**Monte-Carlo analysis **Recalculates the current worksheet for the
specified number of replicates. If the worksheet includes random variables, a
new result will be obtained for each replicate. Statistics for a column of
dependent cells are collected and summary statistics (mean, variance, and
confidence limits) are collected after a given number of replicates. The
procedure also collects the number of times that values in the dependent range
exceed a range of test values (this allows, for example, calculation of
approximate *P*-values for resampling statistics). Together with the
routines for resampling and generation of random
variables, this procedure
allows calculation of bootstrap statistics and randomisation tests for arbitrarily complex
models.

**Sensitivity analysis **Numerically computes sensitivity of dependent
cells to small perturbations in a range of parameters. This routine perturbs
each of the parameters by a small amount and then recalculates the worksheet to
determine how the dependent parameters change. For some reason, the routine does
not work unless you have Excel 2000 or Excel 97 service release 2 installed.
Note: To calculate the sensitivity of the eigenvalues to matrix elements use the
SENSITIVITY function.

**Integrate a system of ODEs** This routine numerically integrates a
system of ordinary differential equations using a either a 4th order Runge-Kutta
algorithm with a fixed number of steps, or Euler's method. The integration is
performed entirely in the PopTools DLL (RANDEVS.DLL) with the results being
returned to Excel as an array formula. Because the step size is not adaptive,
the algorithm best suited to "well behaved" systems. The algorithm can
be unstable if the system is stiff, although you can usually get around this by
choosing a smaller step size - albeit at the expense of some computational
time.

**Numerical projection. **Simulation of a deterministic or stochastic process.
By using this routine, you need only specify in a worksheet how the population
makes a transition from the state at time *t* to *t *+ 1; you do not
need to enter lots of columns with the numbers in each state at each time. You must enter the initial state as
**N**(*t*), which must be a column of values. The state at the next time period is
**N**(*t *+ 1) and can depend on an arbitrarily complex process
specified in the worksheet. **N**(*t *+ 1) must also be arranged as a column, but the cells can
(indeed, should) contain formulae. The routine works by repeatedly copying the
values in **N**(*t *+ 1) to **N**(*t*) and then forcing a recalculation
and storing the new values of **N**(*t *+ 1). The original values are
restored at the end of the procedure, but you should always save the worksheet
before invoking this routine.

**Summary Stats**. See this
page.