The basic dynamics of predatorprey and plantherbivore systems a tendency towards cycles

There have been two main series of models developed as attempts to understand predator-prey dynamics. Both will be examined here. The first (Section 10.2.1) is based on differential equations (and hence, applies most readily to populations in which breeding is continuous), but relies heavily on simple graphical models (Rosenzweig & MacArthur, 1963). The second (Section 10.2.3) uses difference equations to model host-parasitoid interactions with discrete generations. Despite this taxonomic limitation, these models have the advantage of having been subject to rigorous mathematical exploration. (We have also noted previously that there are a very large number of important par-asitoid species.) Although the two series of models are explained separately, they have, of course, a common aim (to advance our understanding of predator-prey dynamics), and they can increasingly be seen as ends of a discrete-to-continuous spectrum of mathematical approaches.

1850

Snowshoe hare Lynx

Snowshoe hare Lynx

1850

1875

1900

1925

Year

1875

1900

1925

Year

Time (days)

Time (days)

Time (weeks)

o ce

J CD

2 aa

Time (weeks)

Figure 10.1 Coupled oscillations in the abundance of predators and prey. (a) The snowshoe hare (Lepus americanus) and the Canadian lynx (Lynx canadensis) as determined by the number of pelts lodged with the Hudson Bay Company. (After MacLulick, 1937.) (b) Parthenogenetic female rotifers, Bracionus calyciflorus (predators, •), and unicellular green algae, Chlorella vulgaris (prey, o) in laboratory cultures. (After Yoshida et al., 2003).

(c) The parasitoid Venturia canescens (-)

and its moth host Plodia interpunctella

(-) in laboratory cultures. (After

Bj0rnstad et al., 2001.)

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