Necessary vs Sufficient: What’s the difference?

Laboratory researchers work to uncover the causes of events, whether the events in question are planetary motions, the movement of proteins within a cell, or the development of an animal tissue over time. In biology research papers, you will often see genes or proteins described as necessary or sufficient for a particular event to occur. What is the difference between these two concepts, and how can we determine when a set of conditions is necessary vs sufficient — or both?

Necessity vs Sufficiency: Defining the terms

Let’s start with a formal definition of the two concepts:

A necessary condition is a condition that must be present for an event to occur. A sufficient condition is a condition or set of conditions that will produce the event.”

Texas State, Department of Philosophy Blog

Here are a few basic real-world examples:

  • Having wheels is a necessary, but not sufficient, condition of being a functional car. In other words, a car needs wheels to function but having wheels is not the only thing required for a car to function (it also needs an engine, transmission, and a lot of other parts).
  • Being a closed figure consisting of four sides of equal length and equal angles is both a necessary and sufficient condition of being a square.
  • A sufficient condition of traveling from New York to Miami would be to take the train. In other words, taking the train from New York could get you to Miami but it’s not the only way to get there. You could also fly, drive, or even walk.

Necessary vs Sufficient conditions in biology research

The distinction between necessary vs sufficient conditions is straightforward in formal logic and geometry, but things get a bit fuzzier when translating these concepts to the messy world of live organisms. How are these terms used in the biology literature?

Below is a typical example of how biologists may establish a gene as necessary or sufficient for a specific behavior, using the common research tools of gene overexpression or gene knockout in Drosophila melanogaster:

necessary vs sufficient
Image Source: Journal of Neurogenetics.
  1. After artificially expressing the eyeless gene and inducing retinal development, the researchers thereby conclude that eyeless is sufficient for retinal development.
  2. After knocking out (i.e. deleting) the eyeless gene and observing that retinal development no longer takes place, the researchers thereby conclude that eyeless expression is necessary for retinal development.

In the above example, the conclusion (2) that eyeless is necessary for retinal development seems to follow logically from the experimental findings. But the conclusion (1) that eyeless is sufficient for retinal development has some problems, which are eloquently summarized as follows:

[To satisfy the sufficiency condition, it must be the case that] If eyeless exists, then a retina is developed (iii). However, proposition (iii) is clearly false as other genes and factors are required for complete retinal development: eyeless’s existence alone is obviously not enough to form a retina. It is evident that the set of cases where ‘eyeless exists’ is larger than the set with cases of ‘retinal development,’ which requires more factors such as genes at the downstream of eyeless and genes cooperatively functioning with it.”

Yoshihara M and Yoshihara M. Journal of Neurogenetics. 2018.1

The concepts of necessity and sufficiency can be clearly understood in the context of formal logic. However, in the biological context, it would be more accurate to say that ectopic or artificial expression of eyeless in a particular location is sufficient to induce retinal development in that location. In itself, the expression of eyeless is not sufficient for normal retinal development because many other genes and proteins are also required to create a retina. Nonetheless, in the biology literature you will often see necessary vs sufficient conditions established and discussed as they are in the example above. It is well worth your time to be aware of the nuanced differences between both concepts.


References

  1. Motojiro Yoshihara & Motoyuki Yoshihara. Necessary and sufficient’ in biology is not necessarily necessary – confusions and erroneous conclusions resulting from misapplied logic in the field of biology, especially neuroscience. 2018. Journal of Neurogenetics. (32):2,53-64, DOI: 10.1080/01677063.2018.1468443

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