# Distribution of the number of clover leaves

Being no expert at all in this field I am just interested in emprical studies of the frequency $f(n)$ of clover plants with a given number $n$ of leaves.

I would suspect naively from general considerations that the frequency follows an exponential distribution.

Any hints are greatly appreciated.

• Roughly: You find around 1/10000 four leaves clover. If you want to get into the details, know that each observation isn't independent from the other (as two "clover" are sometimes the same individual sharing the same genetics) and the time of the observation (summer or spring) may change this rate (more four leaves in summer). I advise you to search this website to find good and referenced answers to your questions. If it is not what you were looking for, edit your answer to give what you understood from other questions and what you are still looking for. – Untitpoi May 13 '18 at 10:11
• @ Untitpoi Thank you for your comment. I would appreciate if you could be a little more specific which website I should search for what? Neither during the formulation of my question nor in the margin section of related stuff something relvant has popped up. – Dr. Wolfgang Hintze May 13 '18 at 21:59
• did you check that answer : biology.stackexchange.com/questions/57860/… the Tashiro et al. 2010 reference seems to be a good empirical study on four leaves clover! – Untitpoi May 14 '18 at 5:23

I have found a study [1] of 2017 (http://www.sharetheluck.ch/single-post/How-rare-are-four-leaf-clovers-really) which answers a great part my question, and I'd like to show those results together with some additional evaluation.

They have counted 5.7 million clovers and found the following numbers compared to 3-leaflet clover:

4-leaflet clover 1 in 5,076
5-leaflet clover 1 in 24,390
6-leaflet clover 1 in 312,500

For the 4-leaflet clover they have corrected appreciably the common figure of 1 in 10,000 (see e.g. the comment of Untitpoi here).

A logartihmic plot of these relative frequencies shows interesting features

(i) a fairly regular exponential decay of the frequency in the range n=4,5,6
(ii) a significant "exception" from this rule is the "normal" clover with n=3

How can these observations be explained?

It would also be interesting to extend the study to n>6, and maybe also to the range of "deficient" clover which posesses only one or two leaflets. The latter are most probably very rare so that the complete log-plot would resemble an inverted letter V.

The question of 2-leaflet clover was raised here [2] https://www.quora.com/What-are-the-chances-of-me-finding-a-two-leafed-clover. But no quantitative answer was given.

References

[3] https://en.wikipedia.org/wiki/Four-leaf_clover#cite_note-auto-6
A comprehensive reference which I have only partially explored up to now

Thank you, Dr. Hintze, for citing our work (http://www.sharetheluck.ch/single-post/How-rare-are-four-leaf-clovers-really). We were frustrated about the lack of a reliable source for the '1 in 10'000' estimation of the prevalence of 4-leaf clovers (it is most likely a circular reference that was once started simply by guessing), so we started our own research (complementing the philantropic side of our project www.sharetheluck.ch). This let us come up with the below-mentioned numbers. We do keep record of clovers with 7 and 8 leaflets, but we believe that the numbers are too small (yet) to be of significance. Substantially higher numbers of leaflets have beeen obeserved only after inbreeding, to our knowledge.

• @ U Sperling Could you provide the numbers for 7 and 8 even though they are not reliable enough? I'd like to put them into my graph and see if the rule continues approximately. – Dr. Wolfgang Hintze May 14 '18 at 11:48