Please place your name(s) in the upper-right corner.
Yesterday Professor Aaron discussed the intricacies of writing
one’s own numiercal solver (in his words, “simulation”). There was an
emphasis and discussion around \(\Delta
t\). What were the two most substantive things you learned about
\(\Delta t\) yesterday?
For the following Lotka-Volterra equations for mutualism, please Please plot two cases of nullclines below: where mutualism is weak and where it is very strong. Include trajectory arrows, slopes, equilibira, and axis intercepts (in the positive plane): \[ \begin{align} \frac{\mathrm{d}N_1}{\mathrm{d}t} = r_1N_1\left(\frac{K_1 - N_1 + \alpha _{12}N_2}{K_1}\right)\\ \frac{\mathrm{d}N_2}{\mathrm{d}t} = r_2N_2\left(\frac{K_2 - N_2 + \alpha _{21}N_1}{K_2}\right) \end{align} \]
What is meant by facultative and obligate mutualism both
ecologically and mathematically?
Please draw two phase planes with nullclines for the cases where: (1) one species is a facultative mutualist and the other obligate, and (2) both species are obligate mutualists.