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I have been reading a book ( Statistics for Biology and Health) and i encountered many of following bold text.

  • Consider a long DNA sequence of length N, where N is assumed to be so large that end effects can be ignored in our calculations.

In Shotgun sequencing also the saw similar thing :

  • The fragments are assumed to be taken at random from the original full-length sequence, so that if end effects are ignored, the left-hand ends of the fragments are independently distributed with a common uniform distribution over [0,G].

What does " end effects can be ignored " means?

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They are considering a model of a DNA sequence of quasi infinite size. They consider a case where the DNA sequence is so long that the fact that it has ends will only negligibly affect the conclusions of their model. This is likely the same as considering the DNA is circular.

To give you a similar logic, imagine a species where individuals live in different populations. All population can be placed on a one dimensional axis. The migration rate from one population to the neighbouring population is 0.1 (this is called a "stepping stone model" btw). Hence, the probability of not migrating is 0.8 (1 - 0.1 - 0.1). I can draw conclusions from such a model but it would be important to specify that I neglected the end effects and hence, I assumed there are a lot of populations (or that the population form a loop). Why did I neglect the end effects. The last population on each side cannot have a migration rate of 0.1 toward a population that does not exist. Hence, their migration rate must differ from the other populations. This is commonly called edge effects (rather than "end effects")

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    $\begingroup$ Out of curiosity, do people actually call these end effects in the context of DNA when this comes up? The more common term for these issues in a broader mathematical context in English is usually "edge effects." $\endgroup$ – Bryan Krause Jan 2 at 16:47
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    $\begingroup$ @BryanKrause I agree the term edge effect sounds more common, esp. in its use in population biology (info added in post). I am not sure I had ever heard "end effects" before but the term makes the meaning quite intuitive. $\endgroup$ – Remi.b Jan 2 at 17:38
  • $\begingroup$ Thanks - I suspect the author (or translator) of the text the OP refers to made a bit of a mistake here. I think if they had called them edge effects it would have been more easily investigated by the OP. That said, anyone familiar with the field would probably quickly infer that they meant 'edge effect' when writing 'end effect.' $\endgroup$ – Bryan Krause Jan 2 at 17:40
  • $\begingroup$ Perhaps end-effects is strictly correct when considering a one-dimensional object, such as a DNA-sequence. If you were considering a two-dimensional object, as you might in ecology when looking at a particular geographical area, then the area would truly have an edge, whereas a DNA molecule could be said to only have 'ends', not edges. $\endgroup$ – Jonathan Moore Jan 4 at 16:49

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