Clarify/fix vitalRatePerturbation

[patrickbarks]

vitalRatePerturbation doesn't work the way I'd expect. If you pass it an age-structured model (i.e. matU is a Leslie matrix with survival probabilities along the subdiagonal), it will return non-zero sensitivities for growth, e.g.

matU <- rbind(c(0.0, 0.0, 0.0),
              c(0.3, 0.0, 0.0),
              c(0.0, 0.5, 0.0))
  
matF <- rbind(c(0.0, 0.0, 0.8),
              c(0.0, 0.0, 0.0),
              c(0.0, 0.0, 0.0))

vitalRatePerturbation(matU, matF)
> # SSurvival    SGrowth  SShrinkage  SReproduction  SClonality ...
> # 0.8760486  0.8760486           0      0.2054321           0 ...

I would've expected the above model to be decomposed into something with no vital rates for growth, like

matA <- rbind(c( 0,  0, f),   # edited... wrote this as a 4x4 initially
              c(s1,  0, 0),
              c( 0, s2, 0))

I've looked at some stage-structured models too, and compared results to popbio::vitalsens. In general the sensitivities to survival produced by vitalRatePerturbation correspond to what I'd expect, but sensitivities to the other vital rates do not.

Is there a ref for this method @robcito? I've looked through Caswell 2001, but haven't been able to figure out a method for what I think we want to do here (at least not a general one).

[patrickbarks]

closed by #34 and #39