How can science support or challenge the concept of Karma?
They are perfectly compatible. The teaching of Karma is about latent (potential) result of our actions and choices. Science is in complete support with the idea of potential energy, latent results etc. It's just normal causation, albeit its subtle/hidden aspect, nothing magical.
It's like, when you act like a jerk, it leaves aftertaste with people, and then it comes up in the middle of other situations sooner or later. Or, you keep rushing in your daily life and leave simple things not taken care of, like taking out garbage or paying bills - and then these little things accumulate and really interfere with your life. It is stuff like that. Our actions, our intents leave residue, they create some little tensions in our mind, in other people mind, in the fabric of everyday things - and that stuff eventually comes up as some funky result downstream. I repeat, it's not magic, it is totally normal stuff - just hard to see because it's subtle.
If you need scientific explanation to Kamma and Vipaka is all about probability and possibility due to chain of causes and relative effects. There are different type of kamma some are generate vipaka at same moment and some take longer time. E.g 1. if you hit a person you will be get the respond within seconds. 2. Think that your house full of rats and you keep some poison to get rid of it and if you have a child in your home there is a great risk of consume poison by child as unaware of it and will be fatal.( I have read news article few months ago. Incident was there are product to kill rats looks like a chocolate and eaten by child and killed.) 3. If you cut a tree today you will not get vipaka sooner. When cut trees collectively long period the vipaka will be generated gradually with the time. So this is about probability of chain of causes and effects. There is no mystery about Kamma and Vipaka. If Kamma and its relevant vipaka are linked to privious life to this life (as rebirth or reincarnation process) is more close to mythical and speculative. It's like saying "Don't kill butterflies as colors of rainbow will fade away". If you mention "Don't cut down trees as earth will burn by sun" is more wise statement and scientific.
The word 'kamma' means 'intentional action' and has no explicit relationship to ideas of reincarnation. The teachings attributed to the Buddha say:
Intention, I tell you, is kamma. Intending, one does kamma by way of body, speech & mind.
From intentional actions (kamma) there arise 'results', called 'vipaka'.
For example, you have an intention to have & maintain a romantic relationship & enter into & engage in such a relationship. This is kamma. Then later, due to certain causes relating to incompatibility, the relationship ends, which is contrary to your intentions. As a result (vipaka), you suffer from sorrow & unhappiness due to not getting what you want. This is 'kamma-vipaka', which science obviously does not deny.
The following link explains kamma: Kamma in Buddhism
According to my opinion... When a child born, he weeps, plays, through his legs without knowing how to do, why to do and what to do. This action of doing things is called karma. After some couple of years, the child gets to know, how to do the things, why to do the things, what to do for them is called the science. In this scenario, to do the things or execute the things is karma, and to doing or execute the thing with rhythm, sequence, a manner is called science. It can be in many forms like psychology, sociology, physics, maths etc... Karma did not tell us how to do, it just an action without knowing anything but science gives us a method of doing things...