Our Lady of Tectonic Process

The following excerpt is a description of what is now the Los Angeles CA area. Note the title of the work, at bottom. The Portola/Crespi expedition is considered the first land-based, Caucasian exploration of what is now the State of California. So…just who were the people these Native Americans referred to, where indeed did they come from, and what route did they take to get there? And how long did they stay? And were the fair- and red-haired children Crespi mentions as having observed, their children?

July 28 [1769]
We set out at six o’clock in the morning from this grand plain and watering place of Santiago, following the same northwestward course of these last days’ marches, keeping on over this same plain, skirting the range on our right (to the north)…The scouts returned last night and said they came upon a full-flowing river a league and a half away…Its course comes out of the mountain range that must lie about two or three leagues away from us, from northeast to southwest…This river bed is very much lined with trees: white cottonwoods, willows, sycamores and other kinds we don’t recognize. By what we’ve seen from the sands along its banks, this river must plainly carry very large floods, and we had some trouble crossing it even now, in the depth of the dry season and dog days. There will be no crossing it in the rainy season…

We made camp close to the river here, and we have felt three strong earthquakes within less than an hour today at noon. The first and most violent must have lasted the length of a Creed, the other two less than a Hail Mary; a great shaking of the ground however was felt during all three. This is a most beautiful spot–with a great amount of soil and water, and this beautiful river going as it does, through the midst of the wide and far-ranging plain here–for founding a mission…

The heathens of this village here, who have been spending the whole day with us, brought and showed us nine cutlasses without hafts, along with four or five eyeless matting needles and a thick spike about half a yard long, all of which, they gave us to understand, had been given to them upcountry, toward the north, by some people there like ourselves, and we also understood there to be Fathers like ourselves. Whether this means they have a connection with New Mexico or the Apaches we cannot tell, or, whether some nation may have intruded upcountry toward the northward whither they were pointing.

Cover Image of Henry Wagner’s book Juan Rodriguez Cabrillo,
California Historical Society

July 29
We set out at two o’clock in the afternoon from here at the famous, large, pleasant and full-flowing River of the Sweetest Name of Jesus of the Earthquakes, crossing its bed with difficulty because of its swiftness…

July 31
On going about two leagues we came across another stream with some running water, which must carry very large floods in season because of the great deal of sand it has on its banks. We came upon such a vast number of rose bushes that a large hundredweight could have been made up with the flowers that we saw open and blooming. From horseback I plucked more than four dozen of them that came into my hands. The grapevines are countless in number, some of them large with very large clusters. We twice came upon woods so dense that it was necessary for the soldiers to clear a way to get through the various sorts of trees, willows, grapevines, cumin, holythistles, and many other kinds of tall weeds, such that it is a vastly pleasant site to see. There are vast numbers of antelopes on this plain…tracks of very large animals are seen…they say that in the mountain range running along on the north, there are a great many bears.

August 2
Our Captain and the scouts reported that about half a league or more from this spot…to the west, they came upon volcanoes of pitch coming out of the ground like springs of water. It boils up molten (and there must have been about forty of these springs, and perhaps many more, they said), and the water runs off one way and the pitch another. They reported…seeing very large swamplands of it, enough they said to have caulked many ships with…we christened them The Volcanoes of Pitch of Porciuncula. We all felt four quakes at dawn today; since we began hearing them at the Sweet Name of Jesus river, there have been fourteen, very persistent and strong though not long-lasting, and we attribute these continual earthquakes to the pitch volcanoes here.

August 6
They told us that upcountry–pointing northeastward–there were people like us–pointing to the soldiers–with guns, swords, and horses–pointing to our mounts–and there were three Fathers like ourselves (pointing to our habits); that two or three of themselves had been there; that it was reached in thirteen days’ travel from sunrise to sunset, and there was sea close by, and many large animals, which from their commentary and gestures, we thought must have been buffaloes; and that a great many people from there had come on horseback to their country, and had returned. Whether this is New Mexico or not, who can say?

Brown, A.K., ed. 2001. A Description of Distant Roads, Original Journals of the First Expedition into California, 1769-1770, by Juan Crespi

A massive mess of old tree data

I’m going to start focusing more on science topics here, as time allows. I’ll start by focusing for a while on some forest ecology topics that I’ve been working on, and/or which are closely related to them.

I’m working on some forest dynamics questions involving historical, landscape scale forest conditions and associated fire patterns. I just got done assembling a tree demography database of about 130,000 trees collected in about 1700 plots, in the early 20th century, on the Eldorado and Stanislaus National Forests (ENF, SNF), the two National Forests that occupy the mid- to upper-elevations on the relatively gradual western slope of the central Sierra Nevada. The data were collected primarily between 1911 and 1923 as censuses of large plots (by today’s standards, each ~2 or 4 acres) as part of the first USFS timber inventories, when it was still trying to figure out just what it had on its hands, and how it would manage it over time. An enormous amount of work was involved in this effort, but only a small part of these data has apparently survived.

The data are “demographic” in that the diameter and taxon were recorded for most trees, making them useful for a number of analytical purposes in landscape, community and population ecology. They come from two datasets that I discovered between 1997 and 2001, one in the ENF headquarters building, and the other in the National Archives facility in San Bruno CA. For each, I photocopied the data at that time, and had some of it entered into a database, hoping that I would eventually get time to analyze them. For the ENF data, this was a fortunate decision, because the ENF, as I later learned, has managed in the mean time to lose the entire data set, most likely along with a bunch of other valuable stuff that was in the office housing it. I thus now have the only known backup. Anyway, that time finally came, but the data were in such a mess that I first had to spend about three months checking and cleaning them before they could be analyzed. The data will soon be submitted as a data paper to the journal Ecology, it being one of the very few journals that has adopted this new paper format. In a data paper, one simply presents and describes a data set deemed to be of value to the general scientific community. There is in fact a further mountain of data and other information beyond these, but whether they’ll ever see the light of publication is uncertain.

An example first page of one of many old field reports and data summaries involved

An example first page of one of many old field reports and data summaries involved

We, and others, are interested in these data for estimating landscape scale forest conditions before they were heavily altered by humans via changed natural fire regimes, logging, and grazing (primarily). These changes began in earnest after about 1850, and have generally increased with time. This knowledge can help inform some important current questions involving forest restoration and general ecosystem stability, including fire and hydrologic regimes, timber production potential, biological diversity, and some spin off topics like carbon dynamics. They can directly address some claims that have been made recently regarding the pre-settlement fire regimes in California and elsewhere, in certain papers.

The data assembly was much slower and more aggravating than expected–I won’t go into it but I’ll never do it again–but the analysis is, and will be, very interesting for quite some time, as much can be done with it. Some of the summary or explanatory documentation associated with the data is entirely fascinating, as is some of the other old literature and data that I’ve been reading over as part of the project. In fact I’m easily distracted into reading more of it than is often strictly necessary, but so doing has reminded me that a qualitative, verbal description can be of much greater value than actual data, scientific situation depending. Possibly the most interesting and important aspect to this is the degree to which really important information has been either lost, completely forgotten about, or never discovered to begin with. This is not trivial–I’m talking about a really large amount of detailed data and extensive, detailed summary documentation. Early views and discussions regarding fire and forest management, and the course these should take in CA, are extensive and very revealing, as we now look back 100 years later on the effects of important decisions made then. There are also lessons in federal archiving and record keeping.

I’ll be posting various things as time allows, including discussions of methods and approaches in this type of research. I’m also applying for a grant to cover the cost of free pizza at the end, although to be honest I’ve not had great success on same in the past. You might be surprised at the application numbers and success rates on that kind of thing.

“Fearfully wild, with a blaze of quick electric light in his dark eye”

Never in several lifetimes of dreams and visions will I ever tire of reading the works of this man.

Visalia is the name of a small town embowered in oaks upon the Tulare Plain in Middle California, where we made our camp one May evening of 1864. Professor Whitney, our chief, the State Geologist, had sent us out for a summer’s campaign in the High Sierras, under the lead of Professor William H. Brewer, who was more sceptical than I as to the result of the mission.

Several times during the previous winter Mr. Hoffman and I, while on duty at the Mariposa gold-mines, had climbed to the top of Mount Bullion, and gained, in those clear January days, a distinct view of the High Sierra, ranging from the Mount Lyell group many miles south to a vast pile of white peaks, which, from our estimate, should lie near the heads of the King’s and Kaweah rivers. Of their great height I was fully persuaded; and Professor Whitney, on the strength of these few observations, commissioned us to explore and survey the new Alps.

We numbered five in camp:—Professor Brewer; Mr. Charles F. Hoffman, chief topographer; Mr. James T. Gardiner, assistant surveyor; myself, assistant geologist; and our man-of-all-work, to whom science already owes its debts.

When we got together our outfit of mules and equipments of all kinds, Brewer was going to reengage, as general aid, a certain Dane, Jan Hoesch, who, besides being a faultless mule-packer, was a rapid and successful financier, having twice, when the field-purse was low and remittances delayed, enriched us by what he called “dealing bottom stock” in his little evening games with the honest miners. Not ungrateful for that, I, however, detested the fellow with great cordiality. “If I don’t take him, will you be responsible for packing mules and for daily bread?” said Brewer to me, the morning of our departure from Oakland. “I will.” “Then we’ll take your man Cotter; only, when the pack-saddles roll under the mules’ bellies, I shall light my pipe and go botanizing. Sabe?”

So my friend, Richard Cotter, came into the service, and the accomplished but filthy Jan opened a poker and rum shop on one of the San Francisco wharves, where he still mixes drinks and puts up jobs of “bottom stock.” Secretly I longed for him as we came down the Pacheco Pass, the packs having loosened with provoking frequency.

The animals of our small exploring party were upon a footing of easy social equality with us. All were excellent except mine. The choice of Hobson (whom I take to have been the youngest member of some company) falling naturally to me, I came to be possessed of the only hopeless animal in the band. Old Slum, a dignified roan mustang of a certain age, with the decorum of years and a conspicuous economy of force retained not a few of the affectations of youth, such as snorting theatrically and shying, though with absolute safety to the rider, Professor Brewer. Hoffman’s mount was a young half-breed, full of fire and gentleness. The mare Bess, my friend Gardiner’s pet, was a light-bay creature, as full of spring and perception as her sex and species may be. A rare mule, Cate, carried Cotter. Nell and Jim, two old geological mules, branded with Mexican hieroglyphics from head to tail, were bearers of the loads.

My Buckskin was incorrigibly bad. To begin with, his anatomy was desultory and incoherent, the maximum of physical effort bringing about a slow, shambling gait quite unendurable. He was further cursed with a brain wanting the elements of logic, as evinced by such non sequiturs as shying insanely at wisps of hay, and stampeding beyond control when I tried to tie him to a load of grain. My sole amusement with Buckskin grew out of a psychological peculiarity of his, namely, the unusual slowness with which waves of sensation were propelled inward toward the brain from remote parts of his periphery. A dig of the spurs administered in the flank passed unnoticed for a period of time varying from twelve to thirteen seconds, till the protoplasm of the brain received the percussive wave; then, with a suddenness which I never wholly got over, he would dash into a trot, nearly tripping himself up with his own astonishment.

A stroke of good fortune completed our outfit and my happiness by bringing to Visalia a Spaniard who was under some manner of financial cloud. His horse was offered for sale, and quickly bought for me by Professor Brewer. We named him Kaweah, after the river and its Indian tribe. He was young, strong, fleet, elegant, a pattern of fine modelling in every part of his bay body and fine black legs; every way good, only fearfully wild, with a blaze of quick electric light in his dark eye.

Shortly after sunrise one fresh morning we made a point of putting the packs on very securely, and, getting into our saddles, rode out toward the Sierras. The group of farms surrounding Visalia is gathered within a belt through which several natural, and many more artificial, channels of the Kaweah flow. Groves of large, dark-foliaged oaks follow this irrigated zone; the roads, nearly always in shadow, are flanked by small ranch-houses, fenced in with rank jungles of weeds and rows of decrepit pickets.

Our backs were now turned to this farm-belt, the road leading us out upon the open plain in our first full sight of the Sierras. Grand and cool swelled up the forest; sharp and rugged rose the wave of white peaks, their vast fields of snow rolling over the summit in broad, shining masses. Sunshine, exuberant vegetation, brilliant plant life, occupied our attention hour after hour until the middle of the second day. At last, after climbing a long, weary ascent, we rode out of the dazzling light of the foot-hills into a region of dense woodland, the road winding through avenues of pines so tall that the late evening light only came down to us in scattered rays. Under the deep shade of these trees we found an air pure and gratefully cool.

Passing from the glare of the open country into the dusky forest, one seems to enter a door and ride into a vast covered hall. The whole sensation is of being roofed and enclosed. You are never tired of gazing down long vistas, where, in stately groups, stand tall shafts of pine. Columns they are, each with its own characteristic tinting and finish, yet all standing together with the air of relationship and harmony. Feathery branches, trimmed with living green, wave through the upper air, opening broken glimpses of the far blue, and catching on their polished surfaces reflections of the sun. Broad streams of light pour in, gilding purple trunks and falling in bright pathways along an undulating floor. Here and there are wide, open spaces, around which the trees group themselves in majestic ranks.

Our eyes often ranged upward, the long shafts leading the vision up to green, lighted spires, and on to the clouds. All that is dark and cool and grave in color, the beauty of blue umbrageous distance, all the sudden brilliance of strong local lights tinted upon green boughs or red and fluted shafts, surround us in ever-changing combination as we ride along these winding roadways of the Sierra.

We had marched a few hours over high, rolling, wooded ridges, when in the late afternoon we reached the brow of an eminence and began to descend. Looking over the tops of the trees beneath us, we saw a mountain basin fifteen hundred feet deep surrounded by a rim of pine-covered hills. An even, unbroken wood covered these sweeping slopes down to the very bottom, and in the midst, open to the sun, lay a circular green meadow, about a mile in diameter.

As we descended, side wood-tracks, marked by the deep ruts of timber wagons, joined our road on either side, and in the course of an hour we reached the basin and saw the distant roofs of Thomas’s Saw-Mill Ranch. We crossed the level disc of meadow, fording a clear, cold mountain stream, flowing, as the best brooks do, over clean, white granite sand, and near the northern margin of the valley, upon a slight eminence, in the edge of a magnificent forest, pitched our camp.

The hills to the westward already cast down a sombre shadow, which fell over the eastern hills and across the meadow, dividing the basin half in golden and half in azure green. The tall young grass was living with purple and white flowers. This exquisite carpet sweeps up over the bases of the hills in green undulations, and strays far into the forest in irregular fields. A little brooklet passed close by our camp and flowed down the smooth green glacis which led from our little eminence to the meadow. Above us towered pines two hundred and fifty feet high, their straight, fluted trunks smooth and without a branch for a hundred feet. Above that, and on to the very tops, the green branches stretched out and interwove, until they spread a broad, leafy canopy from column to column.

Professor Brewer determined to make this camp a home for the week during which we were to explore and study all about the neighborhood. We were on a great granite spur, sixty miles from east to west by twenty miles wide, which lies between the Kaweah and King’s River cañons. Rising in bold sweeps from the plain, this ridge joins the Sierra summit in the midst of a high group. Experience had taught us that the cañons are impassable by animals for any great distance; so the plan of campaign was to find a way up over the rocky crest of the spur as far as mules could go.

In the little excursions from this camp, which were made usually on horseback, we became acquainted with the forest, and got a good knowledge of the topography of a considerable region. On the heights above King’s Cañon are some singularly fine assemblies of trees. Cotter and I had ridden all one morning northeast from camp under the shadowy roof of forest, catching but occasional glimpses out over the plateau, until at last we emerged upon the bare surface of a ridge of granite, and came to the brink of a sharp precipice. Rocky crags lifted just east of us. The hour devoted to climbing them proved well spent.

A single little family of alpine firs growing in a niche in the granite surface, and partly sheltered by a rock, made the only shadow, and just shielded us from the intense light as we lay down by their roots. North and south, as far as the eye could reach, heaved the broad, green waves of plateau, swelling and merging through endless modulation of slope and form.

Conspicuous upon the horizon, about due east of us, was a tall, pyramidal mass of granite, trimmed with buttresses which radiated down from its crest, each one ornamented with fantastic spires of rock. Between the buttresses lay stripes of snow, banding the pale granite peak from crown to base. Upon the north side it fell off, grandly precipitous, into the deep upper cañon of King’s River. This gorge, after uniting a number of immense rocky amphitheatres, is carved deeply into the granite two and three thousand feet. In a slightly curved line from the summit it cuts westward through the plateau, its walls, for the most part, descending in sharp, bare slopes, or lines of ragged débris, the resting-place of processions of pines. We ourselves were upon the brink of the south wall; three thousand feet below us lay the valley, a narrow, winding ribbon of green, in which, here and there, gleamed still reaches of the river. Wherever the bottom widened to a quarter or half a mile, green meadows and extensive groves occupied the level region. Upon every niche and crevice of the walls, up and down sweeping curves of easier descent, were grouped black companies of trees.

The behavior of the forest is observed most interestingly from these elevated points above the general face of the table-land. All over the gentle undulations of the more level country sweeps an unbroken covering of trees. Reaching the edge of the cañon precipices, they stand out in bold groups upon the brink, and climb all over the more ragged and broken surfaces of granite. Only the most smooth and abrupt precipices are bare. Here and there a little shelf of a foot or two in width, cracked into the face of the bluff, gives foothold to a family of pines, who twist their roots into its crevices and thrive. With no soil from which the roots may drink up moisture and absorb the slowly dissolved mineral particles, they live by breathing alone, moist vapors from the river below and the elements of the atmosphere affording them the substance of life.

The Indian system

Just about as prescient, and early, of a description of the California wildland fire and forest development problem as you will find:

As regards the growth of young timber—save only among the heavy redwood forests—the number of young trees which within the last decade or two has sprung up, is very great. All the open pine forests, back of the coast, are becoming rapidly stocked with young trees, and much of the open grazing land is rapidly being converted into brush or becoming covered with young saplings—generally Douglas spruce [Douglas-fir] or yellow [ponderosa] pine.

The cause of this increase is unquestionably the cessation of the old Indian practice (formerly general) of running fires through the country to keep it open to facilitate hunting, or in driving game before the flames into enclosures set with snares. Under this system about half the ground was burned over each year, in alternate halves; thereby the open lands were kept free of brush and all growth of young trees was checked in the forests. The older, well matured trees, however, suffered very little, as so little undergrowth could mature between one fire and another, that sufficient heat was not developed to hurt older trees, fairly covered with bark and with limbs some distance above the ground. In fact, the Indian system became in some sense a method of forest preservation, and to it we undoubtedly owe the noble forests which were transmitted to our hands.

We may acknowledge this debt to the red man, although his methods may no longer be available in a growing country studded if only sparsely with improvements. The Indian’s method may not have been an ideal one, but it was a better one in his day and generation than our lack of all method is in ours.

The very growth of young trees, left uncared for as at present, must be to those with the good of the forest at heart, a source of concern rather than of satisfaction. With forest fires running—often twenty in a county at one time—and public sentiment dormant to the extent that, save where individual property is at stake, few take the trouble to put out even such incipient fires as might be killed with little effort, there can be no question but that in the growth of young trees lies the certain guarantee of total extermination of much of our best forest land, within a few years, unless some effectual methods of protection are inaugurated.

Thirty years ago fires ran yearly through the woods, but forest conflagrations were unknown; the large trees standing sparsely scattered, say five to ten to the acre, were unable to transmit fire, and there was little on the ground to burn. Now thousands of young trees fill the open spaces, and a fire started not only destroys the young trees but the patriarchs of the forest also.

As yet the evil has attained no very serious proportions; but so surely as the young growth is permitted and fires not kept out entirely (which will be found a simply impossible matter) fires will occur, which will sweep everything in their path out of existence.

The longer the matter is left to find its own solution the more difficult and expensive of application remedial measures will become. As a means of protection against fires, one effectual method, and only one, suggests itself—the isolation of such forests as it may be deemed essential to preserve, into blocks of moderate area, separated by strips of waste land, wide enough to insure no spread of fire from one belt to another. This done, the forests may be left to grow up densely, if desired, without fear of extensive damage.

Topographical conditions would generally suggest the location of these waste strips. Ridge summits and canon bottoms (especially the former) are natural barriers to fire, being only crossed with difficulty by flames, when free of brush and litter. The lines of watershed on spurs are generally sparsely timbered, and could be easily maintained free of undergrowth, even if not denuded of their trees. As regards the strips which have been designated as waste, they might in many cases be capable of sodding or being maintained in grass, producing range and pasture, and for the rest, the authorized use of fire by duly commissioned persons, duly provided with adequate means of checking the spread of flames, might suggest itself as the simplest, cheapest, and most efficient method.

Of course these proposals only have reference to the public lands, private holdings must remain subject to private management, and such forests as now are held in private hands must survive or perish, as the owner elects. In any event, private holdings, when lying within the lines of districts which it might be wished to treat on the basis proposed, will always cause complication. If anything is to be done at all, it is time to do it now, while the Government owns whole districts free from settlers, and consequently, in this respect, at least, need have nothing but the public interest to consider.

First Biennial Report of the California State Board of Forestry, 1886-1888

“A systematic record of great biological value”

Paul Sears was an early plant ecologist who did a lot of good work at the University of Nebraska and previously at Ohio State, Nebraska being the nexus of American plant ecology in the early 20th century. He was I believe, the first president of the Ecological Society of America. He was also one of the very first ecologists–of what is now a legion–to estimate landscape scale forest taxonomic composition at pre-settlement time, using the bearing/witness tree record contained within the early federal land survey. Here he takes a humorous swipe at the geometric wisdom inherent in the survey design. Ya can’t put a rectangular grid on a round planet fer cryin’ out loud, but hey, thanks for recording all those trees! 🙂

Surveying of Ohio was begun in July, 1786, under The Geographer of the United States, Thomas Hutchins, employing for the first time his device of sections one mile square. This empirical device was hailed as a great American invention, although the State of Ohio has since been found to possess a curved surface in common with the rest of the earth. All corners which lay within the forest were located with reference to nearby trees, the species of which were noted. These corners becoming permanent, the net result of Hutchins’ plan has been the preservation of a systematic record of such great biological value as to redeem its geometrical shortcomings.

A little background might be useful. Ohio was the first state surveyed under the federal land survey, all previous states being surveyed in all manner of ways by various entities under various authorities and quality control procedures, i.e. without a comprehensive and systematic plan. By law enacted in 1785–the very first congress–a hugely important law affecting how the public domain would be disposed of, all states added to the country from that point forward were to be surveyed under a systematic, regular survey design with very specific instructions regarding how to proceed (Thomas Jefferson being a driving force behind this). Ohio, being the first such state added, in 1803, also served as the test state, where various survey designs were tried out before deciding on the one that, with minor modifications, has been followed the last 200 years in the 30 federal land survey states.

To my knowledge no other branch of ecology has the quality of historic data sets dating to +/- pre-settlement times, i.e. before all the heavy impacts occurred, and most certainly not over such an enormous geographic extent. In fact, I don’t think it’s even close. We’re very lucky in that regard, and we have people like Thomas Jefferson, with his sense of mathematical order and intense interest in all things natural and landscape, for it.

Sears, Paul B. 1925. The Natural Vegetation of Ohio: I, A Map of the Virgin Forest

Around Yosemite walls and through Yosemite forests

So, I’ve been entering bearing tree data collected by land surveyors inside what is now Yosemite National Park, for work on estimating historic forest conditions in the Sierra Nevada. Bearing trees were designed to “bear witness” to the location of on-the-ground survey markers, in case something should happen to them, and several pieces of information on them were recorded in the field notes (previous post here). So up comes the next Township on the list: Township 2 South, Range 21 East, Mt. Diablo Meridian, or T2SR21E MDM in surveyors’ shorthand, an area now inside YNP, surveyed under authority of the General Land Office (GLO) in 1880, 10 years before YNP came into existence.

An original (1880) YNP bearing tree, in 2005, with blaze partially exposed.

An original (1880) YNP bearing tree, in 2005, with blaze partially exposed.

Well, damned if that isn’t a pretty good place to run into the man, Clarence King, and thereby to slow down the scientific progress on which society so utterly depends. Once I start reading King’s writings it’s all over in terms of getting things done. He’s done it to me before, and he will do it again.

Continue reading

Douglas’ “Multnomah pine”

Sugar Pine

…August 19, 1825 Mr. Douglas, who had been exploring the upper country of the Columbia, started from his headquarters at Vancouver to proceed southward, ascending the Multnomah towards the mountains at the extreme (south) end of the Willamette Valley. After a perilous three days’ trip he reaches the natives of the region and finds in their tobacco pouches “seeds of a remarkably large size, which they eat as nuts”, and which he knew to be pine seeds. He learns that the tree grows on the mountains to the south—that is, down nearly to the present California line.

“No time was to be lost,” he writes, “in ascertaining the existence of the tree,” which he at once, with only a few imperfect seeds in hand, names Pinus Lambertiana, in honor of his friend, Aylmer Bourke Lambert, the distinguished Vice-President of the Linnaean Society of England. But sickness and inclement weather, also Indian hostilities, prevented further search southward for that season. However, he explores other regions eastward, discovering two new species of pine, which he names Pinus nobilis and Pinus amabilis (now well known firs, but then included in the genus of pines), making headquarters for the winter at Fort Vancouver. During the spring and summer months of the next year, 1826, he makes various extensive journeys, rewarded constantly by important discoveries, for the country was all unknown then. In February a hunter brings him a cone of his Multnomah pine. It “was 16 inches long and 10 in circuit” and he was assured that “trees were met with that were 170-220 feet high, and 20-50 feet in circumference”.

In June, while at the junction of the Lewis and Clarke Rivers, he planned a long trip southward to the Umpqua River, in search of “the gigantic pine”, but could not get off in that direction until October. On the eighteenth Douglas, with a companion, “set off due south through the dominions of the Chief, Center-Nose, and having climbed wearily a high divide, we were cheered by the sight of the broad Umpqua River in the valley far below”. A raft was necessary for crossing it, and in its construction Douglas “grievous blistered his fingers”..October 23rd they reach the headwaters Of the Umpqua, guided by the son of old Center-Nose, and still “intent upon finding the Grand Pine so frequently mentioned in my journal”.

…Early in the morning of the same day (October 25th) Douglas quitted camp, and “after an hour’s walk met an Indian, who, on perceiving me, instantly strung his bow, then slung his raccoon skin of arrows upon his left arm, and stood on the defensive. Being quite sure that he was not hostile, but prompted by fear only, I laid my gun at my feet and beckoned him to approach me, which he did slowly and with many precautions. I then made him place his bow and quiver beside my gun, and, striking a light, gave him a smoke out of my pipe. Then with pencil and paper I drew a rough sketch of the cone and tree which I desired to find, and exhibited the sketch to him, when he quickly pointed towards the hills, fifteen or twenty miles distant, and southward.”

Hastening on, at midday Douglas “reached the locality of my longwished-for pines, and lost no time in examining them, and endeavoring to collect twigs, specimens, and seeds. “New and strange things,” Douglas pauses here to remark, sententiously, “seldom fail to make strong impressions, and are, therefore, often faulty or overrated; so, lest I should never again see my friends in England, to inform them verbally of this most beautiful and grand tree”.

“I shall here state the dimensions of the largest found among several that had been felled by the wind. At three feet from the ground its circuit was fifty-seven feet nine inches (that is, nearly nineteen feet in diameter). At one hundred and thirty-four feet it was seventeen feet five inches. Extreme length, two hundred and forty-five feet. The trunks are uncommonly straight, the bark smooth, the tallest stems unbranched for two thirds of their height, the branches outreaching or pendulous, with long cones hanging from the points like sugar loaves in a grocer shop. The cones are borne only by the largest trees, high suspended in air, and the putting myself into possession of three of them, all I could procure, nearly brought my life to a close.”

“As it was impossible either to climb the trees or to hew one down I resorted to knocking them off by firing at them with ball. The report of my gun almost instantly brought into view eight Indians, all armed with bows, bone-tipped spears, and flint knives. I endeavored to explain to them what I was doing there and what I wanted, and they seemed satisfied, sitting down to smoke with me; but presently I perceived one of them to string his bow, and another to whet his knife with a pair of wooden pincers. Further testimony of their intention was unnecessary.

“To save myself by flight was impossible, so without hesitation I sprang backwards about five paces, cocked my gun, drew one of the pistols from my belt, and showed myself determined to fight for my life. As much as possible I endeavored to preserve coolness, and thus we stood facing each other without the slightest movement or uttering a word for full ten minutes. At last the leader dropped his hand and made signs for tobacco and pipe. I signified that they should have a smoke if they would fetch me a quantity of cones. They went off immediately, and no sooner were the out of sight than I picked up my precious cones and made the quickest possible retreat.”

Poor Douglas never saw his “Grand Pine” again, and upon his second tour of western exploration the next season, after visiting Monterey Bay and vicinity, where he discovers Pinus insignia and P. sabiniana, he sailed for the Hawaiian Islands, and while exploring there he fell into a pit prepared for capturing wild cattle, and was trampled to death by an entrapped steer.


The Fire Next Time

A short and well-balanced summary of the drivers and repercussions of the present and future wildland fire problem in the western United States. Discussed using 2013’s Rim Fire as a focal point, the enormous and highly unnatural and destructive fire that burned through the Stanislaus National Forest and western Yosemite NP, including an area containing 20 long-term forest monitoring plots of mine. Found at Wildfire Today, which is a great site for all things fire, especially w.r.t. California.

How not to do it

This is a long post. It analyzes a paper that recently appeared in Nature. It’s not highly technical but does get into some important analytical subtleties. I often don’t know where to start (or stop) with the critiques of science papers, or what good it will do anyway. But nobody ever really knows what good any given action will do, so here goes. The study topic involves climate change, but climate change is not the focus of either the study or this post. The issues are, rather, mainly ecological and statistical, set in a climate change situation. The study illustrates some serious, and diverse problems.

Before I get to it, a few points:

  1. The job of scientists, and science publishers, is to advance knowledge in a field
  2. The highest profile journals cover the widest range of topics. This gives them the largest and most varied readerships, and accordingly, the greatest responsibilities for getting things right, and for publishing things of the highest importance
  3. I criticize things because of the enormous deficit of critical commentary from scientists on published material, and the failures of peer review. The degree to which the scientific enterprise as a whole just ignores this issue is a very serious indictment upon it
  4. I do it here because I’ve already been down the road–twice in two high profile journals–of doing it through journals’ established procedures (i.e. the peer-reviewed “comment”); the investment of time and energy, given the returns, is just not worth it. I’m not wasting any more of my already limited time and energy playing by rules that don’t appear to me designed to actually resolve serious problems. Life, in the end, boils down to determining who you can and cannot trust and acting accordingly

For those without access to the paper, here are the basics. It’s a transplant study, in which perennial plants are transplanted into new environments to see how they’ll perform. Such studies have, at least, a 100 year history, dating to genetic studies by Bateson, the Carnegie Institute, and others. In this case, the authors focused on four forbs (broad leaved, non-woody plants), occurring in mid-elevation mountain meadows in the Swiss Alps. They wanted to explore the effects of new plant community compositions and T change, alone and together, on three fitness indicators: survival rate, biomass, and fraction flowering. They attempted to simulate having either (1) entire plant communities, or (2) just the four target species, experience sudden temperature (T) increases, by moving them downslope 600 meters. [Of course, a real T change in a montane environment would move responsive taxa up slope, not down.] More specifically, they wanted to know whether competition with new plant taxa–in a new community assemblage–would make any observed effects of T increases worse, relative to those experienced under competition with species they currently co-occur with.

Their Figure 1 illustrates the strategy:

Figure 1: Scenarios for the competition experienced by a focal alpine plant following climate warming. If the focal plant species (green) fails to migrate, it competes either with its current community (yellow) that also fails to migrate (scenario 1) or, at the other extreme, with a novel community (orange) that has migrated upwards from lower elevation (scenario 2). If the focal species migrates upwards to track climate, it competes either with its current community that has also migrated (scenario 3) or, at the other extreme, with a novel community (blue) that has persisted (scenario 4).

Figure 1: Scenarios for the competition experienced by a focal alpine plant following climate warming.
If the focal plant species (green) fails to migrate, it competes either with its current community (yellow) that also fails to migrate (scenario 1) or, at the other extreme, with a novel community (orange) that has migrated upwards from lower elevation (scenario 2). If the focal species migrates upwards to track climate, it competes either with its current community that has also migrated (scenario 3) or, at the other extreme, with a novel community (blue) that has persisted (scenario 4).

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Outcome probabilities

Continuing from the previous post., where I discussed earth’s recent surface temperature increase hiatus/slowdown/backoff/vacation

Well not really–I discussed instead the very closely related topic of enumerating the outcomes of a given probabilistic process. And actually not so much a discussion as a monologue. But couldn’t somebody please address that other issue, it’s just been badly neglected… 🙂

Anyway, enumerating the possible allocations of n objects into q groups is rarely an end in itself; the probability, p of each is usually what we want. This is a multinomial probability (MP) problem when q > 2, and binomial (BP) when q = 2, in which we know apriori the per-trial p values and want to determine probabilities of the various possible outcomes over some number, n, of such trials. In the given example, the per-trial probabilities of group membership are all equal (1/6) and we want to know the probability of each possible result from n = 15 trials.

One has to be careful in defining exactly what “trials” and “sample sizes” constitute in these models though, because the number of trials can be nested. We could for example, conduct n2 = 100 higher level trials, in each of which the results from n1 = 2 lower level trials are combined. This is best exemplified by Hardy-Weinberg analysis in population genetics; a lower level trial consists of randomly choosing n1 = 2 alleles from the population and combining them into a genotype. This is repeated n2 times and the expected genotype frequencies, under certain assumption of population behavior, are then compared to the observed, to test whether the assumptions are likely met or not. If only two possible outcomes of a single trial (alleles in this case) exist in the population, the model is binomial, and if more than two, multinomial.

There are two types of MP/BP models, corresponding to whether or not group identity matters. When it does, the BP/MP coefficients determine the expected probabilities of each specific outcome. For n objects, q groups and group sizes a through f, these equal the number of permutations, as given by n! / (a!b!c!d!e!f!), where “!” is the factorial operator and 0! = 1 by definition. This formula is extremely useful; without it we’d have to enumerate all permutations of a given BP/MP process. And this would choke us quickly, as such values become astronomical in a hurry: with n = 15 and q = 6, we already have 6^15 = 470 billion possible permutations.

When group identity doesn’t matter, only the numerical distribution matters, and this will decrease the total number of coefficients but increase the value of each of them. For example, in locating the n = 50 closest trees to a random sampling point, one may want to know only the expected numerical distribution across the q angle sectors around the point. In that case, the allocation [2,1,1,0] into groups [a,b,c,d] would be identical to [0,1,1,2] and to 10 others, and these thus have to be aggregated. The number of aggregations is given by the number of permutations of the observed group sizes, which in turn depends on their variation. When all differ, e.g. [0,1,2,3,4,5] for n = 15, the number of equivalent outcomes is maximized, equaling q + (q-1) + (q-2)…+ 1 (in this case, 21) [Edit: oops, confused that with what follows; the number of permutations there is given by q!]. When some but not all of the group sizes are identical it’s more complex, as determined by products of factorials and permutations. When the number of identical group sizes is maximized, the equivalent outcomes are minimized, always at either q-1 or 1. In this case there are 6 variations of [n,0,0,0,0,0].

To get the desired probability density function, the raw MP/BP coefficients, obtained by either method, are standardized to sum to 1.0.

Next time I’m going to discuss a general solution to the problem of estimating the otherwise unknown relationships between pairs of objects involved in a rate process, such as density, the number of objects per unit area or time. These can be deduced analytically using multinomial and gamma probability models in conjunction.

It will make you call your neighbors over for a party and group discussion. If it doesn’t you get a full refund.

Count ’em

Suppose you have n objects and want to enumerate all possible unique allocations thereof among q groups, where “unique” is defined by numerical allocation only, independent of actual group membership for each object. Each group can take any size from 0 to n, contingent on the total in the other q-1 groups. I’m working on a problem where I have to do this; there might well be an available method for doing this, but one can waste a lot of time looking for such things in my experience, you typically learn a lot more when you have to solve a problem yourself. Anyway I couldn’t find one readily so I wrote this R function as a script. Feel free to use if it’s, well, useful.

all.breaks = function(n, groups){
 t1 = cbind(n - 0:n, n - n:0)
 t1 = unique(t(apply(t1, 1, sort)))
 test = groups - 2
  if (test>0){
   for (i in 1:test){
    t2a = sapply(t1[,split], function(x) 0:x)
    t2b = sapply(t1[,split], function(x) x:0)
    reps = unlist(lapply(t2a, length))
    t2a = unlist(t2a); t2b = unlist(t2b)
    temp = t(apply(cbind(t2a,t2b), 1, sort))
    t1 = apply(t1, 2, function(x) rep(x,reps))
    t1 = cbind(t1[,-split], temp)
    t1 = unique(t(apply(t1, 1, sort)))
   } # End for() 
  } # End if()
  t1 = t(apply(t1,1,sort, decreasing=T))
  colnames(t1) = letters[1:groups]; rownames(t1) = 1:nrow(t1)
 } # End function

Example with 15 objects and 6 groups:

> all.breaks(n=15, groups=6)

     a b c d e f
1   15 0 0 0 0 0
2   14 1 0 0 0 0
3   13 2 0 0 0 0
4   12 3 0 0 0 0
5   11 4 0 0 0 0
6   10 5 0 0 0 0
7    9 6 0 0 0 0
8    8 7 0 0 0 0
9   13 1 1 0 0 0
10  12 2 1 0 0 0
11  11 3 1 0 0 0
12  10 4 1 0 0 0
13   9 5 1 0 0 0
14   8 6 1 0 0 0
15   7 7 1 0 0 0
16  11 2 2 0 0 0
17  10 3 2 0 0 0
18   9 4 2 0 0 0
19   8 5 2 0 0 0
20   7 6 2 0 0 0
21   9 3 3 0 0 0
22   8 4 3 0 0 0
23   7 5 3 0 0 0
24   6 6 3 0 0 0
25   7 4 4 0 0 0
26   6 5 4 0 0 0
27   5 5 5 0 0 0
28  12 1 1 1 0 0
29  11 2 1 1 0 0
30  10 3 1 1 0 0
31   9 4 1 1 0 0
32   8 5 1 1 0 0
33   7 6 1 1 0 0
34  10 2 2 1 0 0
35   9 3 2 1 0 0
36   8 4 2 1 0 0
37   7 5 2 1 0 0
38   6 6 2 1 0 0
39   8 3 3 1 0 0
40   7 4 3 1 0 0
41   6 5 3 1 0 0
42   6 4 4 1 0 0
43   5 5 4 1 0 0
44   9 2 2 2 0 0
45   8 3 2 2 0 0
46   7 4 2 2 0 0
47   6 5 2 2 0 0
48   7 3 3 2 0 0
49   6 4 3 2 0 0
50   5 5 3 2 0 0
51   5 4 4 2 0 0
52   6 3 3 3 0 0
53   5 4 3 3 0 0
54   4 4 4 3 0 0
55  11 1 1 1 1 0
56  10 2 1 1 1 0
57   9 3 1 1 1 0
58   8 4 1 1 1 0
59   7 5 1 1 1 0
60   6 6 1 1 1 0
61   9 2 2 1 1 0
62   8 3 2 1 1 0
63   7 4 2 1 1 0
64   6 5 2 1 1 0
65   7 3 3 1 1 0
66   6 4 3 1 1 0
67   5 5 3 1 1 0
68   5 4 4 1 1 0
69   8 2 2 2 1 0
70   7 3 2 2 1 0
71   6 4 2 2 1 0
72   5 5 2 2 1 0
73   6 3 3 2 1 0
74   5 4 3 2 1 0
75   4 4 4 2 1 0
76   5 3 3 3 1 0
77   4 4 3 3 1 0
78   7 2 2 2 2 0
79   6 3 2 2 2 0
80   5 4 2 2 2 0
81   5 3 3 2 2 0
82   4 4 3 2 2 0
83   4 3 3 3 2 0
84   3 3 3 3 3 0
85  10 1 1 1 1 1
86   9 2 1 1 1 1
87   8 3 1 1 1 1
88   7 4 1 1 1 1
89   6 5 1 1 1 1
90   8 2 2 1 1 1
91   7 3 2 1 1 1
92   6 4 2 1 1 1
93   5 5 2 1 1 1
94   6 3 3 1 1 1
95   5 4 3 1 1 1
96   4 4 4 1 1 1
97   7 2 2 2 1 1
98   6 3 2 2 1 1
99   5 4 2 2 1 1
100  5 3 3 2 1 1
101  4 4 3 2 1 1
102  4 3 3 3 1 1
103  6 2 2 2 2 1
104  5 3 2 2 2 1
105  4 4 2 2 2 1
106  4 3 3 2 2 1
107  3 3 3 3 2 1
108  5 2 2 2 2 2
109  4 3 2 2 2 2
110  3 3 3 2 2 2

The next post will examine the probabilities of each such outcome.

This week’s puzzler

This week’s puzzler comes to us from John Storthwaite in Stonyfield, Minnesota, who has been wondering why there are so many trees blocking his view of the rocks up there.

Suppose you have been given the following problem. A number of objects are located in some given area, say trees in a forest for example, and one wishes to estimate their density D (number per unit area). Distance-based sampling involves estimating D by averaging a sample of squared, point-to-object distances (d), for objects of known integer rank distance (r) from the point. The distances are squared because one is converting from one dimensional measurements (distance) to a two dimensional variable (objects per unit area).

So here’s the puzzler. If you run a line through this arbitrary point, and choose the closest objects (r = 1) on each side of it, what will be the ratio of the squared distances of the two objects and how would you solve this, analytically? Would they be about the same distance away? If not, would there be a predictable relationship between them? The problem can be extended to any number of lines passing through said point, just with correspondingly more pairs of distances to evaluate.

The first questions one should ask here are clear: (1) “Why on earth would anybody want to do that?” and (2) “Is that the type of thing you clowns spend your time on?“. We have answers for those questions. Not necessarily satisfactory answers, but answers nonetheless. Giving an answer, that’s the important thing in life. So, if you know the answer, write it on the back of a $100 bill and send it to…

Anyway, there are two possible solutions here. The first one comes readily if one realizes that the densities within sectors must each be about the same as the overall density, since we assume a homogeneous overall density. But, for a given value of r, the squared distances in each of the two sectors must be, on average, about twice those for the collection of trees overall, because there are only half as many trees in each sector as there are overall. So, e.g. the r = 5th closest trees within each half are on average, 2X the squared distance of the r = 5th closest tree overall.

Knowing this, the relationship between the two r = 1 trees (label them r1.1 and r1.2 having squared distances d1.1 and d1.2) in the two sectors becomes clear. Since one of the two trees (r1.1) must necessarily be the r = 1 tree overall, and the mean squared distance of the two trees must be 2X that of the r = 1 tree, this translates to:

2*d1.1 = (d1.1 + d1.2)/2 and thus,
d1.2 = 3(d1.1),

i.e., one member of the pair will, on average, be exactly three times the squared distance of the other. This result can be confirmed by an entirely independent method involving asymptotic binomial/multinomial probability. That exercise is left, as they say in the ultimate cop-out, to the reader.

This work has highly important implications with respect to a cancer research, and for solutions to poverty, malnutrition, and climate change. It can also help one discern if tree samplers 150-200 years ago were often sampling the closest trees or not.

Funding for this work was provided by the Doris Duke Foundation, the Society for American Baseball Research, the American Bean and Tree Counters Society, the Society for Measuring Things Across From Other Things, and the Philosophy Department at the University of Hullaballo. All rights reserved, all obligations denied. Any re-use, re-broadcast, retransmission, regurgitation or other use of the accounts and descriptions herein, without the express written consent of the closest random stranger on the street, or the closest random stranger on the other side of said street, is strictly prohibited.

Golf course succession

A friend’s property, in the county my parents live in, is surrounded by a nine hole golf course that went out of business several years ago, and is about to be acquired by the US Fish and Wildlife Service. It is undergoing rapid ecological succession to a less managed state since they stopped mowing a few years back. This process is very common with abandoned farm land, but this is the first I’ve looked at a golf course. The place is interesting because the area is naturally wet, being originally part of a very large swamp/wetland complex (the “Great Black Swamp”) that stretched over many counties and caused this area to be the last settled in Ohio. The original vegetation, documented in 1820, was dominated by intermixed treeless wet prairie, and swamp or other northern wetland hardwoods, with standing water over the entire year common. The inherently wet soils might well have affected the course’s success, I don’t know.

Several tree species mentioned in the 1820 GLO land survey notes (see bottom image) are still present, including swamp white oak (Quercus bicolor), american elm (Ulmus americana), pin oak (Q. palustris), green ash (Fraxinus pennsylvanica), hickory (Carya cordiformis), eastern cottonwood (Populus deltoides), and unspecified willows (Salix spp.). Others have clearly come in post-settlement, including black walnut (Juglans nigra), northern catalpa (Catalpa speciosa), weeping willow (Salix babylonica), possibly silver maple (Acer saccharinum), and the completely misplaced jack pine (Pinus banksiana) and eastern redcedar (Juniperus virginiana) (most likely both as yard markers and fairway dividers). How the USFWS will manage the property will be interesting; it may be difficult to recreate the wet prairie habitat given that the natural drainage pattern is now highly altered by ditching and drain tiling.

Wet prairie and hardwood swamp, to farm, to golf course, to...

Wet prairie and hardwood swamp, to farm, to golf course, to…

Goldenrod (Solidago spp), a notorious and obvious late bloomer.

Goldenrod (Solidago spp), a notorious and obvious late bloomer.

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Estimating the spread rate in the current ebola epidemic

I’ve now written several articles on the West African ebola outbreak (see e.g. here, here, here, and here). This time I want to get more analytical, by describing how I estimated the ebola basic reproduction rate Ro (“R zero”), i.e. the rate of infection spread. Almost certainly, various people are making these estimates, but I’ve not seen any yet, including at the WHO and CDC websites or the few articles that have come out to date.

Some background first. Ro is a fundamental parameter in epidemiology, conceptually similar to r, the “intrinsic rate of increase”, in population biology. In epidemiology, it’s defined as the (mean) number of secondary disease cases arising from some primary case. When an individual gets infected, he or she is a secondary case relative to the primary case that infected him or her, and in turn becomes a primary case capable of spreading the disease to others. It’s a lineage in that respect, and fractal. I’ll refer to it simply as R here.

The value of R depends strongly on the biology of the virus and the behavior of the infected. It is thus more context dependent than the r parameter of population biology, which is an idealized, or optimum, rate of population growth determined by intrinsic reproductive parameters (e.g. age to reproductive maturity, mean litter size, gestation time). Diseases which are highly contagious, such as measles, smallpox and the flu, have R values in the range of 3 to 8 or even much more, whereas those that require direct exchange of body fluids, like HIV, have much lower rates.

To slow an epidemic of any disease it is necessary to lower the value of R; to stop it completely, R must be brought to zero. Any value of R > 0.0 indicates a disease with at least some activity in the target population. When R = 1.0, there is a steady increase in the cumulative number of cases, but no change in the rate of infection (new cases per unit time): each infected person infects (on average) exactly 1.0 other person before either recovering or dying. Any R > 1.0 indicates a (necessarily exponential) increase in the infection rate, that is, the rate of new cases per unit time (not just the total number of cases), is increasing.

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