A comparative study of models for predation and parasitism

5T
dency towards a number of miniature waves. The explanation of this trend is rather
simple. As the direction and the length of each path are determined by chance, the
predator's track is a kind of MA~KOV'S chain, although the probability distributions
of both the direction of directed paths and the length of all paths are dependent
stochastically on the location of the prey which were encountered9 This is a complex
(or a generalized) 'random walk'9 Thus the predator's path of search was often
deflected in an irregular manner and, because of the nature of a 'random walk', the
predator tended to stay in a restricted area for some time. Consequently, the prey
density in that vicinity was gradually depleted, and this caused a temporary drop in
the predator's hunting efficiency. However, as the density of prey in the vicinity was
lowered, the predator's undirected paths increased in length and eventually led to a
pIace where the prey had not been exploited. Then the hunting efficiency increased
temporarily before decreasing again. Thus the hunting curve was a kind of composite
competition curve and became wavy. Figure 8 also includes a curve (broken line)
calculated from eq. (4e. 9) for the same values of R and V (h=0, of course)9 The
observed curve in this simulation model is always lower than the calculated one,
but this is because factor h is not considered (see p. 54).
Now, the same principle should also apply to an indiscriminate parasite9 The
same set-up was used again except that none of the points (hosts) was removed from
the area and parasitized hosts were left exposed to superparasitism. It was assumed
that one egg was laid at each encounter. The result of the first experiment is shown
•,,• 100
ILl
N
I-.-
8C
/-
2 OBS. .o'"
/ "/jl~ -o
c>- ..... ~ THEOR. /-'/
O'/
oJ"
o
n
k.-
if)
O
212
tL
O
o
Z
9
4s
2c
/
~
..ff7
I I L i i i
0 50 73 93 I10 13C, ~5~
No. OF EGGS LAID (.n)
Fig. 9. An observed relationship (solid line with black dots) between
the total number of hosts parasitized (z) and the total number of
eggs laid (n) in the~first serie~of Monte Carlo simulation of the
parasitism model of continuous search. The broken line with open
circles is a theoretical relationship expected from the binomial distribution9