statistics and r
I have an assignment consisting of 2 tasks where i have to convert a a two species Lotka-Volterra model into a three species Lotka-Volterra model, and then simulate multiple model outputs in order to identify and discuss which parameters might be particularly important for keeping all three species alive, and briefly discuss the implications of this
ASSESSMENT PAPER This assessment comprises two tasks. Firstly, you will have to code a three-species, three trophic level, version of the Lotka Volterra (LV) model, and then demonstrate that the model works. Secondly, you will need to use simulations to identify the key parameters determining the survival of all the species. You should use the workbook from week 7 as a reference document for the modelling. You will discuss and interpret your findings (along with your code) in an Rmarkdown document, illustrating your answer with graphics where necessary. You should present your code alongside text explaining what each section does. Task 1: Write a three species Lotka-Volterra model Three-species Lotka-Volterra model Your three-species L-V model will be comprised of the following equations: dR/dt = r*R – α*N*R dN/dt = f*α*N*R – q*N – e*N*P dP/dt = z*e*N*P – b*P. R is the number of the basal prey species, N is the number of intermediate predators, and P is the number of the top predators. R grows at rate r, alpha (α) is the attack rate of the primary consumers (N) on the basal prey species, f is the conversion efficiency of R to new N, and q is the exponential decline rate of N in the absence of prey. The top predator eats the intermediate predator at a rate defined by the attack rate e of P on N. P then grows in the same way as N does, as a function of z (the conversion efficiency of N’s to new P’s), the attack rate e, and the number of N and P, whilst the population declines exponentially at a rate b. You will type or copy and paste the code below in order to modify it for a two-species model to run simulations under a three-species LV model (paying particular attention to the start values at the beginning and the list output at the end, as well as the parms). ## this defines a two species model lv2 <- function(t, start, parms) { ##set the start values for each of the species ##basal species R <- start["R"] ## consumers N <- start["N"] ##allow R to look within parms for the values of r, a, e, etc with(as.list(parms), { ## dynamics of the resources dR <- r*R - a*N*R ## dynamics of the primary consumers dN <- f*a*N*R - q*N ##return a list of the abundances of each species ##deSolve will then group these into a data frame list(c(dR, dN)) }) } You will also need to modify the following to reflect the change in the number of species (i.e. that there will be three, and not two).
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