# 3R-Research

The discussion about supernumerary animals has been going on for a long time in the general public. An example is the debate about male chicks that are euthanised because they cannot be used for the production of eggs. Another example are male calves which cannot be used later in their life to the production of milk. In research the problem is similar: not all bred animals can be used for certain research projects because they do not have the right genotype for the question of interest. Yet, strong legal rules demand in animal experimentation and breeding of laboratory animals that the 3R principle, replace, reduce, refine, are adhered to. Our project is attempting to reduce the number of supernumerous animals through mathematical modelling, a very complex process. To illustrate this complexity, let us take the example of the Rubik cube. Imagine calculating all the possibilities of movement of the pieces of a Rubik cube to get a solver Rubic cube the solution with the lowest number of movements. In breeding of laboratory animals the basis of the calculations are obviously not the rules of Rubik cube, but the long-known Mendel rules. But, unfortunately it is not all mathematics, it is nature that decides the number of animals and their genotype born at any generation. If we go back to our example of the Rubik cube, it is as if with each movement of a part of the Rubik cube, other pieces would change colorations. This increases the complexity of the calculations tenfold and makes it impossible to manually calculate all breeding strategies to find those that produce the least number of animals. To be able to produce software that allows these complex calculations, it is necessary to combine extended knowledges in three domains: the organization of breeding in animal facilities, knowledge of genetics and mathematics in the calculation of complex systems. The meeting of three people allowed this combination: Dr. Philippe Bugnon who managed genetically modified mouse lines for more than 10 years at the ETHZ, Prof. Dr. Buch who has extensive knowledge in the generation and analysis of gene-modified animals and Prof. Frank Brand who is a theoretical physicist holding a Ph. D. in optimization with evolutionary algorithms and is working on projects in the areas mathematical modelling, evolutionary algorithms, big data analysis and complex systems analysis.

The software which will be programed will ask the researcher to give information and then will compute all possible breeding schemes based on these data and calculate all ways to go from the starting point (animals at disposition) to the end point (animal needed for experimentation). And the final step will be to determine the ways which produced the lowest number of animals.

This software will be made available free of charge to the scientific community in order to reduce the number of animals produced in animal facilities.