 
Summary: Notes on simulating LotkaVolterra
Jeff Achter
j.achter@colostate.edu
March 24, 2004
1 Reminder on Poisson processes
1.1 Single events
Suppose that an event A happens at discrete times; that the probability an event happens in a time
interval [t, t + t] is independent of t; and that the chance a single event happens during a time
interval [t, t + t] is t + o(t). Then the time between events is drawn from the probability
distribution with PDF et.
(Briefly: Let f (t) be the chance that nothing happens on [0, t]. Then
f (t + t) = f (t)f (t)
= f (t)(1  t + o(t))
f (t + t)  f (t)
t
= t + f (t) · o(t)
f (t) =  f (t)
Thus, f (t) = Cet for some t. Since the probability of no event happening on [0, 0] is 1, that
constant must be 1.)
Taking expected values reveals that the expected interevent time is 1/, and that the expected
