January 13, 2021

VARIATION IN POLYSTICHUM ACROSTICHOIDES

NOTE: This post replaces 10 January 2021, whose errors were corrected. Also, a few links were added or replaced.

The Christmas Fern, Polystichum acrostichoides, in the un-glaciated lower Piedmont and Triassic basin of North Carolina, exhibits the diversity of color and form indicated below. erwin_pteridophilos advised that the source of the variation may at least in part be due to the expression (phenotypic re-emergence) of ancestral genes. This appears to be corroborated by observations of individual Polystichum acrostichoides with completely separate fertile fronds (unlike the usual situation in Polystichum acrostichoides where the fertile section is located at the end of an otherwise sterile frond), and in individuals with twice-divided fronds (unlike the usual once-divided fronds of this species).

What variation occurs in previously glaciated realms? Are populations there more diverse? Less diverse? Differently diverse?

LEAFLET COLOR
(1) Green https://www.inaturalist.org/observations/67675217
(2) Darkest Green https://www.inaturalist.org/observations/67971542
(3) Blue-green https://www.inaturalist.org/observations/67326452
(4) Bicolor
a. Blue-Green blade with green central vein https://www.inaturalist.org/observations/66442425
b. Bright Edge https://www.inaturalist.org/observations/67855800

PHYSICAL FORMS OF LEAFLETS
(1) EDGES
a. Shallow Serration https://www.inaturalist.org/observations/67326452
b. Shallow-Lobe https://www.inaturalist.org/observations/67538429
c. Lobed https://www.inaturalist.org/observations/67673243
d. Twice Divided, lobes which themselves are lobed https://www.inaturalist.org/observations/66804039
e. crested/fasciated leaflets, edges terminate in multiple divisions https://www.inaturalist.org/observations/67855570
(2) PLANE
a. Straight-ish; usual https://www.inaturalist.org/observations/67807301
b. Curved, sometimes doubly so (recurved) https://www.inaturalist.org/observations/67537716
c. Undulate (“crisped” in old parlance) https://www.inaturalist.org/observations/67634628
(3) LENGTH
a. Short: less than 2 inches https://www.inaturalist.org/observations/67854694
b. Usual: about 2 inches (5 cm) long https://www.inaturalist.org/observations/67675217
c. Long: much longer than 2 inches https://www.inaturalist.org/observations/67673345
(4) WIDTH
a. Usual: leaflets about 3/8ths inch (1 cm) wide when 2 inches (5 cm) long https://www.inaturalist.org/observations/67872751
b. Narrow (relative to length) https://www.inaturalist.org/observations/67312460
c. Wide relative to length https://www.inaturalist.org/observations/67544636
(5) TIP
a. Acute, pointed – usual case for mature plants https://www.inaturalist.org/observations/67673345
b. Blunt, rounded – all young plants https://www.inaturalist.org/observations/67311024 https://www.inaturalist.org/observations/67156829
c. Divided, also called “crested” https://www.inaturalist.org/observations/67673880
(6) EAR, auricle: located near the stem-side of the leaflet, points toward the stem tip.
a. Short - wider than tall https://www.inaturalist.org/observations/67591938
b. Usual - about as tall as wide
c. Tall - taller than wide https://www.inaturalist.org/observations/67538230
d. Separate - as a lobe, usually restricted to lower (basal) leaflets https://www.inaturalist.org/observations/67592332
(7) GAP (between adjacent leaflet edges)
a. Slight gap, usual https://www.inaturalist.org/observations/67591938
b. Wide gap https://www.inaturalist.org/observations/67635552
c. Overlapping, or touching along long edge https://www.inaturalist.org/observations/67569071

STERILE FROND FORMS
(1) LENGTH
a. Miniature: plants fertile when small, remain small in old age https://www.inaturalist.org/observations/66415414
b. Short https://www.inaturalist.org/observations/66923628
c. Usual frond length https://www.inaturalist.org/observations/67855528
d. Long, larger plants https://www.inaturalist.org/observations/67924419 https://www.inaturalist.org/observations/67855428
(2) DISPLAY
a. Various, upright & lateral https://www.inaturalist.org/observations/67855528
b. Upright https://www.inaturalist.org/observations/67855364
c. Lateral https://www.inaturalist.org/observations/67855428

FERTILE FROND FORMS
(1) Combined with sterile frond
a. Fertile portion of frond constricted in comparison to the infertile leaflets of the same frond; fertile portion of frond restricted to the top of the frond; fertile portion of frond shorter than the sterile portion. https://www.inaturalist.org/observations/67857342
b. Fertile portion of frond gradually blends into the lower infertile portion of frond; fertile portion of frond equals or somewhat exceeds length of sterile portion. https://www.inaturalist.org/observations/67675090
(2) Separate fertile frond https://www.inaturalist.org/observations/67673670

Posted on January 13, 2021 00:57 by mjpapay mjpapay

January 06, 2021

THE FIRST PLANT - Photosynthesis without sunlight.

THE FIRST PLANT (Photosynthesis without the sun!)

Submitted for your consideration, my speculations on the origins of chlorophyll that were very soon proven true by persons who had no idea that I had predicted their discovery whilst simultaneously I had no idea that they were trying to discover it. What? It is like this. In 2017 whilst rewriting the section on Synonymy, I got to thinking about the spectrum of organic molecules in comparison to the spectrum of light. I had a flash of inspiration. Where, I had been wondering, did chlorophyll come from? What was its original funtion? That’s when it struck me. The spectrum of light! We are not accustomed to thinking of heat as light – but it is! Heat is infrared light. And heat was and still is present beneath the ground and at the bottom of the sea in massive quantities, radiating from the earth’s core and mantle. I thought, What if chlorophyll was first used to harness infrared light? It made sense. Life on earth probably began below ground or under water where it was exposed to infrared light. Any organism that could harness infrared light would have the advantage of an almost limitless source of energy! So, I thought chlorophyll might first have photosynthesized infrared light/heat, and only later, when organisms were exposed to sunlight, did a slight modification of the original chlorophyll molecule allow the use of red light from sunshine, the form of photosynthesis we are so familiar with today. I fancied there were descendents of the ancient infrared-harnesing plants at deep-sea vents, and at hot springs like those at Yellowstone National Park. As it so happened, on February 10th, 2018, Christopher Todd Glenn gave a talk at the JC Raulston Arboretum about a North American Rock Garden Society field trip to Wyoming, with a side trip to Yellowstone National Park. Before the talk I approached Mr. Glenn and asked him what he thought of my notion that chlorophyll might have originally been used to harness energy from heat, infrared light. Mr. Glenn pondered a moment, smiled broadly, then suggested the subject would make a nice Master’s Thesis project for me. I wanted to say, I already have a Master’s Degree, but smiled gratefully and thanked him for taking a moment to consider the idea.

Well well well what do you know, a few months later, as was my wont, I was perusing the topics posted at Science Daily News, when this captured my attention: June 14th, 2018: New Type of Photosynthesis Discovered. And there it was. My speculations had been confirmed! Sort of. The lead researcher was Professor Bill Rutherford, Imperial College, England. “The standard, near-universal type of photosynthesis uses the green pigment, chlorophyll-a, both to collect light and use its energy to make useful biochemicals and oxygen. The way chlorophyll-a absorbs light means only the energy from red light can be used for photosynthesis. Since chlorophyll-a is present in all plants, algae and cyanobacteria that we know of, it was considered that the energy of red light set the 'red limit' for photosynthesis; that is, the minimum amount of energy needed to do the demanding chemistry that produces oxygen. The red limit is used in astrobiology to judge whether complex life could have evolved on planets in other solar systems. However, when some cyanobacteria are grown under near-infrared light, the standard chlorophyll-a-containing systems shut down and different systems containing a different kind of chlorophyll, chlorophyll-f, takes over. Until now, it was thought that chlorophyll-f just harvested the [red] light. The new research shows that instead chlorophyll-f plays the key role in photosynthesis under shaded conditions, using lower-energy infrared light to do the complex chemistry. This is photosynthesis 'beyond the red limit'. Lead researcher Professor Bill Rutherford, from the Department of Life Sciences at Imperial, said: "The new form of photosynthesis made us rethink what we thought was possible. It also changes how we understand the key events at the heart of standard photosynthesis. This is textbook changing stuff."

For me it was life changing. Bubbling over with excitement, I shared the news with whoever couldn’t get away. John Foushee, owner of Big Bloomers Flower Farm (BBFF) where I worked at the time, was one of my victims. John listened to my story then said with a wry smile, “You should be awarded the Nobel Peace Prize, Mike.” Laughing at my own stupid vanity I replied “Nah, maybe the Nobel Plant Prize.” I must admit, however, all this time later, I still find it very exciting. As Professor Rutherford stated, this has implications for the way we contemplate life on our planet and the possibility of life at distant places of the universe. Our perspective, understanding, and imagination have been broadened. Science requires an open mind – and inspires it too.

Posted on January 06, 2021 12:50 by mjpapay mjpapay

January 02, 2021

LIFE'S FLUID DYNAMIC INTERCONNECTIONS

LIFE’S FLUID, DYNAMIC, INTERCONNECTIONS
Michael J. Papay, 01 January 2021.

Life is a flowing continuous thing while it lives.
It is ever interesting and beguiling.

Figure 1 provides a very simple, idealized, static depiction of interconnectedness between hypothetical species A, B, C and Z, given as a vertical cross-section through two 3-dimensional bells connected at their bases. The reality of the interconnectedness of living things is more complex than that. It is actually 4-dimensional. However, let us proceed in small steps.

NOTE: Due to formatting of Journal entries in iNaturalist, I had to use dots (periods) as space-fillers in Figure 1 and Figure 2.


Figure 1. Two-dimension, normal, bell-shaped distribution curves depict hypothetical species A, B, C, and Z. Only the distribution curves of species A and B are shown. The tails of the distribution curves of species A and species B flow into the beginning tails of distribution curves for species C and Z.


. . . . . . . . . . . . . . .AAAA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . BBBB . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . AAAAAA . . . . . . . . . . . . . . . . . . . . . . . . . . . BBBBBB . . . . . . . . . . . . . .
. . . . . . . . . . . ZAZAAAAACB . . . . . . . . . . . . . . . . . . . . . ABBBBBBCB . . . . . . . . . . . . .
. . . . . . . . AZAZAAAAAABBAB . . . . . . . . . . . . . . . . AABABBBBBBCCBC . . . . . . . .
ZZAZABAAZAAAAAABAABBABAZAABBABABABBBBBABBBACBCCBCCCB
. . . . . . . . . . . . . . . . . . . . . . .|-------- introgression---------|
|------- variation of species A --------| |------- variation of species B --------|
. . . . . . . . . . . |-- iconic A --| . . . . . . . . . . . . . . . . . . . . . . . .|-- iconic B --|


“Iconic A” represents what we would perceive as the archetypal representation of that species. With only a single glance you would declare, “That is species A”.

“Introgression” represents individuals whose traits are not specifically what we would tend to think of being obviously one species, or the other. However, individuals of the zones of introgression are exceedingly important in the continued procession of life into the dimension of time (the fourth dimension), for they are the substance of adaptation.

If instead of a view of a vertical cross-section of the two interconnected bells, let us consider an aerial view. See Figure 2.


Figure 2. Aerial view of simple, two-dimensional, normal distributions of hypothetical species A, B, C, and Z. Only the distribution of species A and B are shown. The margins of introgression with species C and Z are not shown.


. . . . . . . . . . . . . AZZABAB . . . . . . . . . . . . . . . . . . . . . . . . . . BABCBCBC . . . . . . . . . . . .
. . . . . . . . . . . ZAZABAAACBB . . . . . . . . . . . . . . . . . . . . ABABABBCBCB . . . . . . . . . .
. . . . . . . . . AZABAAAAAABBAB . . . . . . . . . . . . . . . AABABBBBBBCCBC . . . . . . . .
. . . . . . . ZZAZAAAAAAAABBABB . . . . . . . . . .BAABABBBBBBBBCCBCC . . . . . .
. . . . ZAZZAZAAAAAAAAAABAABBAB BZAAABBABBBBBBBBCBBCBCC . . .
ZAZABAAAAAAAAAAAABABAZAABBABABABBBBBBBBBBBBCCBCBCCC
. . . . ZAZAAZAAAAAAABBABABBBABABBABABABBBBBBBBBCBCBCBCB . . .
. . . . . . . ZZAZAAAAAAAABBABB . . . . . . . . . . . BAABABBBBBBBBCCBCC . . . . . .
. . . . . . . . AZABAAAAAABBAB . . . . . . . . . . . . . . . AABABBBBBBCCBC . . . . . . . . .
. . . . . . . . . . . ZAZABAAACBB. . . . . . . . . . . . . . . . . . . . ABABABBCBCB . . . . . . . . . . .
. . . . . . . . . . . . . . AZZABAB . . . . . . . . . . . . . . . . . . . . . . . . .BABCBCBC . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . |------- introgression--------|


I apologize for the non-circular outline of the two “normal” distributions depicted in Figure 2. My artistic skills with mere letters as a medium are not as impressive as one might hope.

What we would perceive as individuals with iconic traits of species A are found in the core of the somewhat circular distribution. The same is true for iconic individuals of species B. However, with this aerial view we see that the numbers of non-iconic individuals of either species is vastly larger than we tend to think. And it is here, at the margins of overlap and introgression, that nature provides novel forms. And this supply of novel forms might be imagined as probing the environment for new opportunities. This action becomes even more dynamic when the dimension of time is applied to the image. Each new generation provides new variation, however subtle it may be.

If the static image depicted in Figure 2 was imagined to be just a single frame in a motion picture, the playing of the motion picture forward, or backward, would show the distributional blob of each species pulsing and probing like an amoeba, or like a Slime Mold, and interacting with other taxa within reach. And the reach may be very far indeed, if one considers the various manners of pollination, and of seed dispersal. That is why life is a flowing continuous thing while it lives, and is ever interesting and beguiling. And it is why the methods of statistics are applicable and necessary in the study of taxonomy.

STATISTICAL PARAMETERS FOR SPECIES: The dynamic nature of life’s fluidity does not defy scientific description. Taxonomy can use the mathematics of statistics for molecular, morphological, behavioral data (et cetera) of species. The “type” of a species would be the datasets and their statistical means, variances, and distribution patterns resultant from detailed scientific studies. Drawings, photos et cetera should accompany the reports to clarify in illustration what the datasets represent.

Via statistical analyses, species (taxa) can be identified and compared mathematically. Too, the changes incurred over the passage of time could be documented in detail. This approach would direct the perception of a species from the narrowly described “Type individual” to the more comprehensive view of a range of variation about a statistical average, inclusive of variants and outliers. There would be consequent benefits to our understanding of the dynamic nature of life at every taxonomic level, accompanied by greater recognition of the importance of areas of connection/interaction

By defining taxa by their statistical averages, the eschelons of taxonomy will be stabilized.

As regards the application of statistics, there are times when the experienced mind must contemplate intervention. The odds of an event occurring may be slim, and the occurrence twice in separate taxa even rarer – that does not mean that such events are impossible. And when the encompassed picture in contemplation suddenly resolves into focus when the improbable is accepted as possible, then learned minds must take heed.

Posted on January 02, 2021 01:06 by mjpapay mjpapay

January 01, 2021

IMPERMANENCE and SYNONYMY

This article in as excerpt from my self-published book, Splendor in Spines. Copies are so scarce as to be almost non-existent, so don’t bother looking.

IMPERMANENCE and SYNONYMY, by Michael J. Papay
No landscape is permanent, no life form is permanent, no plant is permanent, and thus no garden can be permanent. Changes come second by second, minute by minute, hour by hour, day by day, season by season, year by year, generation by generation. Changes come. To garden is to engage with the inevitable changes of the universe. The grandest gardens with the most spectacular views are nature’s untended landscapes. Gardeners tend to think that the plants need us, and many of the ones we select for our gardens probably do, but what nature’s landscapes mostly need is for humans to leave them alone, to stop bulldozing and flattening and digging and ditching and damming and cutting down and paving and poisoning. The moment we stop suppressing nature it will resume its processes of checks and balances. Nature’s equilibriums are not permanent. They are in a constant state of flux – by changes in season, climate, weather, geologic activity, and natural calamities. Nothing is permanent. Impermanence allows change, progression, renewal. Transition is the essence of life. It is the way of the universe. It is the dynamism of species. It is the nature of gardens.

Each time a species reproduces, the offspring are a little different from their parents and from each other as well, usually in multitudinous and subtle ways. This is the inherent fluidity of life – and of species. Just as each individual of a species is different from all the other individuals of the same species, every generation is slightly different than the one before it. Setting aside a “type” specimen of a species is like setting aside a bucket of water from a stream.

If geologists categorized mountains by comparing descriptions of only each summit, they would miss all the geology that is present below the summits where each mountain merges into the surrounding landscape. Geologists don’t do that of course, because it is obviously a silly thing to categorize mountains by only their summits, yet this is in essence what taxonomy does when setting a “type specimen” for each species. Mountains of important information are left out. The diverse and fluid nature of a species is downplayed, and we are led to believe that a species is a “fixed” thing rather than a dynamic composition of all of its individuals that changes with each generation. And by thinking of species as fixed things we do not think about the fluid ways in which each species is in flux through its own reproduction. We are led to think of hybridization as unusual rather than important. In essence, our view of species has been the wrong way around for a very long time. We have been looking at the summits of mountains while the world below remained to us something we didn’t know that we should know.

John Ray (1627-1705) helped invent modern taxonomy, and gave us a definition for “species.” In Daniel J. Boorstin’s fantastic book, The Discoverers, the then Librarian to the Library of Congress admiringly wrote, “What Newton did for students of physics…Ray did for the students of nature.” John Ray recognized the problem of continuums, and made no bones about it. In the preface to his Methodus Plantarum Nova (New Plant Method) published in 1682, John Ray wrote, “I would not have my readers expect something perfect or complete, something which would divide all plants so exactly as to include every species without leaving any in positions anomalous or peculiar; something which would so define each genus by its own characteristics that no species be left, so to speak, homeless or be found common to many genera. Nature does not permit anything of the sort.” John Ray got it right. His axiom is intrinsic to life.

The primary colors (red, yellow, blue) appear to be clearly separate. In fact, however, there is a continuous gradation from one end of the spectrum to the other. Understandably we have difficulty coming up with meaningful names for all the colors in-between, let alone spectra invisible to our eyes. Taxonomy is faced with the same problem, only with living things and their constituent molecules. Just as a species is a pool of its individuals, interaction amongst species is a matter of fluid dynamics, not stringent lines. Scientists now inspect the molecular spectrums of life in ever increasing detail. Life’s chemical rainbows provide endlessly diverse and often interwoven continuums, all realms of fluid dynamism. In its origins, taxonomy relied upon observations of how a living thing looked, behaved, and where it lived to ascertain if and how it was different. Where a thing lived, what it looked like, and how it behaved were all tangible things that even nonscientists could understand – and that knowable quality of early taxonomy made it successful. As we discover the true fluid nature of molecular relatedness amongst living things, we must make all that we discover knowable, comprehensible, and thereby useful.

When a species is named but later deemed the same as a previously recorded species, the newer name is retired in favor of the first given name. Retired names are then said to be synonyms of the original name. Yet it is often true that a synonym was used to describe a population that differed from the “type” in an interesting way, thus tracking down synonymous plants can prove rewarding.

Nurserymen are slow to adopt taxonomic name changes. Doing so would require the nursery stock to be re-labeled and re-organized almost constantly, the result being that only the most up-to-date taxonomist would know where to find a plant - a situation entirely unhelpful to the usual customer.

Posted on January 01, 2021 15:24 by mjpapay mjpapay

December 31, 2020

VARIATION IN THE CHRISTMAS FERN, POLYSTICHUM ACROSTICHOIDES

NOTES: Section 1 was revised and reposted on 12 January 2021. Section, MINIATURE CHRISTMAS FERNS, is retained below.

I submit to iNaturalist members the following information in the hopes that enthusiast will investigate and report upon the variation of Christmas Ferns, Polystichum acrostichoides, in their regions.

I know not how to coordinate any such effort, and encourage those who can manage that feat to do so. Pick up the baton and run, so to speak.

The magnitude of the task of investigating thoroughly the populations of Christmas Ferns across this species vast natural distribution is an insuperable undertaking for one person. It is hoped that many hands will make light work. All credit should go to those who participate.

Cheers to you all,
Michael Papay.


SECTION 1.

The Christmas Fern, Polystichum acrostichoides, in the un-glaciated lower Piedmont and Triassic basin of North Carolina, exhibits the diversity of color and form indicated below. What variation is to be found in previously glaciated realms where this species now occurs. Are populations in previously un-glaciated regions more diverse? Less diverse? Differently diverse? iNaturalist members in eastern North America, the natural realm of Polystichum acrostichoides, can investigate the variation in their Christmas Fern populations, and post photos and info at iNaturalist.

COLOR FORMS
(1) solid medium green;
(2) solid light green;
(3) solid blue-green;
(4) bicolor
- green & blue-green: center-line of leaflet is green whilst margin is blue-green;
- bright edge: green with a highly contrasting light green edge.
PHYSICAL FORMS
(1) EDGES (leaflets/pinnae)
- very shallowly serrated leaflet margin;
- shallow-lobed leaflet margin;
- fully lobed: leaflet subdivided into sub-leaflets;
- twice divided leaflets: leaflets divided into lobes which themselves are lobed;
- crested/fasciated leaflets - edges terminate in multiple divisions, sometimes bizarrely so.
(2) PLANE (leaflets/pinnae)
- leaflets straight-ish;
- leaflets distinctly curved;
- leaflets undulate.
(3) LENGTH (leaflets/pinnae)
- leaflets short
- leaflets usual
- leaflets long
(4) WIDTH (leaflets/pinnae)
- leaflets narrow
- usual
- wide
(5) TIP (of leaflet/pinnae)
- tapered to a single narrow point – usual case for mature plants.
- rounded; not narrowly pointed – all young plants, uncommon in mature plants
- divided into two (or more) points (crested) – more common in miniature forms.
(6) FROND LENGTH, PLANT SIZE:
- miniature fronds: plants fertile when small, remain small in old age, often crested [see study below].
- usual frond length
- longer fronds, larger plants
(7) FROND ASPECT
- fronds variously upright to lateral
- fronds mostly upright
- fronds displayed laterally

Each color form may exhibit each physical form. Each physical form may combine with other physical forms. The potential diversity is staggering. When one form is found, permutations are often nearby.


SECTION 2.

MINIATURE CHRISTMAS FERNS – A STUDY, By Michael J. Papay, 18 December 2020

I have observed miniature Christmas Ferns, Polystichum acrostichoides, amongst local (Raleigh, North Carolina vicinity) natural populations. The miniature forms are distinguishable by: (1) their small frond size; (2) by their leaflets (pinnae) being smaller versions of plants of usual dimensions and specifically not the very rounded leaflets (pinnae) of young plants; (3) presence of fertile fronds; (4) formation of clonal clump via branching of the rhizome. https://www.inaturalist.org/observations/66415436

I conducted a study that included 13 miniature Christmas Ferns with at least 3 fertile fronds each, and 15 randomly selected usual Christmas Ferns with at least 3 fertile fronds each. To assure that small plants were not simply young plants, only plants from clonal clumps produced by rhizomatous branching were included in the study. For each study plant, the longest 3 fertile fronds were measured. All plants occurred in-situ in the wild. Two sites, several miles apart, were visited. Each site had miniature and usual forms in the landscape. Plants were measured at the end of the growing season, on 03 and 08 December 2020. The data are presented below. Fertile Frond Measurements (FFM) are to the nearest sixteenth of an inch.


Table 1. Fertile Frond Measurements of Miniature and Usual plants of
Christmas Fern, Polystichum acrostichoides


MINIATURE

Plant FFMs

1 14.17, 14.00, 14.25

2 15.35, 21.85, 18.62

3 20.86, 18.62, 18.97

4 15.03, 14.37, 14.01

5 16.75, 18.50, 20.50

6 10.31, 11.50, 10.37

7 14.75, 14.75, 14.5

8 17.00, 15.50, 14.25

9 16.26, 16.00, 14.25

10 10.25, 9.37, 8.5

11 11.00, 11.12, 10.37

12 8.69, 8.12, 6.00

13 13.56, 13.25, 13.00

n = 39

average (Xm) = 14.064
standard deviation (SDm) = 3.862

SDm squared (SDm2) = 13.557

USUAL
Plant FFM’s
1 25.62, 21.50, 24.87
2 30.12, 30.37, 32.00
3 25.62, 28.25, 29.25
4 20.12, 21.75, 22.12

5 30.12, 30.00, 30.06
6 25.12, 25.25, 25.00
7 29.50, 29.25, 29.12
8 31.75, 31.56, 31.50
9 21.00, 17.00, 20.25
10 26.25, 26.50, 26.25
11 26.25, 26.87, 23.12
12 23.37, 25.12, 21.00
13 26.50, 25.56, 27.00
14 25.12, 25.50, 24.00
15 29.00, 27.50, 27.00

n = 45
average (Xu) = 26.222
standard deviation (SDu) = 3.507

SDu squared (SDu2) = 12.299

The two-sample standardized test statistic, Z, was used to test the Null Hypothesis that there is no difference between the average fertile frond lengths of miniature versus usual plants of Christmas Fern. The “one-sided” Alternative Hypothesis chosen was that miniature plants on average have smaller fertile fronds than usual plants of Christmas Fern. A 95% confidence interval was selected for testing, giving a Z value of -3.9 based on a one-sided Standard Z Test Statistic Table. Thus, if the calculated value of the test statistic Z is less than -3.9, the 95% confidence interval is reached and the Null Hypothesis is rejected in favor of the Alternative Hypothesis.
Test statistic Z = [(Xm – Xu) – 0] divided by the square root of [SDm2/39 + SDu2/45].
Z = [(14.064 – 26.222)/square root (13.557/39 + 12.299/45)] = -15.43. The Null Hypothesis is rejected with 95% confidence. The Alternative Hypothesis is accepted, that on average the fertile fronds of miniature Christmas Ferns are significantly shorter than the fertile fronds of usual Christmas Ferns.


This study does not resolve what may be the cause of the miniature size.

Posted on December 31, 2020 00:40 by mjpapay mjpapay | 3 observations

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