Once upon a time, there was a bored CS student. He wanted to know if a population could be stable. He decided to fiddle with the lovely Ruby language, objects and contracts.

Disclaimer: I'm not a biologist, mathematician or any kind of reproduction expert, just a bored student ¯\_(ツ)_/¯

For 10 generations with an initial population of 50 individuals in which each couple can have a maximum of 4 offsprings:

Possible output:

$ ruby rgs.rb 10 50 4
  GEN       POP     MALE%   FEMALE%   AVG OFF       NRR
-------------------------------------------------------
    1       050    56.000    44.000     2.091     0.789
    2       046    56.522    43.478     1.800     0.667
    3       036    61.111    38.889     1.714     0.500
    4       024    37.500    62.500     1.556     1.200
    5       014    42.857    57.143     3.500     1.500
    6       021    47.619    52.381     2.600     1.111
    7       026    53.846    46.154     2.000     0.800
    8       024    50.000    50.000     1.583     0.875
    9       019    42.105    57.895     2.625     0.000
   10       021    23.810    76.190     2.200     0.000

Legend:

multi_sim.rb is used to create multiple simulations with one or more varying parameters. Results are stored as CSV files under a newly created results/yyyy-mm-dd_hhmmss/raw/ directory.

sym_to_graph.py can then be used to obtain a serie of graphs for each CSV file which will be put in the under the results/yyyy-mm-dd_hhmmss/graph/ directory.

Example tree of the result/ folder after making 3 simulations on 15 generations with an initial population of 10.000 individuals and 3, 4 and then 5 maximum offsprings:

.
└─ 2020-4-21_20222
   ├── graph
   │   ├── result_15_10000_3.png
   │   ├── result_15_10000_4.png
   │   └── result_15_10000_5.png
   └── raw
       ├── result_15_10000_3.csv
       ├── result_15_10000_4.csv
       └── result_15_10000_5.csv

In the first phase, I fixed the number of offsprings.

In the second phase, I let this number vary between 0 and a maximum.

In the third phase, I implemented the net reproduction rate.

The sex of each offspring was always randomly determined.

Results eventually are the same in both phases but overall, the population were quicker to proliferate or go extinct whith a fixed number of offsprings per couples.

The generation of extinction or the growing rate vary depending on the initial number of indivuals and the number of offsprings per couple. Lowers values for these two parameters result in a quicker extinction/grow.

Replacement level fertility is said to have been reached when NRR=1.0

In this phase, I tried to implement the net reproduction rate of each generation compared to the one that follows. With my understanding, I hesitated: should I keep the possibility for couples to have no offsprings? I came to the following conclusion:

The simulation doesn't take into account any kind of mortality and the NRR assumes that surviving daughters will have offsprings if they can. Female mortality before childbearing years is kind of simulated by the fact that some couples can have 0 offsprings.

Mass data analysis pending...

I didn't succeed in finding parameters such as the population is stable in time. Enforcing the NRR to 1.0 is yet to be explored. What will then be the average number of offsprings per couple?

Those observations only reflect the simplicity of this simulation and were not made in a rigourous and scientific way.

The code and features are still to be extended.

Net reproduction rate (2008) Net Reproduction Rate (NRR). In: Kirch W. (eds) Encyclopedia of Public Health. Springer, Dordrecht

Gross reproduction rate (2008) Gross Reproduction Rate (GRR). In: Kirch W. (eds) Encyclopedia of Public Health. Springer, Dordrecht