Briefly describe why parameter estimation is so important to Systems Biology and discuss the pros and cons of estimating individual parameters from experimental data versus estimating parameters by fitting models to state variable data (e.g. time series).
Assess the residuals below taken from two attempts at fitting a straight line to data (i.e. simple linear regression):
Use independent variable to explain dependant variable so come up with linea regression model
Residuals of Line Fit 1 Residuals of Line Fit 2
1.03 1.03
2.78 3.55
-8.76 -7.23
7.74 10.04
3.47 6.53
0.05 3.87
-9.71 -5.12
-1.79 3.56
2.38 8.49
Which line is the best fit for the data?
What is the method you used in question 2 called?
Fit the basic form of the Lotka-Volterra predator-prey model, and the form that contains both logistic growth and the Holling Type II functional response (see below), to the data contained in the csv file “parasitoid_wasp_weevil_interaction.csv”. These data describe the dynamics of parasitoid wasp and a bean weevil populations through time.
Basic Lotka-Volterra Predator-Prey Model
dN/dt= r*N*- a*N*R
dR/dt=c*a*N*R - δ*N
Lotka-Volterra Predator-Prey Model with logistic growth of prey and Holling Type II functional response describing the capture and handling of prey by the predator
dN/dt= r*N*(1-N/K)- a*N*R/(h+N)
dR/dt= c*a*N*R/(h+N) - δ*N
Where: N = prey density, R = predator density, r = prey growth rate, a is the rate at which the predator encounters prey (think of it as hunting efficiency) and h = the predator handling time (i.e. time taken to eat the prey), c describes the conversion coefficient (you can think of this as an offset to explain that you need more than one prey item to give rise to the birth of a new predator), and delta = death rate of the predator.
Present your fit function below
Explain the form of the fit function that you used (explaining for example, whether you included initial=T) and why you made that decision.
Which equation do you believe most closely describes the real data?
Briefly explain the decision you made in c.
Record the parameters for your best fitting model below.
Complete if your answer to c. was Basic Lotka-Volterra Complete if your answer to c. was Lotka-Volterra with logistic growth and Holling Type II functional response
r r
a K
c a
δ h
start N c
start R δ
start N
start R
The most basic model describing infection dynamics of a microparasite is called the SI model, which takes the form:
dS/dt=-β*S*I
dI/dt=β*S*I-γ*I
These two equations describe two classes of host, those who are susceptible to infection (S) and those who are infected (I). Beta is the transmission coefficient which describes the probability of infection per unit time given a contact between a susceptible and an infected individual. Gamma describes the loss of infected hosts, this could be due to recovery (assuming life-long immunity), death or quarantining of the individual – effectively removing them from the infectious pool. This model is often extended to the SIR model where the recovered group is recorded but as this is simply dR/dt = γ*I we will ignore it for this exercise. Note that the model assumes that you start with a fixed number of susceptible hosts (i.e. there is no birth, death, immigration or emigration in your population, as such your susceptible number can only ever fall. You are provided with the dataset, “CDC_data_H3N2_influenza_2004-2005”, which as the name suggests is data from the 2004-2005 outbreak of the H3N2 influenza virus. Fit the above model to these data and estimate values for the number of susceptibles, and for parameters β and γ.
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