Transitions: The Evolution of Life

bootstrap analysis has given me permission to crosspost this interesting post on leaves. Thanks!

I spend a lot of time in forests. As an ornithologist, I spend a lot of time looking up in forests. With luck, I see the bird I am searching for. If not, my eye will wander the canopy, appreciating the play of light through the leaves. One day, my mind, as well as my eye, wandered. Was there a pattern to this seemingly chaotic riot of green? Nature, I know, is a most efficient master. It seemed reasonable that leaves, as food factories designed to carry out photosynthesis, should probably be positioned in order to maximize their exposure to sunlight.

This is, in fact, the case. It may not always be easy to see,
because environmental conditions, physical constraints, injuries, etc.
obscure the patterns, but the method of leaf arrangement, or phyllotaxis, on plants is both precise and quite astounding.

There are three basic ways that leaves are arranged on the stems of plants or trees. One is whorled, with three or more leaves arranged in a whorl around the stem. This is found on catalpa trees, as well as many herbaceous plants. A quick look will verify that the leaves of each whorl are placed so that they do not block the light of the previous whorl.

Another is opposite. Among tree species featuring opposite leaves are maples, ashes, dogwoods, and horsechestnuts — you can remember these genera by the acronym "MAD Horse". Each rank of leaves will emerge at right angles to their successors, thereby not interfering with light transmission.

The third and most common leaf arrangement is alternate, which is found on nearly every other deciduous tree and many plants. In this array, leaves are ordered up a stem in an alternating pattern. The leaves don’t just alternate, they actually spiral around the stem so that each leaf gets maximum light exposure. Nor are these just ordinary spiral patterns. They are organized with mathematical precision.

Each leaf is positioned a partial turn around the stem from its successor. In each species of tree, this angle remains constant throughout the tree: every branch around the trunk, every twig around each branch, and every leaf around each twig is at the same angle. The pattern of any given species can be written using a fraction. Although this is easier said than done, is accomplished as follows.

Start with a leaf. Count the leaves going down the stem until you reach another leaf directly below the leaf you started with (in other words, located in the same vertical position on the stem). Also note how many turns around the stem it took to reach that leaf. A pattern of five turns consisting of eight leaves is written as the fraction 5/8, shown in the illustration (click to enlarge; image source Jill Britton’s Investigating Patterns page).

Many grasses have a fraction of 1/2 while beech trees come in at 1/3, and oaks, like many hardwoods, are 2/5. Holly leaves are arranged in a 3/8 pattern, and willows have the 5/13 phyllotaxy. If you have any mathematical prowess (I don’t), you are getting a creepy feeling here. The numerators and denominators of phyllotaxic fractions are nearly always numbers in the following series:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, and so on, where each number
is the sum of the two numbers preceding it. This is known as a
Fibonacci sequence, named for an Italian mathematician.

Fibonacci numbers abound in nature. If some enlightened teacher had pointed this out to me in grade school, I would have been inspired by numbers rather than bored and intimidated by them.

One of the most frequent and easy to observe examples of Fibonacci numbers in the natural world are flower petal numbers. Go count some. And the preponderance of botanical examples of Fibonacci numbers leads me to believe this is why four-leaved clovers are so rare.  But I digress.  Let me continue to dwell on those phyllotaxic fractions.

Take a look at the head of a sunflower*, packed with seeds. The seeds are arranged in collapsed spirals, one winding clockwise, and the other counterclockwise. For example, 21 counterclockwise spirals crossing clockwise spirals creates the fraction 21/34, another fraction in the Fibonacci sequence. Why would florets, and therefore seeds, need to be in such an exact pattern? Rather than the most efficient use of light, in this case it is the most efficient use of space, resulting in the maximum number of seeds.

Then there are pine cones*. A fraction of 8/13 is found in a pine cone where it takes five circuits around the axis of the cone touching 13 scales to reach a scale directly above the first. Not only an efficient use of space and increased structural stability, but cones configured in this fashion channel wind-borne pollen to the ovules for the best probability of pollination and reproduction.

This is an elegant example of evolution at work, for any small
adjustment that resulted in an advantage in light gathering, optimal
seed arrangement, or increased fertilization would put a plant at a
competitive advantage, and would be selected for. Over millennia, plant cells have evolved a way to organize themselves for optimum performance, following precise mathematical models.

It’s something you can count on.

*Links to animated
gifs.  Let them load to show you the spirals.

Additional resources:

• Why
  Fibonacci numbers and Phi appear in nature.
• Explore another interesting aspect of the Fibonacci series, the ratio found by dividing one number by the one preceding it, which in all the higher pairs of numbers is around 1.618, known as Phi or the Golden Mean.  This is compelling number that has many mathematical properties and appears not only in plants but in the proportions of the human body, throughout nature, and has been co-opted in great works of art and architecture.
• A quick look at the Golden Mean and the Golden Angle. The angle of divergence (angular distance between two successive leaves) in all of plants with Fibonacci spirals approaches an average of 137.5 degrees, or the Golden Angle.
• Click through models of how plants create new parts according to mathematical rules.
• Fibonacci books and posters by Trudi Hammel Garland.

Butterflies are used quite frequently in the study of evolution. For example, one type of study involves the evolution of mimicry - that is one form imitating another.

The above is a picture of a tiger swallowtail. They inhabit a large part of the United States. In one part of their range, however, they look a little different.

The butterfly on the bottom left is also a tiger swallowtail. As you can see it looks a little different from the tiger swallowtail on the bottom right. Why the difference? The range of the tiger swallowtail overlaps with the range of the pipevine swallowtail.

The pipevine swallowtail is somewhat poisonus - any predator that eats it soon winds up sick, so most predators have learned to avoid it. If you compare the pipevine swallowtail to the blue form of the tiger swallowtail you will notice that they look a lot alike. The tigerswallow tail has evolved a coloration that mimics the pipevine swallowtail in an effort to avoid predation. Interestingly enough, the blue form of the tiger swallowtail is female. Which brings us to what I really want to talk about.
Below is a picture of a male peacock. Note the large spectacular tail. How can evolution explain it. If natural selection were at work you would expect that this tail would interfere with, for example, the peacock escaping from predators.

How to explain it? There is another type of selection, called sexual selection, that researchers use to explain things like the peacock’s tail. Sexual selection involves competition for mates and can be broken down into two different.
First is male competition. Here males compete with each other for females. In the picture of the baboon below note the large canines.

Although they serve a defensive purpose (they help defend he animal against predators) they also serve a purpose in male competition for mates. They are displayed prominately towards other males in the baboon troop and their is some evidence to indicate that males with larger canines have more mates.

Another type of sexual selection is female choice. Females choose mates with some characteristic they find desirable in a mate. Over time the characteristic, such as the peacock’s tail, becomes exagerated in size or some other quality. The question is how can we tell if some trait or characteristic has evolved by means of sexual selection?

Enter the butterflies. Below is a picture of a butterfly called Bicyclus anynana. On the left is a wet season form (when the butterflies mate) and a dry seaon form.

Bicyclus has been used in studies of mimicry (such as those on the swallowtails mentioned above) but recently an clever experiment was performed to study sexual selection in Bicyclus anynana. The results were interesting. Notice along the edge of the wing there are round (eye) spots. Researches belived that females chose males based on the size and color of these spots. To test the theory researchers carefully altered, via painting, a wide variety of characteristics on male butterflies including: wing size, eyespot size, quantity of eyespots on the wing, eyespot and pupil color, and pupil reflectivity. They then introduced the altered males and kept track of which males were choosen and how often they were choosen by the females. A picture of one of the altered males is below.

The article goes on to point out:

“Once we found a trait that appeared to be important, we then would exaggerate it or reduce it to pin it down,” said Monteiro.

None of the variations induced on the ventral side appeared to have any affect on the females’ mating decisions, leading the researchers to conclude that the ventral side of the wing does not play a role in the decision making.

But when the researchers painted the white pupil on the dorsal side with black paint, thereby eliminating the pupil, these males were much less desirable to females by a ratio of two to one, demonstrating clearly that females preferred the presence of the white pupil.
However, a large white pupil, about twice the diameter of a natural pupil, also was not found desirable by females, indicating strong sensitivity to a set of rather narrowly defined features, such as eyespot pupils that measure approximately half of one millimeter.
The most conclusive finding resulted when the researchers painted the white pupils in male eyespots on the dorsal side with a plant extract, rutin, which maintained the pupils’ whiteness, but eliminated their ultraviolet reflectivity.

“When there was no UV reflectivity, which butterflies can see, females registered a strong distaste,” said Monteiro. “Selection against the absence of UV reflectivity was as strong as selection against the absence of a pupil altogether.”

The reasons for this phenomenon are complex, but Robertson noted that the UV reflectivity may be important in what is known as photic stimulation — a flashing light effect — during the series of events that lead up to mating.

“When the male approaches the female, he opens and closes his wings in rapid succession so she can observe his pupils,” she explained. “We believe the purpose of the fluttering of his wings is two-fold: to spread pheromones to her antennae and to stimulate her visually. The female appears to be very sensitive to this rapid flickering, which probably looks to her like a strobe-light effect.”

The important point here is that the researchers came up with a theory about evolution. Defined somes variables they felt were related to the theory and then systematically tested the theory by altering those variables. Another interesting point. Female Bicyclus anynana butterflies also have these eyspots so the results of this study have led researchers to start a study the effects of the eyspots on male competition and to see if they play a role in how male butterflies choose females. The point here iis that the results of the original study created new questions for future research.