As has been mentioned in other articles, evolution is one of the more misunderstood theories ‌in biology.  This isn't because it is complicated.  Its beauty derives from its simplicity, but often the nuances that are overlooked.  

We hear about "survival of the fittest" and many immediately think of strength.  We hear about natural selection and many immediately focus on speciation.  Yet, the first claim is simply wrong, while the second isn't the most important element of the theory.

So, if it's not about strength or how species originated, then what is important.

The elegance of the Theory of Evolution is due to the concept of "fitness".  In its simplest sense, fitness refers to reproduction.  If you reproduce, "your kind" have another chance at life (1).  If one were to imagine an organism that had no competitors, no enemies, adequate resources, and a static environment then it could do whatever it wanted and survive.  It wouldn't matter if there were only one.  There would be no pressures to filter the reproduction process and there would be no evolution, beyond that which might occur by random errors.

Yet, even in this situation, we could make some predictions due to the nuances of the concept of "fitness".

Fitness requires that every organism survive long enough to reproduce.  So, even in our imaginary organism, there would still be selection pressures (2).  Those pressures would operate against random errors since there were no other elements to force change.  So one would expect to see more and more energy and development to ensure faithful reproduction of the parent organism, since the greatest threat to fitness would be the introduction of change.  If we were to consider the DNA model, then one might see more sophisticated error correction mechanisms.  In short, fitness would tend to converge towards uniform replication.

However, aside from our imaginary scenario, that isn't how things actually work.  There is the environment in which an organism finds itself, and potential competitors [NOTE:  Not predators and prey since they are not in competition] (3). So, true to any theory, evolution and natural selection allow us to make predictions about what we might expect to see happen.

In the following discussion it is taken as given that the environment is the primary factor affecting survival.

Obviously any creature will tend to be selected that possesses the minimum traits to survive and reproduce.  Any creature that doesn't, simply loses any opportunity to be represented in future generations.  Insofar as the developmental traits an organism possesses convey a benefit, only those that advance this capability will be represented in the future.

So, the first, almost trivial prediction from evolution is that we would expect to see all the organisms around us as being quite successful at the act of reproducing. This may seem obvious, but it does allow us to recognize those species that are robust versus those that are more readily threatened.  

Yet, reproducing isn't sufficient.  Offspring also have to survive.  So, again, we would expect to see traits that support organisms that are not just capable of reproducing but also having some means of ensuring that their offspring survive.  This provides a kind of generational overlap that ensures the continuity of a particular species.

In some cases this may involve parental involvement, in others it may simply be producing offspring in such huge numbers that probability is sufficient to ensure some degree of success.  Of course, once we have such processes in place, it is easier to predict that those organisms that have more opportunities to improve their offspring's chance for survival will also have greater representation in future generations.

Again, this could involve teaching offspring, it could simply involve protecting them.   Regardless of the process, we can use natural selection to predict that such a thing must exist and then we can examine a species behavior or traits to see how it achieves it.

Yet, natural selection is even more subtle than that.  Besides the organism, the specific traits necessary for increased fitness are also subject to selection.  Those traits are represented by a variety of phenotypic expressions that will determine form and function of the organism in question.

This can give rise to the impression that an organism is perfectly adapted to its environment, yet this would be missing the point.  It is precisely the environment that has shaped the organism.  The organism possesses the traits it does, because that is what the environmental filter it is subject to has "selected" for survival.  One doesn't discuss the usefulness of fins and gills for an animal living in desert sand, yet if we observed such a creature we would be forced to consider the role these structures play in promoting fitness.  

Moreover, natural selection then can also offer the ability to predict the persistence of traits in an organism.  As an example, the concept of vestigial organs is the antithesis of natural selection.  So, if we encounter something considered vestigial, what does evolution predict?

If an organ is vestigial, then it indicates that the organ cannot contribute to fitness.  It clearly doesn't require enough energy, nor does it incur a "cost" to the organism that has any material affect on fitness (4).  However, if an organ is considered vestigial and does incur a fitness cost, then we have a problem.  Such a claim is counter to what natural selection predicts, so it would appear that our concluding that an organ is vestigial, in that case, is probably wrong.

Any cost, no matter how small can impact fitness.  Why?  Unless we're using our imaginary organism mentioned in the beginning, then all organisms will have competitors for resources.  Whether it be for the same food, or the range, or something that is necessary for the organism to survive.  Therefore evolutionary "victory" invariably occurs to the organism that can capitalize on those resources faster or more efficiently than its competitors.  Efficiency may be producing more offspring, producing them faster, using less energy to do so, etc.  In every instance, there is a small but finite advantage accrued which will eventually result in such a competitor being capable of dominating the environment.  Once this occurs, the costs of survival to the other organism are increased [i.e. have to expend even more energy to acquire resources] and then their survival rate will diminish and the species will eventually go extinct (5).

From this we can see that natural selection isn't about strength or even speciation.  It is an explanatory theory that allows us to examine why we are the way we are [or any creature].  This is precisely why we share such a surprising heritage with other organisms.  Speciation is simply our classification process to show the subtle, but ultimately significant divergence experienced by varying levels of success (6).

Again, one of the success factors that can give rise to such speciation events, are to circumvent the competitive challenge of a superior species, by changing the rules of the game.  If you stop competing for the same resources, then an organism can gain an edge.  Cooperative social behaviors may create economies of scale over that of competitors.  From these simple processes, divergence begins.

In addition to the issues of natural selection, sexual selection must also be considered as a factor in determining traits present in a species.  However, this requires more careful consideration.  Sexual selection cannot trump natural selection.  In other words, a trait that reduces or is detrimental to fitness cannot prevail.  It cannot be made to prevail simply because it may be sexually selected for.  In that case, the selection process would be maladaptive.

Therefore when one considers sexual selection it can only play a role if it enhances fitness [i.e. accelerates natural selection] or has no fitness impact (7).  In the latter case, it would be exceedingly difficult to explain the presence of a trait since it may appear to be selected for, but it incurs no fitness cost whether it exists or not.

In that sense, sexual selection becomes a secondary selection pressure [as well as numerous other micro-selection pressures that may exist] and consequently acts as a secondary filter that is exerted upon a pool of viable mates that already meet the basic survival criteria.

(1) While evolution is often viewed from the perspective of individuals, it is important to remember that evolution operates on populations, not individuals.  Therefore, it is insufficient for individuals to succeed alone.  As a result, natural selection must favor the population for a species to be viable.

(2) The term "selection" often invokes a sense of purpose or direction in evolution.  However, there is no directed effort in determining survival.  Consequently the term "selection" is intended to convey the idea that an organism's survival is somehow contingent on its traits.  For example, falling off a cliff or being struck by lightning are not selection mechanisms although they may certainly have consequences for a population.  It is equally important to recognize that selection doesn't account for all traits, but only those that are capable of having a material effect on fitness.  For example, blue eyes may have no direct fitness effect [i.e. it doesn't specifically effect survival], but they may have a sexual selection component that allows such traits to extend into a population, but since there are no direct fitness consequences they represent a secondary selection criteria.

(3) Predators and prey are not direct competitors.  They represent a different kind of selection pressure in the same way that environmental influences do.  

(4) Fitness "costs" are often invoked to raise the question of why a particular trait exists or persists in a population.  Yet, this question is meaningless if there are no resource constraints that will affect fitness.  Everything "costs" something.  If that were the sole criteria of natural selection, then there wouldn't be any multicellular organisms [or life for that matter].  

(5) Depending on all the combined factors of organism traits and the environment, it is also possible for populations to achieve a kind of equilibrium where neither group achieves a sufficient advantage to dominate the environment.  Clearly in such situations, then any particular change can create an imbalance that accelerates an advantage or disadvantage in a short period of time.

(6) Much confusion occurs regarding gradual changes giving rise to speciation.  Usually the problem occurs because comparisons between radically different species are used.  This overlooks the millions of years necessary for such changes to manifest.  For example, it is easy to see the differences in dog breeds as a result of artificial selection.  Yet, the argument is often made that they are still all dogs and don't represent different species.  However, let's consider that all these different breeds have different characteristics.  Some may be stronger, bigger, smaller, faster, etc.  If we take these basic traits and now speculate how they would operate under natural selection, we can begin to see how this works.  The most obvious issue occurs because of size differences in animals which restricts breeding.  It doesn't matter that they are all genetically "dogs" at this point, this simply marks the beginning of whatever evolutionary trajectory they will follow individually according to their breed.  As their respective requirements for food change [because of differing abilities], then little traits that allow them to be better at something will begin to manifest.  Over a sufficiently long period of time, such differences may well have diverged to the point of where they are considered completely different species.  Some may go extinct, while others dominate.  However, there is little doubt that they would diverge because of their differing starting points. Contrary to some popular myths, such transitions do not typically occur in a single generation.

(7) Traits due to sexual selection are more apt to occur when there is an abundance of suitable mates.  In other words, the fitness of the population must already be assured against competitors.  Under those circumstances, then sexual selection can promote or attentuate other traits as long as it doesn't diminish the population's fitness.