In keeping with the concept that people of earlier ages were not stupid, it was long understood that most reproduction produced offspring that somehow displayed combinations of the traits of the parents.  If you bred individuals with some particular trait in common, you increased the chance that such a trait would be prominent in the offspring, but it didn't always work that way.  You could make plant cuttings and pretty much get a duplicate plant, traitwise, but pollination produced the same sort of mixtures that animal reproduction gave.  How did it all work?  Were there hidden rules that could be discovered and applied?

Gregor Mendel was fascinated with science and Nature, but in order to get enough training he had to enter a monastery in what was then Austria (now Brno in Czechia).  In a classic example of using the materials at hand (and the fact that the place needed him to be a farmer), Mendel took advantage of the monastery's production of peas:  for years he bred peas in special separate plots, focusing on a few features that seemed to come in just one-or-the-other varieties (such as Tall / Short, or Wrinkly Pea / Smooth Pea) that he could isolate in a "pure" form.  After hundreds of tests, with new plots of hybrid plants and plots of hybrid-hybrid crosses, Mendel developed the first basic rules of what would come to be called genetics.

Mendel decided that traits were determined by some sort of internal code pieces called genes.  For any particular trait, there might be code variations that changed the nature, like leaf color, or degree (height) of the trait, such as a variation in the Height Gene for Tall and one for Short.  These variations he called alleles, which are carried in each individual in pairs (although there may be way more than two allele variations in a whole population, each individual generally just gets two ,with exceptions for multiple copies of the same gene, one from each parent), of which only one is passed on to each offspring.  For each trait that is determined by a single gene (many traits are coded through multiple genes), an individual's particular version of that trait is a product of their two alleles.  Mendel thought that every single allele pair was sorted separately for reproduction, which turned out later to not be true, but many of them do sort independently.

As a side effect of Mendel's choice of "either / or" pea traits, he also discovered a genetic feature called dominance, where the presence of a dominant allele can completely hide the presence of a recessive allele.  This either-or condition was necessary to his working out genetic rules, but it has since been found (and he probably realized) that many traits don't follow such a pattern.  Many allele effects are not that strong or weak, but rather blend to produce the trait.  (In human eye color, very dark alleles can be dominant over very light alleles - brown can dominate blue - but middle-strength alleles blend, such as when green and light brown produce hazel)  It also turns out that many traits, in fact most traits, are a product of at least two genes working together, two alleles per gene;  these multiple-gene traits do follow rules based upon Mendel's discoveries, but the complex mixing of many alleles makes predictions of offspring traits a matter of complex probability.  With all that we know of genetics, breeding racehorses is still a matter of mating parents with desired traits and hoping everything mixes properly in the offspring (racing ability is a multiple-gene trait), which is what people have been doing since long before Mendel was born.

Mendel wrote and published several papers on his discoveries, but no one in the scientific community seemed to notice, possibly because no one had taken such a mathematical approach to biology before.  When he died, as far as he knew his research and findings would make no difference to the world.  However, in the very early 1900's, three scientists investigating the same sorts of processes discovered Mendel's work, and those papers became the foundation of a basic building block of biology today.

We know a bit more about genes today.  The researchers who followed up on Mendel's work through the 20th century discovered some additional details:

Groups of genes can be linked together.  Researchers in Britain and the Netherlands, building upon Mendel's rules, found that seemingly unrelated alleles might follow patterns to suggest that they were being passed on as a connected whole (Mendel thought that genes were all separate when passed on).  It turns out that our cells do not carry thousands of separate codes floating about;   we know now that the DNA of gene codes are bound together along the lengths of chromosomes.  This is called linkage:  for example, genes that are found on sex chromosomes (but aren't necessarily connected to gender) exhibit what's called sex linkage.  One feature of any species is its characteristic chromosome number, usually an even number in sexually-reproducing species because of the pairs  (humans have a chromosome number of 46, for 23 pairs).  There are advantages and disadvantages to both low and high chromosome numbers:  with low numbers, the distribution of copies that must happen whenever new cells are made is more reliable - there are fewer chromosomes to copy and chromosome copies to distribute properly;  but with higher numbers, the sorting of various potential combinations goes up, increasing variability in offspring, which increases evolutionary flexibility.  The numbers can vary widely.

For each chromosome gotten from one parent, there's one from the other that "matches" it, with spots for all of the same genes even if the specific codes, the alleles, differ.  These pairs are called homologous chromosomes.

About twenty years later, as it became obvious that linkages could occasionally be broken, it was discovered that pieces of  homologous chromosomes could be swapped during certain cell events.  This process, called crossing over, supplied yet another way that alleles could be recombined.

One weakness of Darwin's original theory is that it could not explain where "new" features came from - natural variations couldn't really explain how snake venom evolved from salivary proteins, for instance.  But many years later, in work mostly with fruit flies, mutations were discovered:  spontaneous changes in genetic material, producing new alleles that produced new variations on traits.  Soon it was found that x-rays could induce mutations, with greater doses making more changes.  We now consider any change in DNA, whether it is in gene codes or not, to be a mutation, and it is known that mutations to a gene will usually have no effect on the coded trait. When an effect does happen, it is most likely going to be bad, but occasionally it will produce a valuable change.  And a particular type of mutation from crossing over can produce duplicate genes in offspring, allowing for the mutational change of an existing trait (say, snake saliva to venom through changes of the "extra" saliva gene) while preserving the original action (not losing the original saliva protein).  This might also explain why more "advanced" organisms seemed to have more genes than more "primitive" ones.    Genetic redundancy works these two ways - coding is redundant and is hard to effectively alter, and "extra" or redundant genes may be produced.  The extra genes, according to recent research, have at least 4 functions if they are not shut off or deleted:  they can help produce more of the coded protein;  they can be available to perform if the "original" fails;    they can become involved in differential expression, allowing fine-tuned regulation of production (especially in multi-step chemical pathways);  and they can develop a new function, possibly dramatically different from the original, which was mentioned above as important to evolutionary "jumps." 

Work with a bread mold, Neurospora, in the 1940s, led to the discovery that allele mutations were producing changed traits by affecting single enzymes (which are proteins) in the mold's metabolic pathways, leading to a clear idea of what exactly a gene is:  a code that is used to make particular proteins.  Cells then use those proteins to create the "traits" that Mendel connected to genes.  Mendel's height gene, for instance, codes for a type of plant growth hormone protein.  What makes alleles different is that they produce proteins that have slight (or major) molecular differences, changing how they work.  The definition of "gene" itself has continued to evolve;  this simple one works at the introduction level.

As mentioned, the Neurospora mutations affected single enzymes in a pathway that used several.  This is one way that multiple-gene traits work.

DNA had long been suspected of being the coding material in cells, but when broken down to its handful of components, it seemed too simple to be able to carry such complex information.  However, during the late 1940s, work done with phages, viruses that use bacterial cells as sources to produce more viruses, showed that in many circumstances the only viral material getting into the host cell was DNA, and that lone molecule supplied all that was necessary for the cell to make and assemble the next generation of viruses.  DNA could act as a code, and it could carry all critical information all by itself.

During the 1950's, work done by James Watson, Francis Crick, Maurice Wilkin, and Rosalind Franklin led to an understanding of how DNA can hold complex information on a molecular level.  They found that the molecule was a two-stranded, cross-connected spiral, called  a double helix, and that a type of component called a nitrogenous base, in only 4 varieties, produced the code from their sequential order along one strand.  Since each base type will only connect to one other type across the way, the two strands could be separated and a new strand added on that would exactly duplicate the old complement.  Most mutations arise when some aspect of the sequence is changed.

The four nitrogenous bases (there is a fifth, used in RNA) are Adenine, which cross-connects only to Thymine (and vice versa), and Cytosine, which only connects to Guanine.   In RNA, Uracil replaces Thymine and cross-connects to Adenine.   Inside an actual gene sequence, each 3-base sequence on the DNA strand is a codon that will be translated into one amino acid of the protein coded for.  Often a single base-change in a codon will translate to exactly the same amino acid (or one very similar), which is the molecular basis of that one type of genetic redundancy.  More detail on how this all works appears much later in the book.

Since Mendel, it has been discovered that in some circumstances for an individual, having two different alleles for a trait can be better than a matched pair of the same alleles, a condition called hybrid vigor.  This often is the reason that human genetic diseases have spread through a population.  For example, the gene for the oxygen carrier hemoglobin has a allele that makes a nonround version of the protein when no oxygen is on it;  if you get a pair of these alleles, it gives you sickle-cell anemia, a dangerous disease that affects the shape of red blood cells and impairs circulation.  In areas where malaria, a disease caused by a blood parasite, is common, people carrying one regular hemoglobin allele and one sickle-cell allele have more resistance to malaria than those with two regular alleles, giving them an advantage that passes sickle-cell alleles to their offspring.  Other genetic diseases may have similar effects:  cystic fibrosis alleles might make single-carriers resistant to diarrhetic diseases (which kill huge numbers across the world), Tay-Sachs seems to produce a tuberculosis resistance, and schizophrenia (which is a multiple-gene trait and harder to sort out) may in some combinations increase creativity and the willingness to take risks, important features in human societies.

Over recent decades, the role of genetics in traits of all kinds has become a major focus of research.  As a bridge to answering those questions, lots of high-profile work has been done in the analysis of genomes, or the analysis of the total DNA carried by particular species of organisms (or, really, by an individual selected as a representative).  Genomes have been determined for many disease organisms and popular research organisms, as well as through the Human Genome Project.  Of course, knowing the sequence of all of human DNA doesn't tell you which gene does what, or even what all of the non-gene DNA does, but its a useful step.

Very recent work has led to the hypothesis that changes in parts of the DNA involved in regulating gene expression, especially a type called a cis-regulatory element, may be even more important to evolutionary changes than gene mutations.   It may not be so much what we have as how we use it.  Also, since epigenetic modifications, defined below, can sometimes pass an "adjusted" form of a gene to offspring, that has evolutionary implications as well.

Warning:  prepare to abandon your preconceived notions about reproduction!!!   Some of this repeats earlier concepts, but they bear repeating.  And some otherwise-reliable sources of basic biology information gets these wrong as well.

There are two basic forms of reproduction in living things, asexual reproduction and sexual reproduction.

ASEXUAL REPRODUCTION.   In asexual reproduction, offspring are genetic copies of the original. They may or may not be physical copies - all of your cells, produced asexually, have the same genetic make-up, but they are not physically identical (you'd be a formless blob if they were).  This ability to exactly pass on a parent's genes to offspring is a huge evolutionary advantage - it's the only form of reproduction that really is reproduction.  But there is a problem:  evolution, adapting to changing environments, depends upon variation in a population, and there just isn't much in this approach.  A change that can hurt one individual should be equally damaging to all.  To survive over the long haul, asexual reproducers usually produce huge numbers of offspring.  This allows some variation, from mutation (which rarely is good, but if you make a trillion offspring your odds for a beneficial change get better) and often can spread offspring out so harmful local changes will miss some.  This evolutionary need to generate offspring on a large scale usually keeps such reproducers small.  Many prokaryotes make and share small collections of select genes, plasmids - this is another way to introduce variation, and often the shared alleles are beneficial under local conditions.

SEXUAL REPRODUCTION.  It does not require two parents;  many many sexual reproducers can accomplish it with just one individual that is simultaneously male and female (and even genders are not required - many sexually- reproducing protistans and fungi do not have male and female forms, or have more than two genders).  In sexual reproduction, single sets of alleles from two sources are combined in offspring.  The huge advantage here is the mixing aspect of the allele sets:  potentially, every individual produced can be different from every other one, increasing the variation that evolutionary selection works on.  This allows evolution when only small numbers of offspring are made, a necessity for the sustaining populations of larger organisms.  The disadvantage, of course, is that exact genetic copies cannot be made, even of extremely successful individuals.  You can't pass on everything that makes you what you are, or even preferentially the best aspects - it's all luck, even if the natural selection odds work in your favor for a population.

In general, asexual reproducers are small, often tiny, and capable of producing the huge amounts of offspring needed for meaningful variation.  Sexual reproducers exist across the range of organism sizes, and produce offspring numbers roughly according to their chances of surviving long enough to make offspring on their own.  Some organisms are capable of reproducing either way according to circumstances - one wonders why this option isn't more common - and a few groups of organisms reproduce first asexually, then sexually, then asexually again, and so on, following a pattern called Alternation of Generations.

Of the three major circumstances under which alternation of generations has evolved, only one seems connected to the evolutionary advantages of being able to produce both ways:  several types of parasites, organisms that live by stealing resources from other, larger organisms, will go through an asexual stage in one host then a sexual phase in another, then back to a host of the first type, etc.  Making copies of a successful form alternates with mixing genes from successful forms, worthwhile for complex life cycles with the odds stacked against them.  The other two circumstances where alternation of generations is common involve life cycles with at least one stage stuck in one place:  in animals, such types as corals asexually produce huge colonies, then generate swimming jellyfish-like forms that swim off and mate sexually and help to distribute offspring away from the original site;  in the early land plant groups, still tied to using open water for sperm to swim during mating, larger asexual reproducers could spread by way of airborne spores, but the sexual reproducing forms stayed small and in places where water could accumulate to support sperm.  

Today, relationships among organisms are often determine by comparative biochemistry, which can be done by looking for homology in three different types of molecules:

- Metabolic molecules.  Snakes might be grouped according to similarities in their venoms, for instance.

- Proteins.  These long sequential molecules provide lots of comparison points.

- DNA.  Also a long sequential molecule, its assumed that close relatives will share similar sequences, but once two groups lose contact, they will accumulate mutations at different spots at a predictable rate over time, especially in non-gene areas (which may or may not be true).  Differences in DNA sequences are used like molecular clocks to decide when the family tree forked, how far back in time two organisms shared an ancestor.  There's a huge amount of uniformitarianism in the assumptions involved, but for the moment folks seem to accept the calculations as trustworthy.

It was soon recognized that what really changed in an evolving population was the frequencies at which certain alleles appeared, since they were what produced Darwin's selected traits.  What changes is a gene pool - the overall totalities of alleles in a population.  But what might influence how allele frequencies might change over time?

Godfrey H. Hardy, an English mathematician, and Wilhelm Weinberg, a German doctor, developed a set of rules under which the allele frequencies in a population would stay the same indefinitely:  this is called Hardy-Weinberg Equilibrium, sometimes the Hardy-Weinberg Law.  It kind of has had a backwards effect on evolutionary theory.  We know that allele frequencies do change as species evolve - this law about the conditions under which they would not change tells us what factors must be involved.  These rules work best applied to "new" alleles that appear through mutation, and how once in place they can "hang around" until a change in conditions makes them useful.

NO NATURAL SELECTION.  Well, obviously natural selection has an impact on evolution, but a potentially-useful mutated allele can be selection-neutral at first.

NO SEXUAL SELECTION.  (Originally no mating selection, also, all population  members needed to breed and produce the same number of offspring)  This amount to No sexual selection.  Mathematically, all members must reproduce as well.  The original rule needs to be reinterpreted for modern knowledge;  Hardy and Weinberg only considered sexual reproduction with separate parents, but any kind of sexual selection (even in asexual reproducers) could affect allele ratios.

NO MIGRATION of members in or out.  This would remove alleles from a population or bring in others.  This led to the realization that the more isolated a population is, the more chance that the other evolutionary effects could work without blending with alleles from populations adapted to perhaps different conditions.  It also became obvious that connections between populations in somewhat different environments might preserve a "type" suited to both but not particularly suited to either.  Something else can happen in isolated groups evolving in similar environments:  genetic drift comes from the unique combinations and mutations (which, after all, occur randomly) that change the flow of evolution in each group, producing separate species when it would seem that natural selection would have kept them the same.

NO MUTATION.  This process actually alters alleles.  Even though the odds for a beneficial mutation are not good, it still can have a profound effect on how a group evolves.  For a new mutant allele, once in place, it is very unlikely to mutate again.

POPULATION MUST BE HUGE.  In a population of only 100, any loss of an individual (and their alleles) will have a strong effect on the gene pool frequencies;  the more individuals in the group, the harder it is for chance occurrences to strongly affect the gene pool.  This also means that all of the other factors will affect a small group more powerfully than a large one.  Some processes are based upon this principle:

- The founder effect is used to describe what happens when a small group breaks off from a large population and becomes isolated.  The group's gene pool probably is not a duplicate of the larger group's allele mix, changing the possible combinations and altering the potential direction of the founder group's evolution.

- The bottleneck effect is made when some catastrophe reduces a population to a much smaller group, which then evolves based on that restricted gene pool.

Basically, any situation that reproductively isolates one group from another allows them to set up their own separately-evolving gene pool.  It turns out that this can be done in more than the obvious way...

- Geographic isolation.  When groups become physically isolated from one another - one winds up on an island, or separated by a river, mountain range, desert, whatever - this will give you separate breeding populations.

- Niche isolation.  A niche is a functional "spot" or "job," a role in an ecosystem that can be performed by some type of living thing.  Niches are determined by place, time, and relationships.  Most ecosystems have a top predator, for instance, although just what species occupies that niche varies in different places, and in a single place that may change from day to night or season to season.   Darwin's finches represent a founding population whose descendants split into different specialist species.

- Temporal isolation (time-based).  This can be a type of niche isolation, if a single species begins to break into a day-active group and a night-active group.  It also might be when a parts of a group vary by breeding periods, which is not a type of niche isolation.

- Behavioral isolation can arise from many different types of behavior:  groups with different courtship rituals, or which cease to recognize each other as potential mates, are examples.

- Mechanical isolation.  In groups that copulate (and many do not), occasionally changes in the physical features of genitals can isolate a group.  There are species of beetle that show this isolation.  It also occurs in plants that interact physically with pollinators, where the shape of pollen or flower parts can prevent exchanges.

- Gamete or zygote-based isolation.  Sometimes a mutational change in chemistry will cause a rejection of sperm or zygote (the first cell of the next generation) so that one subgroup can no longer reproduce with the other.  This may be more common with plants, where acceptance or rejection of pollen can be an important trait.

These ideas are important aspects of a biology discipline called biogeography, which is concerned with the broader distribution of living things.  Biogeography has been a huge source of evidence for the theory of evolution by natural selection, by how often features of related organisms in different ecosystems reflect the differing natures of the environments.

You have inherited features that are not in your genes - a particular language and culture, a particular community and physical location, things that came to you both from parents and from others.  These can be passed down through generations, but are not passed as packets of DNA code;  factors such as these are called memetics factors.  This term is new and going through quite a bit of fluctuations of meaning - more and more, this refers to the details of DNA processing, packaging, and regulation mentioned above.  To others, this is a broad area including anything heritable but not necessarily carried by  DNA primary gene sequences.

Other organisms can pass along memetic factors through learning, placement, and other things (this area seems to be gradually being separated from the "mainstream" definition of epigenetic).  Sometimes cells pass altered parts on to offspring, which duplicate the altered parts and pass them on also.  The maternal environment around developing seeds, eggs, or embryos can affect developmental processes.  This is, in a way, the inheritance that Lamarck's theories were based upon, so he wasnt completely wrong.

An entire subdiscipline, memetics, has grown up around this idea, with memes being essentially inherited non-genetic information.  Whether such inheritance can really be described in classic evolutionary terms is a bit controversial still, but the term has caught on big time in cyberspace.  This term seems to be more and more separating out as what was one of the broader bits of epigenetics.

When the term epigenetics was first applied, it referred to what are now called memetic features.  It now is used to refer to the activation and deactivation of genes.  This involved small molecules "clipped" onto the DNA to prevent the codes from being accessed.  It would make sense that most of our genes would be deactivated in any given cell, or at any given time.

RELATED LINKS - 

A TIMELINE of genetics discoveries (pdf).

Manic-Depressive Disorder as a Multiple-Gene Trait.