I've previously argued for a conceptual breakdown of natural selection into components representing death and reproduction: natural production and natural elimination. The rest of this post describes some orthogonal concepts.
The term "selection" commonly refers to a choice between alternatives - and the term "natural selection" was coined to indicate that the chooser didn't have to be a breeder, or even an agent: nature could choose. However, IMO, things went rather downhill for natural selection after that. After a while, biologists started to use the term "subset selection" to refer to this simple choosing but they decided that this wasn't much use when considering how a sexual population produced the next generation, since that process also involved transformational changes. The conception of selection was enlarged to handle this more complicated case. That was, I think a big mistake.
Scientists outside biology have another word for "subset selection". They call it "filtering". Filtering is an important process which explains a lot about adaptation in nature. Filtering applies to organisms when they die. Filters may also be applied while choosing mates, or during sperm competition. However, though filtering is an important concept, it doesn't explain everything.
In computer science, filtering is often combined with sorting. Sorting is a common and important process in nature. Rocks are sorted on beaches and molecules are sorted in the atmosphere. I think we can get some clarity back by using the terms "natural filtering" and "natural sorting" instead of "natural selection". I have previously written a whole article about natural sorting.
Unfortunately, sometimes explanations of natural phenomena in terms of filtering and sorting can also become contrived. One problem is that filtering is a binary process: either items make it through the filter or they don't. Filtering is a reasonable metaphor for life or death situations. However it seems less applicable to other aspects of reproductive success. Offspring counts are still somewhat discrete, and it could be argued that they consist of a series of selection events. Resource acquisition can be treated in the same way: either an item of resources is obtained or it isn't. However, here it looks as though we are approximating a continuous function with a series of discrete steps. That kind-of works - but sometimes, it is just contrived and pointless: shoehorning the phenomena into the model.
When phenomena appear continuous, using a continuous model makes sense. My proposal for a continuous modeling framework involves the common concepts of "reward" and "punishment". The idea is that events can have positive or negative on fitness. Positive impacts are rewards and negative impacts are punishments. Other consequences of events are deliberately neglected - for the sake of keeping things simple. As with natural selection, we can have agent-free versions: natural reward and natural punishment.
Reward and punishment are common consequences of actions by agents. However here it is important to remember that natural rewards and natural punishments may happen without regard to the agents previous actions. There need not be any attempt reinforcing of behaviour going on. Nature may be capricious.
In standard evolutionary theory, natural reward and natural punishment are currently most frequently referred to as favorable and unfavorable selection pressures. What I'm proposing here are new names for these existing concepts.
Reward and punishment are concepts from psychology. This is one of the expected application domains. Rewards lead to reinforcement and reproductive success of patterns af various levels in the brain, from synapses to axon firing patterns. Similarly punishment results in weakening and destruction of such patterns. In other words, use of these terms isn't intended as a metaphor, reward and punishment in psychology would be a straightforwards applications of these evolutionary concepts.