On The Meaning of Nature’s Patterns and Orchard Design

“Everyone wishes a measure of mystery in their life that they have done nothing in particular to deserve.”—-Jim Harrison

How much do you think we, as human beings, really know or are capable of knowing? What are the limits of science? What, if anything, do nature’s patterns tell us? Why do we, as humans, search for meaning (and sometimes find it) in those patterns? These are questions that have stirred minds for centuries.

In 2023, nuclear physicists were able, for the first time, to visualize two entangled light particles in real time. Not exactly earth-shattering news to most of us who don’t understand quantum physics and subatomic particles. But, in many ways it was a big deal. You see, quantum physics is so weird that most of us can’t even get our heads around it. There are aspects of the subatomic world in which the laws of physics that exist everywhere else, don’t necessarily work. For instance, with quantum entanglement, two photon particles can become bound to each other in some strange way in which, even though they exist far apart from each other, when you cause a change to one, inconceivably, the other is also changed. This makes them difficult to measure because any measurement or observation of one distorts the other. So what, right? Well, stay with me here.

If you don’t understand quantum physics and subatomic particles, don’t worry. I don’t either and I won’t dwell on this topic long except as an example. The interesting thing about this discovery is that the image produced by the physicists revealed that the wavefunction of the entangled photons exists at the sub-atomic level in a perfect likeness of the famous yin/yang symbol-the familiar circle divided in half by a curved line, with one half of the circle light and the other dark and a circle of one shade at the center of the other’s half.

What are the odds that a group of 14^th century Chinese philosophers would create a symbol to represent the idea that the universe or nature is governed by a cosmic duality of opposing and complementing principles, and then that same symbol is revealed 700 years later by some complicated 21^st Century technology to be an actual pattern that exists in a part of nature that we can’t see with the naked eye? That seems a bit much for a random coincidence. It boggles the mind. It also makes me think a little more deeply about the value of nature’s patterns.

I may be stretching things here, but if an image created by ancient Chinese philosophers representing one of nature’s patterns can be reproduced as a holographic image of light particles by today’s nuclear physicists, it strikes me that nature may have something to say regarding pecan farming. As a pecan farmer and as an agricultural scientist, I work with nature on a daily basis. I see her secrets revealed regularly in the way pecan trees work, the way they respond to sunlight, water, the manipulation of their crop loads, their interactions with the soil, each other, as well as with other plants, insects, fungi, bacteria, etc. of good, benign, and ill intent toward the trees. I have learned that nature’s language is written in the genetic background of the various pecan cultivars, and we are generally more successful when we pay attention to that genetic background, the needs of the tree, and the tree’s response to its environment. These are all patterns reflected in the growth and development of the pecan tree and its crop.

In light of all this, why do we not give nature’s patterns more trust, when it comes to practical matters like orchard design? I think the answer to this question rests on human ambition, hubris, and the ever-present temptation to bend or even replace nature’s will with our own. It may also stem from the seeming absence of pattern at times. When we do find one, we like to cling to it or perhaps make more of it than is really there.  

Pecan farming is full of decisions, but perhaps none more far-reaching than that of tree spacing, or the pattern of tree arrangement in the orchard. Once the trees are set in the ground, there’s no going back, or at least not without a lot of time, trouble, and expense. You want to plant enough trees to make the orchard as profitable as it can be as soon as it can be. But trees grow larger with time, they crowd each other, and they compete with each other for resources. You can plant them so densely that you defeat the purpose.

Pecan production depends upon a host of factors, but none so foundational as the two things required by all plants; sunlight and water. Here in the Southeastern U.S, the water is satisfied largely by rainfall, supplemented in dry periods, by irrigation in most commercial orchards. But managing the sunlight takes foresight and planning from the start. We cannot produce more sunlight. We can only make use of that which we are given.

               There is a tendency by many to fit as many trees as possible on an acre of land, but that is almost always a mistake. These are not olive trees, apple trees, cherry trees, or almond trees. Pecan trees have no known dwarfing trait inherent to their genome. They are a tree of the North American hardwood river bottoms and, as a result, they want to grow big in search of sunlight. In the orchard, they grow and crowd one another for this precious resource. Left unattended, the resulting shade restricts foliage and nut production almost exclusively to the upper canopy in old, mature trees, reducing the fruiting surface of the tree to only about 20% of the tree’s architecture. When optimal sunlight is available to a tree, the majority of the tree’s surface area produces pecans. Regardless of the orchard design, it is inevitable that sunlight will become a limiting factor as the trees grow in size, and one must plan accordingly.

               It takes a long time for pecan trees to become profitable. Under normal management practices, pecans will begin bearing fruit in three to five years depending on the cultivar. But, it is usually 8-10 years before there is enough nut production to make a dent in the cost of growing them. Thus, there is incentive to plant trees at a higher density to maximize early production. However, this comes at the costly price of managing the sunlight earlier than most would like. The more trees you plant per acre, the higher your early nut production will be. But, the more trees you have per acre, the sooner the trees crowd, requiring that you address the lack of sunlight. One must find the appropriate balance between these two competing variables. This is the yin and yang dilemma of orchard spacing. Because, as human beings, we tend to under-estimate risks we can put off to the future, for most, there is a greater desire to produce early than there is to reduce the risk of tree crowding. But, pecans are a long-term crop and when working with them we need to try and see the world from their perspective. So, how does one deal with sunlight management in a pecan orchard?

               There are two ways you can go about this task. The historical way, which may, on the surface, seem a bit drastic, is to remove trees. This usually involves removing about ¼ to 1/2 of the trees in an orchard. It may seem counter-intuitive to remove trees to increase your orchard’s production but the impact of sunlight far outweighs the potential found in a higher number of tree trunks in the orchard. The key to good pecan production is not trees per acre but bearing surface per acre. Alternatively, one can employ the practice of hedge pruning, in which large machines with rotating saw blades remove all the growth on the trees beyond a certain distance from the trunk along the length of the tree row and reduce the height of the tree. The combined effect increases sunlight in the orchard, water efficiency of the tree, nut size, nut quality, and reduces wind damage. You keep the original number of trees in the orchard. They become smaller, yet more efficient.

               The problem with both of these solutions is that they can be expensive. You don’t want to have to implement them before you have enough production from the trees to afford it. The more trees you fill an orchard with, the sooner you will have to begin one of these practices. If you wait too long, you lose production. If you have to begin too early, you don’t achieve each tree’s full potential and the cost of addressing the problem may not be offset by the yield produced on more trees per acre. If you plant too few trees per acre to begin with, you do not achieve the full production potential of the land. The balance between sunlight and yield potential is a precarious one. I provide all of this technical background on pecan production to get to this question; Where is that goldilocks zone and can nature offer any clues to help us find it?

               I have been planting pecan orchards for 20 years and throughout this time, I have been in search of that balance.   Fortunately, mother nature knows something about balance and efficiency. It seems to me that we may be able to find that narrow seam of balance by taking note of and working within nature’s laws. We can push against those laws. We can stretch them to an extent, but to fight against them and ignore them completely, is almost always to our own peril in the long run.

               At the time I planted my first pecan orchard, the spacing most commonly used was 40 feet between trees in the row and 40 feet between the rows, or 40 X 40. This places 27 trees on a given acre and allows plenty of sunlight for the trees to maintain good production for 15-20 years, at which point one must hedge prune or remove some trees. If you remove trees, you eventually end up at 80 X 80 and your tree spacing is too wide to maintain good production. With hedge pruning, the original 40 X 40 spacing can be maintained indefinitely and near optimal production is achieved. My first orchard is a testament to this. But, is this the highest efficiency we can achieve? Can or should we push the spacing tighter?  What clues does nature offer to making our tree spacing more efficient, and yes, even more pleasing to the eye?

               Around 300 B.C., Greek mathematician Euclid published a treatsie called The Elements, consisting of 13 books, much of which was gleaned largely from earlier mathematicians like Pythagorus. The Elements is considered a masterpiece of the application of logic to mathematics. Within it, we find the first mention of the mathematical proportion, 1.618:1. This produces an irrational number (1.618) that has no ending. It arises from the Fibonacci sequence of numbers where, each number after the first two is the sum of the two preceding ones (0, 1, 1, 2, 3, 5, 8, 13, 21, 34, etc). The golden ratio reflects the ratio of two consecutive Fibonacci numbers ( >55) calculated as the sequence progresses towards 1.618…. So, 34 + 55 = 89 and 89/55 = 1.618, and 1.618 is the result for 144/89, and onward. You may be thinking, “This sounds like a neat trick but what’s the big deal?”

In 1509, an Italian mathematician named Luca Pacioli published the book De divina proportione, which, alongside illustrations by Leonardo da Vinci, acclaimed this ratio as representing divinely inspired simplicity and orderliness. It was later given the moniker, “the Golden Ratio” sometime in the 19^th century.

The relationship between numbers that generate the golden ratio is said to create a unique sense of balance and proportion that has reportedly been used in geometry, art, and design. It is supposedly found in such notable man-made works as the Great Pyramid of Giza, the Parthenon, Leonardo Davinci’s Mona Lisa, The Last Supper, and Vitruvian Man, Michaelangelo’s The Creation of Adam on the ceiling of the Sistine chapel, and Hokusai’s “The Great Wave Off Kanagawa”, among others. The golden ratio is popularly considered the mathematical distillation of beauty, universally recognized for its ability to bring order, symmetry, and beauty to design. Interestingly, it has been suggested that the human eye processes images constructed with the golden ratio more quickly than images without it’s presence. As a result, many modern companies like Apple, Google, Twitter, National Geographic and Pepsi proclaim to have used it in their logo designs.

 Perhaps the most frequently cited uses of the golden ratio are the many examples reported to be found in nature. If true, this would be one of the marvels of creation. The divine proportion is said to be seen most famously in the structure of the chambered nautilus, the arrangements of leaves on stems, branches on trees, flower petals, seed heads, the spiraling curvature of galaxies, the swirl of hurricanes, pine cones, the flight patterns of hawks, the number of females to males in a honeybee colony, the dimensions of the DNA molecule. The golden ratio is said to be found even within our own bodies (the ratio of forearm to hand, the proportions of the face, the height of the adult body to that of the navel, etc.), the fractal branching patterns of our vascular systems, as well as that of other animals and plants, the coursings of rivers and streams, etc.

But, in reality, the golden ratio is just one mathematical representation that can be found in nature. For example, the “golden curve” purported to describe the spiral pattern of the chambered nautilus is part of a larger family of curves and spirals collectively known as “logarithmic spirals”, in which the distances between the turnings of the spiral increase in geometric progression.  There are still other spirals found in nature, such as the “Archimedian spiral”, in which these distances remain constant. 

The legend of the golden ratio is a fascinating one. Some of these legends have a kernel of truth to them. Others do not. It is not difficult to find examples of known mathematical patterns and sequences that fit a particular pattern found in nature, but when such a fit is found, it is seldom exact. Many of the reported examples of the golden ratio, including some of those listed earlier, have considerable variations from 1.618:1. Some are pretty close, but few are exact.  Mathematics serve to help describe the patterns and laws found in nature, and there are many such patterns. All of this brings up an interesting topic of consideration, what, if anything, do these patterns mean and what possible significance could this have for the design of a pecan orchard?

 You see the golden ratio often represented as a curved structure like that of the nautilus, but this proportion can be used in rectangular form, often called the golden rectangle. Therefore, one could lay out an orchard in a manner that the ratio of the distance between tree rows and the distance between trees in the row are equivalent or close to the golden ratio (1.618:1).  Like the many patterns found in nature, there are any number of tree spacings I could use to achieve the golden ratio but I must first weigh my choices against a knowledge of the pecan tree’s needs and the environment in which I am growing it. I have to be aware of sunlight needs, the cost:benefit ratio of planting too many trees per acre and not planting enough. I have come to my decision through a combination of observation, anecdotal experience, scientific research, and trusting that nature’s way is often the best way.

               I came to the conclusion that a tree density of about 35 trees per acre is about as high as we can successfully go here in the southeastern U.S. This conclusion arose from watching the experiences of other growers who planted their trees too closely. They pushed the density up to 54 trees per acre, 65 trees per acre, and even 109 trees per acre. As a result, the trees crowded quickly and needed hedge pruning or tree removal at an early age, costing them a lot of money and production.

Defining the best spacing for pecan trees is a complex interaction between the tree’s biology, climate, geography, sunlight, air-flow, tree size, and tree density within the orchard. There are likely many spacings that can work but the goldilocks zone is so narrow and specific that it takes some time to tease out the answers from a long-lived tree species like pecan. If you evaluate 2,5,10, or 100 different spacings in a field trial from the time of planting, you’re looking at a full 25-30 years before the answer is known. It would also require an enormous amount of land. Therefore, there are many challenges to running a field experiment on pecan orchard spacings

               I’m sure someone who is savvy enough could use artificial intelligence to create models and algorithms to compute an answer relatively efficiently. But, models are only as good as the data fed into them and due to the vagaries of pecan cultivars, their precocity, growth habit, the variability of tree structure within and between cultivars, etc., it seems to me there are simply too many variables at work to develop an accurate model.

So, I take my clues from nature, observation, and experience. My estimates of ideal tree spacing are stabs in the dark but they are informed stabs. I chose a spacing of 50 feet between tree rows and 30 feet between trees in the row. This provides 29 trees per acre and after running the numbers I found that this spacing provides a ratio of 1.67: 1. Not precisely on the golden ratio, but like the chambered nautilus, fairly close. It would have been more exact at 30.9 X 50 or 31 X 50, or perhaps more appropriately, 34 X 55, but I included observation and experience in this decision rather than a direct attempt to achieve the golden ratio. Chalk that up to practicality, hubris or just a wee attempt at stretching nature’s law.  

Since I began planting trees at 30 X 50 and recommending it to others, I have personally planted three orchards at this spacing. Yields have been good and I have been pleased. I began hedge pruning the oldest at 12 years of age and enjoyed several years of good harvests prior to the beginning of hedge pruning. I believe I can maintain yields and tree spacing in this manner. If worse comes to worse, I can remove every other tree on the diagonal. This will leave my rows 50 feet apart, while maintaining 100 feet between trees across the rows and 60 feet between trees in the row.  This will provide 14.5 trees per acre (plenty to maintain good production where hedge pruning is not used) and still leave me with a 1.67:1 ratio, not that there’s anything magical about that, but experience tells me it sets a good balance of trees and sunlight.

The patterns of nature continue to stick in my mind, prodding me, enticing me to give them greater consideration.  Scottish zoologist D’Arcy Wentworth Thompson explained that even nature’s creativity is constrained by the laws of physics and chemistry. Forces like natural selection may explain the why of natural patterns but physics and chemistry explain how. The preponderance of patterns like the golden ratio, the fractal branching of tree limbs, veins, and streams, the hexagonal symmetry of a snowflake, the Turing patterns formed upon the skin of a trout or by wind upon rippling sand dunes, even the yin/yang image of quantum entangled light particles, are evidence of nature’s patterns. They are all around us and there must be some reason why. They gnaw at my curiosity like a puppy with a new shoe. They lead me into questions much deeper than that of pecan orchard spacing. In fact, they lead to that ultimate question.

We are free, at least at the time of this writing, to believe what we choose to believe. I do not mean to sound mystical, and at the risk of being shunned by fellow scientists, I do believe that the nature of the universe is, in some way, ordered by God. I don’t fully understand how, or why, or what that means. Maybe these patterns, the mathematics behind them are a language. Maybe they are the thoughts of God written down upon creation like words in a journal. Maybe they are just a part of the creation, as we are. I don’t know. The one thing I do feel confident enough to declare as factual is that we human beings will never know everything about how nature works. Nor, is it likely now that we even know what we think we know. Science, by its very definition, is composed of facts that change with more data, more information. The mystery grows in proportion to increasing knowledge. As the scripture says, “we see through a glass poorly”.

Some say we search for meaning in natural patterns because we want to find it there. Fair enough. But, sometimes we find meaning just the same. And maybe finding meaning is the whole point. For me, that meaning doesn’t have to come entirely in the form of answers. Many questions are eventually answered. Others are not. Why is the universe unfolding? Why is the world here at all? I am ok with the existence of mystery in the world. Mystery, in itself has meaning. I am thrilled by discovery. Yet, I don’t have to have THE answer. It is enough to be curious and admire the wonder that remains.

               I am humble enough in my regard for the limits of human knowledge and the limits of science to feel that there must be more to the story than what our minds are capable of comprehending. If there isn’t something greater out there, some meaning behind the way nature works, then what is it exactly about all this, the beauty and peace we find in the natural world, the efficiency of its patterns, that speaks to us so? And in finding that meaning, why would we not consider it worth listening to? These are questions that scientists generally do not pose and which science is not capable of answering.

Pecan orchards are a semi-natural system, you might say. When done correctly, a human and nature-influenced pattern of partnership between people and the natural world. It is no secret that human beings have a tendency to make a mess of things. So, as I consider the orchards, I feel it wise to pay attention to the direction nature points with its patterns. After all, nature has a pretty big say in things. But, as a human being myself, I can’t help but push against those boundaries. Our own minds, one of the greatest of nature’s designs, allow us to make sense of what we observe and to use experience, and knowledge to understand where the limits of those boundaries may be. In doing so we bend and sometimes, even break those laws to discover what is possible. Nature is incredibly resilient, but she will only take so much before pushing back. There is a fine line there for us to recognize. There is a well-won humility to admitting that we exist within limits, that indeed, we too exist within nature’s patterns. That acknowledgement is where we find a mystery and a meaning. It is where we find an answer.