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When we say simple or complex organisms we are talking in terms of evolutionary history of an Organism. A ‘simple organism’ is considered to be primitive and has simple thallus organisation; The level of complexity of metabolism is also low. On the other hand a ‘complex organism’ refers to a more evolved form forming higher levels of structural and functional complexities. They are believed to have arisen from simple organisms.

One can say that it is the similar habitat that has resulted in selection of similar adaptive features in different groups of organisms but toward the same function. Spins of Opuntia and cactus are modifications of leaves to prevent the loss of water in desert.

These are the terms to classify organisms according to their evolutionary history. Simple organisms have simple structural and functional organisation and are considered primitive, whereas complex organisms have complex structural and functional organisation and are said to have arise from simple organisms.

The primitive earth or primordial earth contained large amounts of hydrogen, nitrogen, water vapour, ammonia and gases evolved from molten lava but no free oxygen was found. The primitive atmosphere was reducing which favoured abiotic origin of life.

Very high temperature, volcanic storms, Reducing atmosphere containing CH₄, NH₃, H₂ and water vapours.

Differential reproduction.

Evolution of marsupial mammals has resulted in flying phalanger, through adaptive radiation.

Evolution of placement has led to the evolution of a flying squirrel (independently).

The resemblance between the two, proves convergent evolution. 

S.L. Miller created an environment in a laboratory similar to the one that existed before life originate. In a closed flask containing CH₄, H₂, NH₃ and water vapour at 800^o C, electric discharge was created. The conditions were similar to those in primitive atmosphere. After a week, they observed presence of amino acids and complex molecules like sugar, nitrogen bases, pigments and fats in the flask. This provided experimental evidence for the  theory of chemical origin.

(i) Fore limbs of whale and bat and 

(ii) Thorns of Bougainvillaea are homologous organs.

Similar in function (fly) / different in structure and origin / analogous organs, convergent evolution.

Detailed Answer : 

Wings of a bird and a bat perform the same function of flying despite their structural dissimilarity. This infers that they are analogous organs and are the result of convergent evolution.

Darwin was influenced by Thomas Malthus and his book "An essay on the principles of population" in which he discussed that there are 'positive checks' that control geometrically growing population. The work of Malthus on human population growth in{act influenced him.

Fossils represent extinct organisms. Fossils show life forms restricted to certain geological time spans existing in the past. Fossils show ancestry of present day organisms. Some of the fossils are the connecting link between two groups of organism.

The forelimbs of frog, lizard, pigeon, bat, whale and horse have the same basic structural plan as human hand. In each case, the forelimb consists of an upper arm, forearm, wrist, palm and fingers. The upper arm is made up of humerus, forearm is composed of radio-ulna, the wrist consists of carpals, and the palm contains metacarpals and digits. The forelimbs of all these vertebrates are categorized as homologous organs because these are similar in structure and arrangements but are different in shape and function because as they developed along different direction due to adaption to different needs.

Miller's experiment - An electric discharge, was created in a closed flask containing CH₄ - H₂ - NH₃, and water vapour at 800^o C, thus creating condition of early earth with reducing environment high energy radiations and high energy radiations and high temperature, in the laboratory. This resulted in the formation of amino acids, supports chemical evolution of life. 

Miller's experiment does not support theory of Biogenesis it supports chemical evolution of life.

Detailed Answer: 

Experimental set-up : In a closed flask containing CH₄, H₂, NH₃ and water vapour at 800^oC, electric discharge was created. The conditions were similar to those in primitive atmosphere. 

Observations : After a week, they observed presence of amino acids and complex molecules like sugars, nitrogen bases, pigments and fats in the flask. 

Conclusions : 

(i) It provides experimental evidence for the theory of chemical origin, 

(ii) It showed that the first non-cellular form of life was created about 3 billion years ago. 

(iii) It showed that non-cellular biomolecules exist in the form of DNA, RNA, polysaccharides and protein.

Fossil-remains/impression of hard parts of lifeforms existed in past, preserved in sedimentary rocks volcanic ash, peat etc. They are written documents of evolution. 

Study of fossils in different sedimentary layers indicates the geological periods in which they existed, and showed that life forms varied over time. This indicates that new forms of life have evolved at different geological times in the history of earth.

When DDT was used for the first time, maximum mosquitoes died but few survived due to variation in a population. These mosquitoes show resistance to DDT and survived to reproduce successfully in the presence of DDT and gradually such mosquito population become DDT resistant within a time span of few years. According to Hugo de Vries, evolution is caused by sudden large differences in the population and not minor variations.

The use of DDT for the first time resulted in the death of maximum number of mosquitoes but a few survived. Later on it was found that mosquitoes continue to survive and reproduce even in the presence of DDT. It is because the sustained use of DDT made the mosquitoes resistant to DDT within a few years due to variation and change in gene frequencies in their population in relation to changes in environment within a time span of few years only.

According to Hugo de Vries the evolution is caused by a single step large mutation arising out suddenly in a population.

The fossils are the written documents of evolution Study of fossils in different sedimentary layers indicates the geological period in which they existed and showed that life forms varied over time. This indicates that various forms of life have evolved at different geologic times and hence new forms of life similar to modern organisms have arisen at different times in history of earth and forms the study of fossil record it has been concluded that evolution has taken place from simple to complex in a gradual manner.

(a) Development of DDT resistant mosquitoes. 

(b) Industrial melanism-Development of melanoid moth.

DDT is an insecticide-kills most of the insects, but some become resistant varieties, in much less time scale of just month or years. It is a chance event in nature-so chance mutation.