Odd pinnate 1

I have been pondering about the botanical category 'odd pinnate', the property of compound leaves, such as that of the ash tree, of having an odd number of leaflets, aka pinnae. As it happens, all the examples of ash leaves turned up by Bing are odd pinnate, with just the one terminal leaflet. Pondering most recently in the second half of reference 1.

The other day I picked a shoot from a bush with alternate rather than compound leaves to see whether that threw any light on the business. Probably from a bush over a wall at the corner of Pound Lane and Hook Road, across the road from the school.

In the snap above, apart from at the tip (below), the leaves are alternate and spaced at roughly equal intervals - which suggests to me that most of the growth takes place at or near the tip.

Additional buds in all the leaf axils, presumably ready to spring to life if needed.

I can't resolve the very tip of the stem with zoom on the laptop and a handheld magnifying glass is worse. But there is clearly something going on to the right of the base of the last leaf, edge on in the snap above, presumably the growing tip. And neither that leaf nor the one behind it, the penultimate leaf, have taken up anything like their final positions on the stem, with a lot of growth between the two yet to come. Plus some rotation.

Which may inform further inspection of pinnate leaves, but the concept of odd-pinnate is not relevant here. The leaves do not come in pairs and do not end in a pair or otherwise. The number of leaves on a stem is probably not very well defined and probably varies a good deal.

Google images suggests Cotoneaster, and a nursery from Ireland has some snaps which look very similar at reference 2. Cotoneaster dielsianus var. elegans. We have some kind of cotoneaster on our front wall, dominated at this time of year by red berries, but very attractive to bees and such like when flowering.

Bentham & Hooker, in their glossary, talk of abruptly pinnate for even pinnate and unequally pinnate or imparipinnate for odd pinnate. Abruptly captures the case rather well, while imparipinnate seems very old-fashioned, inkhorn even. But then, the first edition appears to date from 1886. With my copy being a 1954 reprint from RPPL.

I have not yet made much progress with reference 4, but I find this morning that the alternate arrangement of leaves is the first of the five orders identified by Bonnet in the middle of the eighteenth century, as snapped above from page 59. Later workers went on to characterise it as the simplest and degenerate form of the more general spiral, with a 180° step.

I expect I will find something about growing tips if I keep digging.

PS: more Google images. Not much for him to go on, from a plant sale near Cambridge. He says maybe a palm, maybe specifically a date palm. Apparently they are commonly grown from seed, presumably the stone from a date, for sale. We shall see!

References

Reference 1: https://psmv5.blogspot.com/2025/09/trolleys-998-999-and-1000.html.

Reference 2: https://www.promessedefleurs.ie/shrubs/shrubs-by-variety/cotoneaster/cotoneaster-dielsianus-var-elegans.html.

Reference 3: https://en.wikipedia.org/wiki/Cotoneaster.

Reference 4: Do plants know maths: Unwinding the story of plant spirals, from Leonardo da Vinci to now - Stéphane Douady, Jacques Dumais, Christophe Golé, Nancy Pick - 2024. Published by the Princeton University Press, printed in China.