Few weeks passed from our last blog post and until now we wanted to try to investigate mathematical models as many as we could. To remind our readers once again, our goal is to find a way how to reconstruct population fluctuation of Venice over time.

For solving this problem, first we proposed whole set of different methods how to approach and how to try finish successful population reconstruction. Last week we were trying to implement any kind of proposed laws and approaches, but for every single case we got quite unrealistic representation of population. From natural growth model we didn’t expect to have anything that would have looked like nice population representation. As well, we knew that our other models were not really reliable, so we were not that confused when we saw models auch as adapted Nicholson-Baily’s model, Nurgaliev’s law and Couttsian model were far from our expectations.

At the end of day, we conclude for mentioned models that they are only appliable for doing future predictions and optimistically based on growth population. After realizing that, we came up with two ideas how to try to do a reconstruction of population without integrating any existing model.

Our first idea was to try to get function of population by doing regression of data that we have collected and then to try to fit regression model as better as we could towards to real data. We had an opinion that regression model would be nice blind prediction how population were changing over time. We expected that we would get a polynomial function of 3^{rd} or 4^{th} order. In that case, we thought that polynomial function would follow real data nicely and our next step would be put the weights on the specific segments of it based on the historic events. Since, we got a polynomial function of 9^{th} order that was the closest fit to real data we had to drop our idea and to try something new.

Finally, we decided to divide the real data into period segments and to weight curves only at specific years . We would like to explain through the example. If you give a look to our real data and imagine that one period segment is part between 1300 and 1450, we were looking to events for years in between which had any kind of influence on population. Depends on our interpretation of influence we were giving respectively positive and negative scores that we used to weight curves.

In mentioned period we had 8 years with specific influence, 1348 there was a Black Plague and here we didn’t use specific score, since it was more realistic that population were shinked by half. In 1350 Third war with Genoa breaks out and lasts until 1355, so here we provide score of -0.5, because there was probably decrement of population by recruiting people for army. 1363 we gave the score of -0.25 because of the similar reason, since colonial revolt broke out in Crete that needed considerable military force and five years to suppress. 1368, the War of Trieste begins in order to secure Adriatic trade routes and it ends in 1370, but here we thought that this war was really important to maintain their trade routes so we gave score +1. 1378, outbreak of the fourth and final Venetian–Genoese War, the “War of Chioggia”, which lasts until 1381, as we explained for these kind of wars we gave -0.5. 1454, the Ottoman Turks grant the Venetians access to their ports and trading rights which was push-up for Venetian trading and probably were influencing, so we scored with +1. 1463 Outbreak of the First Ottoman–Venetian War, score was -0.5, and then end of the war 1479 they had to cede four important trading ports in Albania and Greece, score -0.5. In 1489 they got Cyprus, score +0.5. 1492, Christopher Columbus discovers the Americas launching further explorations that ultimately begin to weaken trade in the Mediterranean, score +1. In 1499 outbreak of the Second Ottoman–Venetian War, score is -0.5. 1509, Venice regains Brescia and Verona from France, here we gave score +0.5.

After this monotonic representation how to give scores, we will explain how to implement them.

First, we take difference between beginning and ending years, *ydiff*. Then we create an array with population at specific years from extracted from real data. In that array we will weight specific years by multiplying assigned score with *ydiff* and adding to value from real data, so our formula would look like this:

ynew=[yp1300 yp1348/2 yp1350+(-0.5)*ypdiff yp1363+(-0.25)*ypdiff yp1368+1*ypdiff yp1378+(-0.5)*ypdiff yp1388+1*ypdiff yp1409+1*ypdiff yp1425+(-0.5)*ypdiff yp1450],

where *yp1300* presents “population in 1300” and so on.

We have done this procedure for periods: 1300-1450, 1450-1509, 1509-1540, 1642-1696 and 1696-1760. Why only for these periods? Give a look at the next figure and you will see for 1540-1568, there is a huge population increment in short period of time and other thing is that nothing historically important happened in that period, so there is no reason to make any predictions. The same case is for rashly decrements in 1563-1581 and in 1624-1633. Other periods were full of non-influencing historic events.

Our goals until next stop are to improve score assignment, since we are aware that is not that precise this time, as well to try to find more population-influencing events and to incorporate them into the model and at the end to match together all reconstructed periods. Also, our task for next time is also to see what to do with population prediction between 1797 and 1871, since there are no many information about population in that period, since Venice became a property of Austria.

At the end we present other reconstructed periods: