Mammillaria Spiral arrangement

Hi all , i would like to complete some data about spiral arrangement
to know what it's mean and how count look here (point3) :
http://www.mammillarias.net/wordpress_uk/f-a-q/

could you please do the count on some of your mammillarias ?
il will update the first post with results

Thanks

franck

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Mammillaria bocensis - (8;13) or (13;21)
Mammillaria deherdtiana ssp deherdtiana - (8;13)
Mammillaria deherdtiana ssp dodsonii - (5-8 )
Mammillaria hahniana ssp bravoae - (13;21)
Mammillaria heyderi ssp gaumeri - (8;13)
Mammillaria heyderi ssp gummifera - (13;21)
Mammillaria jaliscana ssp jaliscana - (13;21)
Mammillaria johnstonii - (13;21)
Mammillaria lenta - (13;21)
Mammillaria lindsayi - (13;21)
Mammillaria lloydii - (8;13)
Mammillaria longiflora ssp longiflora - (5;8 )
Mammillaria magallanii - (13;21)
Mammillaria magnimamma - (8;13)
Mammillaria mainiae - (8;13)
Mammillaria mammillaris - (8;13)
Mammillaria melanocentra ssp melanocentra - (8;13)
Mammillaria mercadensis - (8;13)
Mammillaria morganiana- (13;21)
Mammillaria muehlenpfordtii- (13;21)
Mammillaria mystax- (13;21)
Mammillaria napina - (8;13)
Mammillaria neopalmeri - (8;13)
Mammillaria nivosa - (8;13) or (11;17) or (13;21)
Mammillaria nunezii ssp nunezii - (13;21)
Mammillaria orcuttii - (13;21)
Mammillaria peninsularis - (5;8 )
Mammillaria perbella - (13;21)
Mammillaria petrophila ssp arida - (8;13)
Mammillaria petrophila ssp baxteriana - (8;13)
Mammillaria petrophila ssp petrophila - (8;13)
Mammillaria petterssonii - (13;21)
Mammillaria phitauiana - (8;13)
Mammillaria picta ssp picta - (8;13)
Mammillaria plumosa - (8;13)
Mammillaria polyedra - (13;21)
Mammillaria polythele ssp durispina - (8-13)or(21;34)
Mammillaria polythele ssp obconella - (13;21)
Mammillaria polythele ssp polythele - (13;21)
Mammillaria pottsii - (8;13)
Mammillaria prolifera ssp arachnoidea - (5;8 )
Mammillaria prolifera ssp prolifera - (5;8 )
Mammillaria prolifera ssp texana - (8;13)
Mammillaria rekoi ssp rekoi - (8;13)
Mammillaria rettigiana - (8;13)
Mammillaria rhodantha ssp fera-rubra - (13;21)
Mammillaria roseoalba - (8;13)
Mammillaria sartorii - (8;13)
Mammillaria schiedeana ssp schiedeana - (13;21)
Mammillaria sempervivi - (13;21)
Mammillaria sheldonii - (8;13)
Mammillaria sinistrohamata - (13;21)
Mammillaria sonorensis - (5;8 ) or (8;13) or (10;16)
Mammillaria sphacelata ssp sphacelata - (5;8 )
Mammillaria sphacelata ssp viperina - (3;5)
Mammillaria spinosissima ssp pilcayensis - (13;21)
Mammillaria spinosissima ssp spinosissima - (13;21)
Mammillaria spinosissima ssp tepoxtlana - (13;21)
Mammillaria standleyi - (13;21)
Mammillaria stella-de-tacubaya - (13;21)
Mammillaria surculosa - (5;8 )
Mammillaria tetrancistra - (8;13)
Mammillaria thornberi ssp thornberi - (5;8 )
Mammillaria thornberi ssp yaquensis - (5;8 )
Mammillaria uncinata - (8;13)
Mammillaria vetula ssp gracilis - (5;8 )
Mammillaria voburnensis ssp eichlamii - (8;13)
Mammillaria voburnensis ssp voburnensis - (8;13)
Mammillaria wagneriana - (13;21)
Mammillaria weingartiana - (13;21)
Mammillaria wiesingeri ssp wiesingeri - (16;26)
Mammillaria winterae ssp aramberri - (8;13)
Mammillaria winterae ssp winterae - (8;13)
Mammillaria wrightii ssp wilcoxii - (5;8 )
Mammillaria wrightii ssp wrightii - (8;13)
Mammillaria zeilmanniana - (13;21)
Mammillaria zephyranthoides - (5;8 )

i found an intereting doc while searching for info about spiral arrangement :


Phyllotactic Spectra in Cacti: Mammillaria Species and Some Genera from Rebutia Group
https://pbsociety.org.pl/journals/index.php/asbp/article/viewFile/asbp.1997.030/671

have fun

and another on the same "spirit" but about
Variable cotyledon numbers in Mammillaria beneckei:
http://www.stanoome.nl/wp-content/uploads/Article-M.beneckei.pdf

Interesting articles, though I was surprised to see him say that M. sphacelata ssp. viperina was related to M. beneckei. I know that Crozier's work on DNA placed M. beneckei next to M. sphacelata, but then it also placed M. halei next to Ortegocactus macdougalii, and M. theresae next to Neolloydia conoidea.

Which probably goes to show the difficulty in Mammillaria of determining the "right" set of markers and regions to sample within the DNA. I wouldn't want it just to confirm existing classifications, but these are a bit strange.

Hi Chris , i make a special page about articles found on the web here:
http://www.mammillarias.net/wordpress_uk/publications-and-articles/
since Crozier's work, other phylogenetic works have been done

if you know other study tell me i will add them