There are two “sizes” of evolution: micro and macro. Microevolution is when there are small changes over short periods of time (centuries). Macroevolution is when there are large changes (like forming new species) over large periods of time (many millions of years).
In a way, these are the same thing, just over different timescales. Let’s start with the short-term version.
There are a few main points:
1) There is variation between different individuals. No two animals (of the same species) are exactly alike.
2) Much of this variation is inherited from parents and passed on to children. Children have similar traits to their parents. This is all due to the passing of DNA.
3) There are limited resources. Life is a competition for survival. Individuals must compete to find enough resources for survival, or to find a suitable mate.
4) An individual’s traits affect its chances of reproduction. An animal that is more adapted to the environment will be able to find food more easily, be able to defend itself, will better avoid predators, etc.
The main idea is that, given a population of animals, the individuals more adapted to their environment will produce more offspring than those who are less adapted. As a result, the next generation will be, on average, more adapted.
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Let’s say that you had a species of moth, which was mainly light-colored, but some individuals were dark-colored:
LLLLLLLLLLDDDDDD (38% dark)
Due to a recent change in the environment, the light-colored moths are more likely to be eaten than the dark-colored moths. Let’s say that half of the light moths die, while only a third of the dark moths die.
LLLLLDDDD (44% dark)
Now, all of the moths reproduce:
LLLLLLLLDDDDDDDD (44% dark)
Hopefully this (much simplified) example has helped you to see the basic mechanics involved for a single generation. You can see how the the proportion of dark moths has increased. If given enough time, there will no longer be any light moths. The species has evolved slightly to fit the environment.
Now, this example is actually based off of a documented event. During the industrial revolution, pollution darkened the color of trees and caused the light-colored peppered moth to die while the dark-colored version of the peppered moth was able to survive. Wiki: Peppered Moth Evolution.
Now, my example has a very clear distinction between between the dark and light groups, but that is not usually the case. More likely, one of the groups has a 57% chance of death before reproduction, while another group has a 56.5% chance of death. The differences are really small, but over enough time they can eventually change the species.
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Macroevolution is the consequence of microevolution. Let’s say that you have an original species. It is then separated into different groups, each of which occupies a different environment. This is basically what happened to the Darwin finches. The birds traveled from mainland South America onto the Galapagos Archipelago, a group of several islands. The finches were thus divided into separate groups because there was not much travel between islands.
Now, since the environment is different and the groups are isolated (independent), the different groups will evolve separately. On one island, the birds with long beaks might be more likely to survive. On another island, a short powerful beak might give better odds.
Eventually, the single species will diverge into several different species, because the groups will no longer be similar. This was the result.
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Now, this still leaves a hole yet to be explained: birds can evolve into other birds, but how to bigger changes occur (lizards -> birds for example)?
The explanation is that people tend to be unable to comprehend the amount of time involved.
People first developed farming around 10,000 years ago.
Earliest human remains: 400,000 years ago
The first hominids arrived 2,000,000 years ago.
Dinosaurs went extinct around 65,000,000 years ago.
Dinosaurs appeared around 230,000,000 years ago (lasted about 165 million years until extinction).
The first vertebrates appeared 380,000,000 years ago.
Earliest life was about 4,000,000,000 years ago.
Here is a chart that is somewhat to-scale.
Here is a neat example: Crocodiles are more closely related to birds than to lizards. At first this might seem impossible, but their common ancestor species lived literally a hundred million years ago, in the form of dinosaurs. There was never a half-bird-half-crocodile.
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Second, people tend to underestimate the complexity of the evolutionary tree. Many people imagine it as a very linear process. It is not. There are dozens upon dozens of branches at every step.
For example, take the evolution of horses. This is what people imagine: image. Now, this isn’t completely incorrect, but there is a lot of stuff left out. It gives the impression of one group of animals. In reality, a more accurate diagram is this image. Notice how there are over 20 different labels on the diagram, each of which is an entire genus (not species, each genus contains many species).
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I am literally running out of time to type this, so that’s all for now.