Darwin's Postulates

Four Postulates of Evolution

(1) The potential for a species to increase in number

In nature not all organisms are strong enough to survive. Some of them die earlier before they reach the reproductive age, leading to a decrease in their species and their population as a whole. Then there are others who reach the reproductive age but don't reproduce easily because their reproductive age is much more older than other species. For example turtles, they have a long life-span but little signs of reproductive senescence. They reach their reproductive age somewhere between 10 to 59 years of age. Their long life-span compensates the fact that they don't reproduce that often or that easily.

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(2) The heritable genetic variation of individuals in a species due to mutation and sexual reproduction;

When Darwin developed the theory of natural selection he lacked the model of mechanism of inheritance. This left him unable to interpret and understand his own data which showed Mendelian ratios. Even though Darwin couldn't totally reach to evolution like we do today he helped us understand today's concepts. Variation exists in genes because of mutation. In sexual reproduction we can see there's genetic variation because the sperm and the egg are produced containing different combinations of genes than those from their parents.
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(3) Competition for limited resources

All organisms compete for limited resources, especially when it comes to resources that help them stay alive like food. Today competition is an important factor which influence our animal and plants distributions. Competition eventually leads an influential role in evolution because of natural selection. It becomes even more intense with intraspecific competition, intraspecific means members of the same species are competing for the same thing. We know that members of the same species need the same resources, let's say all gorillas like bananas and they are lacking bananas, they are all competing for bananas.
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(4) The proliferation of those organisms that are better able to survive and reproduce in the environment.

This goes back to the idea of natural selection, defined as the process whereby organisms better adapted to their environment tend to survive and produce more offspring. Natural selection can be seen in all aspects, for example when it comes to reproduction. Some organisms might consider other members of their species more attractive than others so those who aren't that attractive inside the species end up dying without reproducing. Leading the others to create offsprings and repeat the cycle. We can also see it when it comes to survival, like members with short legs. They might run slower than those with long legs making it more likely for a predator to eat them. So those who have longer legs run faster, therefore survive because of natural selection.
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Works Cited

De Magalhães, J. (2014). Some Animals Age, Others May Not. Retrieved April 5, 2016, from http://senescence.info/aging_animals.html

Charlesworth, B., & Charlesworth, D. (2009, November 1). Darwin and Genetics. Retrieved April 5, 2016, from http://www.genetics.org/content/183/3/757

Lavergne, S., & Molofsky, J. (2007, March 6). Increased genetic variation and evolutionary potential drive the success of an invasive grass. Retrieved April 5, 2016, from http://www.pnas.org/content/104/10/3883.full.pdf

Michigan, U. O. (2008, November 26). Competition and Resource Scarcity. Retrieved April 5, 2016, from http://www.globalchange.umich.edu/globalchange1/current/lectures/competition/competition.html

Nguyen, D. H. (2016). Ways in Which Sexual Reproduction Provides Greater Genetic Diversity Than Asexual Reproduction. Retrieved April 5, 2016, from http://education.seattlepi.com/ways-sexual-reproduction-provides-greater-genetic-diversity-asexual-reproduction-6284.html