First off, Tylor's entire theory is just that; it has no basis on really going out into the field an analyzing direct data. In fact, he addresses a concern of the reader that the data he collects from people out in the field might be disingenuous, or erroneous. On this note, Tylor, unlike Morgan, enters into a question begging premise with his explicit explanation of culture ``clearly'' evolving. While he states that the same causes could have produced different culture, the fact that the cultures are similar, is clear and distinct proof of the evolution. To this end, he states the fact that two distinct people let's call them Smith and Jones, in the East and the West come up with identical observations of two different cultures proves the veracity of the observations, to which one may conclude that these cultures have evolved from the same ``causes''. Something he does not directly address is the fact that if the two observations are different, then what does that say about the two cultures? Tylor argues that it shows that the cultures are in different stages of development. To use a cliche, it is a win-win situation; to reference Popper, he does not put his theory forth for falsification, making the theory about as accurate as Freudianism: there's no evidence, so ad hoc patches may be made. The link between Tylor and Herbert Spencer then is apparent: they are working, not from the ground up, but from theory down. Both Spencer and Tylor are making the facts fit the theory, not the other way round, as a result their arguments are tautological.
Tylor's argument about the diffusion culture within a nation and its resulting similarity being based on common consensus is another link to Spencer. Through this common consensus of people, can we then classify culture in order to compare them.[4, p. 32] Spencer noted that the will of the people, or a society is based on the averages of the will of individual. [5, p. 13]
Lastly, the largest link between Spencer and Tylor is the use of nature to justify the evolution of human-kind. Throughout Tylor's article there are common analogical references between nature and humans. His entire section on causality demonstrates that link: just as in nature nothing happens without due cause, in human-kind, nothing happens without due cause. Hence, the natural evolution of human-kind from savages to civilization is demonstrated through differences - advanced technology.
The evolutionary theory of mankind was not endemic to Tylor and Spencer, both Marx and Morgan held this belief. However, Marx and Morgan grounded their theories on the material production of cultures. Morgan worked his way up from the actual practices of the varying cultures he observed. Unlike Tylor, this placed Morgan's theory on the table to be falsified (leading to the easy deconstruction of his theory later). However, it also made his theory stronger at that moment.
Time and again, Morgan referred to the creation and evolution of the savage and barbarian civilizations as a necessary product of the living conditions of the tribes. From the evolution of the body politic, property based governments through the necessity of the establishment of the family for kinship based governments.[3, p. 43] Morgan also makes reference and explains in detail the necessity of a seemly insignificant artifact with which to draw the evolutionary lines, pottery, as resultant of a material need for storage of food, pointing to the existence of other low-tech storage mechanisms like basket-weaving, as a pre-cursor to hi-tech pottery making.[3, p. 49-50] In these respects, it seems that Morgan is using Marx's argument that evolution is not applicable in the natural physical sciences sense, but rather as a means to an end: survival.
Morgan's base premise as outlined in the beginning of his essay also points to the fact of material causation: ``[the tribes'] struggle with opposing obstacles while winning their way to civilization.''[3, p. 41] And mentions this point again, when referring to the powers of comparative study not in temporal relations, which he regarded as ``immaterial'', but conditional relations: ``...different tribes and nations on the same continent, and even of the same linguistic family, are in different conditions at the same time, ... the condition of each is the material fact, the time being immaterial.''[3, p. 48]