Explanation of cascades

[gustavdelius]

In the vignette, in section 5.4, there is an example of a trophic cascade. In the explanation it says: "...leading to an increase in their abundance. This in turn increases the predation mortality on their smaller prey, which reduces their abundance, and so on."

From this explanation one would expect the distance between the peak and the trough to be roughly equal to beta, the preferred predator-prey size ratio. However in Figure 6 we can see that that is not the case. The value of beta for that figure is beta=100, but the distance between peak and trough is only about 10.

I then changed beta to 10, expecting to see at least a decrease in the distance between peak and trough, but it stays roughly the same, as the attached image shows. The dotted line is that for beta=10. If anything, the distance between peak and trough has become wider by decreasing the predator/prey ratio, which appears to be in conflict with your explanation.

Do you know what is going on?

Here is the code used to produce that image:

params_knife <- set_community_model(z0 = 0.1, recruitment = 4e7, 
                                    alpha = 0.2, f0 = 0.7, knife_edge_size = 1000)
sim0 <- project(params_knife, effort = 0, t_max = 50)
sim1 <- project(params_knife, effort = 1, t_max = 50)
relative_abundance <- sim1@n[51,,] / sim0@n[51,,]
plot(x=sim0@params@w, y=relative_abundance, log="x", type="n", 
     xlab = "Size (g)", ylab="Relative abundance")
lines(x=sim0@params@w, y=relative_abundance)
lines(x=c(min(sim0@params@w),max(sim0@params@w)), y=c(1,1),lty=2)
abline(v=1000, lty=2)
abline(v=10, lty=2)

params_knife <- set_community_model(z0 = 0.1, recruitment = 4e7, beta = 10,
                                    alpha = 0.2, f0 = 0.7, knife_edge_size = 1000)
sim2 <- project(params_knife, effort = 0, t_max = 50)
sim3 <- project(params_knife, effort = 1, t_max = 50)
relative_abundance2 <- sim3@n[51,,] / sim2@n[51,,]
lines(x=sim0@params@w, y=relative_abundance2, lty=3, lwd=2)