How to build bridges between mathematicians, computer scientists and biologists? I am part of a recently founded laboratory in computational biology and we are trying to get all the parts (biologists, computer scientists, mathematicians, and so on) to speak the same language, or at least one we can all understand. To do so, we want to figure out some strategies beside seminars and weekly lectures.

I am not the only one who went through this challenge, see: [1]. For example, How to explain core biological concepts like evolution and selection to a mathematician? How to explain a mathematical formalization to a biologist (beyond the very basic models the majority of biologists know, such as predator-prey and logarithmic growth)? 

There must be strategies; for instance, books that are in an effective middle (mathematically rigorous, but stepped enough that a biologist can understand it). This is a long term project and we need to devise strategies to progressively "retrain" ourselves. (Bibliography suggestions are welcome.)

[1] https://liorpachter.wordpress.com/2014/12/30/the-two-cultures-of-mathematics-and-biology/
Disclosure: I'm a mathematical biologist that came into it from the biology side. 

I don't think it is necessary to retrain the biologists so they understand maths and retrain the mathematicians so they understand biologists, although these things should occur naturally to some degree with interdisciplinary work. Rather, I think it is important to understand the motivations of each 'type' and to tailor the language to the audience. 

To grossly generalise, biologists are more interested in quantitative methods as a tool to answer interesting biological questions and mathematicians are more interested in the method/analysis used to answer that question. 

So when mathematicians talk to biologists, they need to place less emphasis on the technical details of a model/analysis and focus on the general features. For example, if you are building a model to answer an evolutionary or ecological question, a biologist is more interested in the biological assumptions the model is making and whether or not the model is a reasonable abstraction of the biological system. In turn, the mathematician may need to explain why certain details of the system can't or shouldn't be included in the model (e.g. because they would complicate the analysis for little gain in intuitive understanding).

When biologists talk to mathematicians they need to frame their questions in a way that is conducive to a quantitative framework. If a mathematician is trying to build a model, they don't need or want to know every minute detail of a system. It's overkill and will just lead to confusion. What are the most relevant points? For example, if a biologist is interested in how the density of cows affects the density of grass in a paddock, then it isn't helpful for the biologist to give the mathematician a lesson on all the intricacies of grass growing and grass eating. It would be better if the biologist comes with a defined question, such as 'how does increasing the number of cows in a paddock affect grass regeneration?' and points out that the main elements in the system are 1. how grass grows (as some function of grass density) and 2. how grass is eaten (as some function of cow density).

If you want a book about mathematical biology that is written for biologists then I'd recommend "A Biologist's Guide to Mathematical Modeling in Ecology and Evolution" by Sarah P. Otto &amp; Troy Day