlation is suspected in
both variables compared under the null hypothesis. We outline alternative
strategies. The R code used for our computer simulations is distributed as
supporting material.
