 Let us convert this CLD model into a stock flow diagram model, the CLD is on left side as we had this exactly same as what we saw before. So, if you want to convert it into a stock flow diagram, the population is the only stock, net birth rate connection that is the same. So, carrying capacity is a parameter and then we define the population by capacity ratio and we link it to effective birth rate and the net birth rate and the fractional birth rate. So, we can assume that the carrying capacity is fixed, let us see is equal to 1000 and let us assume p naught or the initial value of population is 2 and let us assume the small b is 0.2. So, these are all the constants. This population capacity ratio is as the name defines, it is nothing but population p divided by c, we can write that equation non-digital. Now, let us see how the net birth net rate is defined, so this net rate is defined as b into 1 minus p by c into p, since p is capital p is directly linked here, this effective birth rate, this small b into 1 minus p by c represents effective birth rate. So, this value here b into 1 minus p by c represents effective fractional birth rate value here, this is the percentage here, b is constant, so 1 minus p by c now represents the relation that we are trying to capture where it was constant and then it reduced, so I am just making it a simple straight line 1 minus p by c for modeling purposes. Let us see what happens when we do that, so first whenever you get such models you click the equation and try to understand what is the underlying equation, you know open population ok, it is a level and it is initial values 2 ok, carrying capacity initial value is 1000 or rather it is values 1000, population by capacity ratio is defined as just population divided by carrying capacity you know what I have used. I urge you to rename carrying capacity and then I would have put a bracket c, remove the parenthesis and just write it as carrying capacity c, to do that either you can open it or you can just click this variable and then when you click on the same it will allow you to edit the title, so you can edit it. Once you finish editing that you have to go to the equation and delete the rolled value and select the new value, new variable name carrying capacity c, because it does not include that sub parenthesis as variable name, yeah apologies for that, you can check the fractional birth rate it will be it will take a value 0.2, effective fractional birth rate you will observe that it is nothing but fractional birth rate b into 1 minus population capacity ratio that is p by c which we saw in the slides and net birth rate will be population times the effective fractional birth rate, yeah you made this you can just click simulate, run the model then you can click population and click the left side the causes strip you should get these two graphs, then it will immediately shows you that the population is showing an shape growth as well as an exponential growth and then finally, saturating at saturation will be at 1000, so carrying capacity is 1000, so saturated at 1000 that is because the equation that we wrote was 1 minus p by c, so as p is equal to c that became 0, so beyond that it is not allowing us to increase and here the net birth rate increased and after the inflection point the net birth rate starts to decrease as expected finally, reaching 0, observe this see some questions have written pattern we observed S shape stable population size is 1000, when does population reach stability and when is inflection point that we can see it from here, when does the population reach stability is about 70 weeks I guess 70 to 80 weeks this is when population is kind of reaching stability or if you want to discount all the small fractions then around maybe around 65 years is what it is reaching or 65 months rather it reaches stability. The inflection point how do you find it, do you need to differentiate anything just using the simulation result what do you find it, it will be the peak of the rate the time at which this peak occurred to find the exact time we can click and shift click select both, click the table time down observe the net birth rate it keeps increasing 0, 1, 2, 4, 5.8, 6.92, 34, 38, 47, 49, 40, so 32 is 49.01, 33 is 49.9, 34 is 49.83. So, 33 is when it has reached the peak value after which it starts to fall down. So, the inflection point occurs at time since time step is 1 it occurs at time 33. Observe the stock value at that time 33 is 478, time 34 it became 528 that is what has happened. When we solve it analytically maybe you will see it next week or so for this kind of system when you solve it analytically it will show that the inflection point will be exactly at C by 2 that is the carrying capacity divided by 2 will be the inflection point which is kind of intuitive 1000 okay. So, inflection point should occur when population actually reach 500 here is quite close you do not get exact find it because of the integration time step we have used. If you use smaller time step you might get a more accurate estimate or if you solve it analytically you can use the same ideas of integration to figure it out you will be able to get that the inflection point at C by 2.