import matplotlib.pyplot as plt

def populations(prey0,pred0,growth,predation,conversion,death,years,stepsPerYear,starveCutoff,starveRate):
    """Returns the predicted populations of two species, given their
       initial populations, the prey's growth rate, the predation
       rate, the predator's food conversion rate, the predator's
       death rate, and the number of years to predict.
       stepsPerYear determines how many populations will be computed per
       year, with larger values giving more accurate calculations."""

    times = [0]
    prey = [prey0]
    pred = [pred0]

    for y in range(years*stepsPerYear):
        times.append(float(y)/stepsPerYear)
        
        #prey.append(prey[y] + prey[y] * (growth-predation*pred[y])/stepsPerYear)
        prey.append(prey[y] + prey[y] * (growth-predation*pred[y]-starvation(prey[y],starveCutoff,starveRate))/stepsPerYear)

        pred.append(pred[y] + pred[y] * (conversion*prey[y]-death)/stepsPerYear)

    return times, prey, pred

def starvation(prey,cutoff,rate):
    if prey < cutoff:
        return 0
    else:
        return rate

def plotPopulations(times,prey,pred,preyname,predname):
    """Displays a plot of two populations over the given times."""
    
    preyPlot = plt.plot(times, prey, '-' )  #solid line
    predPlot = plt.plot(times, pred, ':' )  #dotted line
    plt.legend( (preyPlot, predPlot), (preyname, predname), 'best')  #best location
    plt.xlabel('Years')
    plt.ylabel('Population')
    plt.title('Predator-Prey Model')
    plt.show()


times, prey, pred = populations(100,50,.5,.0025,.002,.6,30,500,500,1.0)
plotPopulations(times,prey,pred,"Hare","Lynx")