presentation.md

Backwards simulation

For the forward simulation, the psudo-code from Marks book was followed with the same parameterization. These parameters are set in the config file (see README.md).

The majority of the backwards simulation algorithm is in backward.py, with comments delimiting the sections described in the pseudo-code:

    # STEP 1 - initialize fitness arrays
    print('\nInitialize vectors...')
    F0, F1, D = init_f(x_crit, x_max)

    # Print and/or log fitness values
    dtypes = numpy.dtype([('t',  int),      # timestep
                          ('state', float), # state
                          ('F0', float), # state
                          ('F1', float), # state
                          ('patch', int),    # organism id
                          ])

    landscape = numpy.zeros(n_timesteps*(x_max), dtypes)

    # STEP 2 - Iterate over timesteps, getting max fitness values
    for t in reversed(range(n_timesteps)):
        F0, D = max_v(x_crit, x_max, patches, F0, F1, D)

        # STEP 3 - Print/log fitness value and optimal index with t
        landscape = log_vals(t, x_crit, x_max, F0, F1, D, landscape)

        if display:
            print_vals(t, x_crit, x_max, F0, F1, D)

        # STEP 4 - Copy F0 to F1, updates fitness function to F(x,t,T)
        for x in range(0, x_max+1):
            F1[x] = F0[x]

        # STEP 5 - Reduce timestep
        t -= 1

I managed to get the pseudo code to work without fully understanding the concept of the model. A chat with Gabby and Tom sorted that out. Thanks guys! 👍

Forward simulation

I didnt see the bit about the forward simulation in the book until after I winged it. The majority of the forward simulation algorithm is in forward.py, which goes through the following steps for each timestep and organism:

    # Get index for row corresponding to timestep and state
    idx = (landscape['t'] == t) & (landscape['state'] == o.state)
    # Move organism to optimal patch (i.e. D[x])
    o.patch = int(landscape[idx]['patch'])

    # Only update feeding and mortality for living organisms
    if o.alive==True:

        # Find food based on patch probability of finding food
        prob_food = patches[o.patch]['prob_food']
        cost = patches[o.patch]['cost']
        increment = patches[o.patch]['state_increment']

        food_found = numpy.random.choice([1,0], 1, p=[prob_food, 1-prob_food])

        # Subtract cost, add increment if food found
        # only allow state to be increased to maximum
        if food_found & (o.state-cost+increment <= x_max):
            o.state = o.state - cost + increment
        elif food_found & (o.state-cost+increment > x_max):
            o.state = float(x_max)
        elif food_found == 0:
            o.state = o.state - cost

        # Kill organism if critical state reached
        if o.state <= float(x_crit):
            o.alive = False

        # Kill organism based on patch probability of predation
        prob_pred = patches[o.patch]['prob_pred']
        alive_pred = numpy.random.choice([1,0], 1, p=[1-prob_pred, prob_pred])
        # if died from starvation or predation, set dead
        if (o.alive==False) | (alive_pred==False):
            o.alive = False

After winging it I made a plotting app using Bokeh (located in main.py), which revieled I had almost correct numbers, but there were still organisms in patch 1 (using python indexing convention), which shouldnt have been according to the optimal strategy landscape. See the readme for directions on running it.

I went to back to the book, but when reading it, it felt far more complicated than my interpretation of things, so I stopped reading. He quickly pointed out the errors, and I went and fixed them.

By far the longest use of my time on this was making the Bokeh app, but it helped quite a lot in the end seeing that my numbers were alright (I think), so time well spent.