Capillary comes from the Latin word capillaris, meaning "of or resembling hair", with use in English beginning in the mid-17th century. The meaning stems from the tiny, hairlike diameter of a capillary. While capillary is usually used as a noun, the word also is used as an adjective, as in "capillary action", in which a liquid flows without influence of external forces, such as gravity.
Structure
Diagram of capillary bed
Blood flows from the heart through arteries, which branch and narrow into arterioles,
and then branch further into capillaries where nutrients and wastes are
exchanged. The capillaries then join and widen to become venules, which in turn widen and converge to become veins, which then return blood back to the heart through the venae cavae. In the mesentery, metarterioles form an additional stage between arterioles and capillaries.
Individual capillaries are part of the capillary bed, an interweaving network of capillaries supplying tissues and organs. The more metabolically
active a tissue is, the more capillaries are required to supply
nutrients and carry away products of metabolism. There are two types of
capillaries: true capillaries, which branch from arterioles and provide
exchange between tissue and the capillary blood, and sinusoids, a type of open-pore capillary found in the liver, bone marrow, anterior pituitary gland, and brain circumventricular organs. Capillaries and sinusoids are short vessels that directly connect the arterioles and venules at opposite ends of the beds. Metarterioles are found primarily in the mesentericmicrocirculation.
Lymphatic capillaries
are slightly larger in diameter than blood capillaries, and have closed
ends (unlike the blood capillaries open at one end to the arterioles
and open at the other end to the venules). This structure permits interstitial fluid to flow into them but not out. Lymph capillaries have a greater internal oncotic pressure than blood capillaries, due to the greater concentration of plasma proteins in the lymph.
Types
Blood capillaries are categorized into three types: continuous, fenestrated, and sinusoidal (also known as discontinuous).
Types
of capillaries: (left) continuous with no big gaps, (center)
fenestrated with small pores, and (right) sinusoidal (or
'discontinuous') with intercellular gaps
Continuous
Diagram of a continuous capillary
Continuous capillaries are continuous in the sense that the endothelial cells provide an uninterrupted lining, and they only allow smaller molecules, such as water and ions, to pass through their intercellular clefts. Lipid-soluble molecules can passively diffuse through the endothelial cell membranes along concentration gradients. Continuous capillaries can be further divided into two subtypes:
Those with numerous transport vesicles, which are found primarily in skeletal muscles, fingers, gonads, and skin.
Fenestrated capillaries have pores known as fenestrae (Latin for "windows") in the endothelial cells that are 60–80 nanometres (nm) in diameter. They are spanned by a diaphragm of radially oriented fibrils that allows small molecules and limited amounts of protein to diffuse. In the renal glomerulus there are cells with no diaphragms, called podocyte
foot processes or pedicels, which have slit pores with a function
analogous to the diaphragm of the capillaries. Both of these types of
blood vessels have continuous basal laminae and are primarily located in the endocrine glands, intestines, pancreas, and the glomeruli of the kidney.
Sinusoidal capillaries or discontinuous capillaries are a special type of open-pore capillary, also known as a sinusoid, that have wider fenestrations that are 30–40 micrometres (μm) in diameter, with wider openings in the endothelium.
Fenestrated capillaries have diaphragms that cover the pores whereas
sinusoids lack a diaphragm and just have an open pore. These types of
blood vessels allow red and white blood cells (7.5 μm – 25 μm diameter) and various serum proteins to pass, aided by a discontinuous basal lamina. These capillaries lack pinocytotic vesicles,
and therefore use gaps present in cell junctions to permit transfer
between endothelial cells, and hence across the membrane. Sinusoids are
irregular spaces filled with blood and are mainly found in the liver, bone marrow, spleen, and brain circumventricular organs.
Annotated diagram of the exchange between capillary and body tissue through the exchange of materials between cells and fluid
Development
During early embryonic development, new capillaries are formed through vasculogenesis, the process of blood vessel formation that occurs through a novel production of endothelial cells that then form vascular tubes. The term angiogenesis denotes the formation of new capillaries from pre-existing blood vessels and already-present endothelium which divides.
The small capillaries lengthen and interconnect to establish a network
of vessels, a primitive vascular network that vascularises the entire yolk sac, connecting stalk, and chorionic villi.
Simplified image showing blood flow through the body, passing through capillary networks in its path
The capillary wall performs an important function by allowing
nutrients and waste substances to pass across it. Molecules larger than
3 nm such as albumin and other large proteins pass through transcellular transport carried inside vesicles,
a process which requires them to go through the cells that form the
wall. Molecules smaller than 3 nm such as water and gases cross the
capillary wall through the space between cells in a process known as paracellular transport. These transport mechanisms allow bidirectional exchange of substances depending on osmotic gradients. Capillaries that form part of the blood–brain barrier only allow for transcellular transport as tight junctions between endothelial cells seal the paracellular space.
Capillary beds may control their blood flow via autoregulation. This allows an organ to maintain constant flow despite a change in central blood pressure. This is achieved by myogenic response, and in the kidney by tubuloglomerular feedback. When blood pressure increases, arterioles are stretched and subsequently constrict (a phenomenon known as the Bayliss effect) to counteract the increased tendency for high pressure to increase blood flow.
In the lungs, special mechanisms have been adapted to meet the needs of increased necessity of blood flow during exercise. When the heart rate
increases and more blood must flow through the lungs, capillaries are
recruited and are also distended to make room for increased blood flow.
This allows blood flow to increase while resistance decreases. Extreme exercise can make capillaries vulnerable, with a breaking point similar to that of collagen.
Capillary permeability can be increased by the release of certain cytokines, anaphylatoxins, or other mediators (such as leukotrienes, prostaglandins, histamine, bradykinin, etc.) highly influenced by the immune system.
Diagram of the filtration and reabsorption in capillaries
Starling equation
The transport mechanisms can be further quantified by the Starling equation. The Starling equation defines the forces across a semipermeable membrane and allows calculation of the net flux:
where:
is the net driving force,
is the proportionality constant, and
is the net fluid movement between compartments.
By convention, outward force is defined as positive, and inward force
is defined as negative. The solution to the equation is known as the
net filtration or net fluid movement (Jv). If positive, fluid will tend to leave the capillary (filtration). If negative, fluid will tend to enter
the capillary (absorption). This equation has a number of important
physiologic implications, especially when pathologic processes grossly
alter one or more of the variables.
According to Starling's equation, the movement of fluid depends on six variables:
Disorders of capillary formation as a developmental defect
or acquired disorder are a feature in many common and serious
disorders. Within a wide range of cellular factors and cytokines, issues
with normal genetic expression and bioactivity of the vascular growth
and permeability factor vascular endothelial growth factor
(VEGF) appear to play a major role in many of the disorders. Cellular
factors include reduced number and function of bone-marrow derived endothelial progenitor cells. and reduced ability of those cells to form blood vessels.
Formation of additional capillaries and larger blood vessels
(angiogenesis) is a major mechanism by which a cancer may help to
enhance its own growth. Disorders of retinal capillaries contribute to
the pathogenesis of age-related macular degeneration.
Reduced capillary density (capillary rarefaction) occurs in association with cardiovascular risk factors and in patients with coronary heart disease.
Therapeutics
Major
diseases where altering capillary formation could be helpful include
conditions where there is excessive or abnormal capillary formation such
as cancer and disorders harming eyesight; and medical conditions in
which there is reduced capillary formation either for familial or
genetic reasons, or as an acquired problem.
In patients with the retinal disorder, neovascular age-related macular degeneration, local anti-VEGF therapy to limit the bio-activity of vascular endothelial growth factor has been shown to protect vision by limiting progression.
In a wide range of cancers, treatment approaches have been studied, or
are in development, aimed at decreasing tumour growth by reducing
angiogenesis.
William Harvey
did not explicitly predict the existence of capillaries, but he saw the
need for some sort of connection between the arterial and venous
systems. In 1653, he wrote, "...the blood doth enter into every member
through the arteries, and does return by the veins, and that the veins
are the vessels and ways by which the blood is returned to the heart
itself; and that the blood in the members and extremities does pass from
the arteries into the veins (either mediately by an anastomosis, or
immediately through the porosities of the flesh, or both ways) as before
it did in the heart and thorax out of the veins, into the arteries..."
Marcello Malpighi was the first to observe directly and correctly describe capillaries, discovering them in a frog's lung 8 years later, in 1661.
Historical ecology studies the interactions between people and their environment over the long term.
Historical ecology is a research program that focuses on the interactions between humans and their environment over long-term periods of time, typically over the course of centuries.
In order to carry out this work, historical ecologists synthesize
long-series data collected by practitioners in diverse fields.
Rather than concentrating on one specific event, historical ecology
aims to study and understand this interaction across both time and space
in order to gain a full understanding of its cumulative effects.
Through this interplay, humans adapt to and shape the environment, continuously contributing to landscape
transformation. Historical ecologists recognize that humans have had
world-wide influences, impact landscape in dissimilar ways which
increase or decrease species diversity, and that a holistic perspective
is critical to be able to understand that system.
Piecing together landscapes requires a sometimes difficult union between natural and social sciences,
close attention to geographic and temporal scales, a knowledge of the
range of human ecological complexity, and the presentation of findings
in a way that is useful to researchers in many fields. Those tasks require theory and methods drawn from geography, biology, ecology, history, sociology, anthropology,
and other disciplines. Common methods include historical research,
climatological reconstructions, plant and animal surveys, archaeological
excavations, ethnographic interviews, and landscape reconstructions.
History
The
discipline has several sites of origins by researchers who shared a
common interest in the problem of ecology and history, but with a
diversity of approaches. Edward Smith Deevey, Jr. used the term in the 1960s to describe a methodology that had been in long development.
Deevey wished to bring together the practices of "general ecology"
which was studied in an experimental laboratory, with a "historical
ecology" which relied on evidence collected through fieldwork. For
example, Deevey used radiocarbon dating to reconcile biologists’ successions of plants and animals with the sequences of material culture and sites discovered by archaeologists.
In the 1980s, members of the history department at the University of Arkansas at Little Rock organized a lecture series entitled "Historical Ecology: Essays on Environment and Social Change"
The authors noted the public's concerns with pollution and dwindling
natural resources, and they began a dialogue between researchers with
specialties which spanned the social sciences. The papers highlighted
the importance of understanding social and political structures,
personal identities, perceptions of nature, and the multiplicity of
solutions for environmental problems.
The emergence of historical ecology as a coherent discipline was
driven by a number of long-term research projects in historical ecology
of tropical, temperate and arctic environments:
E.S. Deevey's Historical Ecology of the Maya Project (1973-1984)
was carried out by archaeologists and biologists who combined data from
lake sediments, settlement patterns, and material from excavations in
the central Petén District of Guatemala to refute the hypotheses that a collapse of Mayan urban areas was instigated by faltering food production.
Carole L. Crumley's Burgundian Landscape Project (1974–present)
is carried out by a multidisciplinary research team aimed at identifying
the multiple factors which have contributed to the long-term durability
of the agricultural economy of Burgundy, France.
Thomas H. McGovern's Inuit-Norse Project (1976–present) uses
archaeology, environmental reconstruction, and textual analysis to
examine the changing ecology of Nordic colonizers and indigenous peoples
in Greenland, Iceland, Faeroes, and Shetland.
In recent years the approaches to historical ecology have been expanded to include coastal and marine environments:
Stellwagen Bank National Marine Sanctuary Project (1984–present) examines Massachusetts, USA cod fishing in the 17th through 19th centuries through historical records.
Florida Keys Coral Reef Eco-region Project (1990–present) researchers at the Scripps Institute of Oceanography
are examining archival records including natural history descriptions,
maps and charts, family and personal papers, and state and colonial
records in order to understand the impact of over-fishing and habitat
loss in the Florida Keys, USA which contains the third largest coral reef in the world.
Monterey Bay National Marine Sanctuary Historical Ecology
(2008–present) seeks to collect relevant historical data on fishing,
whaling, and trade of the furs of aquatic animals in order form a
baseline for environmental restorations of the California, USA coast.
Relations with other disciplines
Manmade nature: In Idaho Falls, Idaho, these waterfalls replaced naturally occurring ones
Historical ecology is interdisciplinary in principle; at the same
time, it borrows heavily from the rich intellectual history of environmental anthropology. Western scholars have known since the time of Plato
that the history of environmental changes cannot be separated from
human history. Several ideas have been used to describe human
interaction with the environment, the first of which is the concept of
the Great Chain of Being,
or inherent design in nature. In this, all forms of life are ordered,
with Humanity as the highest being, due to its knowledge and ability to
modify nature. This lends to the concept of another nature, a manmade
nature, which involves design or modification by humans, as opposed to
design inherent in nature.
Interest in environmental transformation continued to increase in
the 18th, 19th, and 20th centuries, resulting in a series of new
intellectual approaches. One of these approaches was environmental determinism, developed by geographer Friedrich Ratzel.
This view held that it is not social conditions, but environmental
conditions, which determine the culture of a population. Ratzsel also
viewed humans as restricted by nature, for their behaviors are limited
to and defined by their environment. A later approach was the historical
viewpoint of Franz Boas
which refuted environmental determinism, claiming that it is not
nature, but specifics of history, that shape human cultures. This
approach recognized that although the environment may place limitations
on societies, every environment will impact each culture differently. Julian Steward's cultural ecology
is considered a fusion of environmental determinism and Boas'
historical approach. Steward felt it was neither nature nor culture that
had the most impact on a population, but instead, the mode of
subsistence used in a given environment.
Anthropologist Roy Rappaport
introduced the field of ecological anthropology in a deliberate attempt
to move away from cultural ecology. Studies in ecological anthropology
borrow heavily from the natural sciences, in particular, the concept of
the ecosystem from systems ecology.
In this approach, also called systems theory, ecosystems are seen as
self-regulating, and as returning to a state of equilibrium. This theory
views human populations as static and as acting in harmony with the
environment.
The revisions of anthropologist Eric Wolf
and others are especially pertinent to the development of historical
ecology. These revisions and related critiques of environmental
anthropology undertook to take into account the temporal and spatial
dimensions of history and cultures, rather than continuing to view
populations as static. These critiques led to the development of
historical ecology by revealing the need to consider the historical,
cultural, and evolutionary nature of landscapes and societies. Thus,
historical ecology as a research program developed to allow for the
examination of all types of societies, simple or complex, and their
interactions with the environment over space and time.
Landscapes in historical ecology
In historical ecology, the landscape
is defined as an area of interaction between human culture and the
non-human environment. The landscape is a perpetually changing,
physical manifestation of history. Historical ecology revises the notion of the ecosystem
and replaces it with the landscape. While an ecosystem is static and
cyclic, a landscape is historical. While the ecosystem concept views the
environment as always trying to return to a state of equilibrium, the
landscape concept considers "landscape transformation" to be a process
of evolution. Landscapes do not return to a state of equilibrium, but
are palimpsests of successive disturbances over time. The use of "landscape" instead of "ecosystem" as the core unit of analysis lies at the heart of historical ecology.
Various individuals and schools of thought have informed the idea
of the landscape as historical ecologists conceive of it. The Old
English words landskift, landscipe or landscaef refer to environments that have been altered by humans.
As this etymology demonstrates, landscapes have been conceived of as
related to human culture since at least the 5th century CE. Cultural and
historical geographers have had a more recent influence. They adopted
this idea from nineteenth-century German architects, gardeners, and
landscape painters in Europe, Australia, and North America. Landscapes are not only physical objects, but also "forms of knowledge".
Landscapes have cultural meanings, for example, the sacredness in many
cultures of burial grounds. This recognition of landscapes as forms of
knowledge is central to historical ecology, which studies landscapes
from an anthropocentric perspective.
The idea of the cultural landscape is directly attributed to American geographer Carl Sauer.
Sauer's theories developed as a critique of environmental determinism,
which was a popular theory in the early twentieth century. Sauer's
pioneering 1925 paper "The Morphology of Landscape" is now fundamental
to many disciplines and defines the domain. In this, the term landscape
is used in a geographical sense to mean an arbitrarily selected section
of reality; morphology means the conceptual and methodological processes
for altering it. Hence to Sauer, wherever humans lived and impacted the
environment, landscapes with determinate histories resulted.
The perception of the landscape in historical ecology differs from other disciplines, such as landscape ecology.
Landscape ecologists often attribute the depletion of biodiversity to
human disturbance. Historical ecologists recognize that this is not
always true. These changes are due to multiple factors that contribute
to the ever-changing landscape. Landscape ecology still focuses on areas
defined as ecosystems.
In this, the ecosystem perpetually returns to a state of equilibrium.
In contrast, historical ecologists view the landscape as perpetually
changing. Landscape ecologists view noncyclical human events and natural
disasters as external influences, while historical ecologists view
disturbances as an integral part of the landscape's history. It is this
integration of the concept of disturbance and history that allows for
landscape to be viewed as palimpsests, representing successive layers of change, rather than as static entities.
Historical ecologists recognize that landscapes undergo
continuous alteration over time and these modifications are part of that
landscape's history. Historical ecology recognizes that there is a
primary and a secondary succession that occurs in the landscape. These
successions should be understood without a preconceived bias against
humanity. Landscape transformations are ecological successions driven by
human impacts. Primary landscape transformations occur when human
activity results in a complete turnover of species and major substrate
modifications in certain habitats while secondary landscape
transformations involve human-induced changes in species proportions.
The stages of landscape transformation demonstrate the history of a
landscape. These stages can be brought on by humans or natural causes. Parts of the Amazon rainforest exhibit different stages of landscape transformation such as the impact of indigenous slash-and-burn horticulture on plant species compositions.
Such landscape transformation does not inherently reduce biodiversity
or harm the environment. There are many cases in which human-mediated
disturbance increases biodiversity as landscapes transform over time.
Historical ecology challenges the very notion of a pristine landscape, such as virgin rainforests.
The idea that the landscape of the New World was uninhabited and
unchanged by those groups that did inhabit it was fundamental to the
justifications of colonialism.
Thus, perceptions of landscape have profound consequences on the
histories of societies and their interactions with the environment.
All landscapes have been altered by various organisms and mechanisms
prior to human existence on Earth. Humans have always transformed the
landscapes they inhabit, however, and today there are no landscapes on
Earth that have not been affected by humans in some way.
Human alterations have occurred in different phases, including the period prior to industrialization.
These changes have been studied through the archeological record of
modern humans and their history. The evidence that classless societies,
like foragers and trekkers, were able to change a landscape was a breakthrough in historical ecology and anthropology as a whole.
Using an approach that combines history, ecology, and anthropology, a
landscape's history can be observed and deduced through the traces of
the various mechanisms that have altered it, anthropogenic or otherwise.
Understanding the unique nature of every landscape, in addition to
relations among landscapes, and the forms which comprise the landscape,
is key to understanding historical ecology.
Human-mediated disturbance
Man-made irrigation canal
Homo sapiens have interacted with the environment throughout
history, generating a long-lasting influence on landscapes worldwide.
Humans sometimes actively change their landscapes, while at other times
their actions alter landscapes through secondary effects. These changes
are called human-mediated disturbances, and are effected through various
mechanisms. These mechanisms vary; they may be detrimental in some
cases, but advantageous in others.
Both destructive and at times constructive, anthropogenic fire is the most immediately visible human-mediated disturbance, and without it, many landscapes would become denatured. Humans have practiced controlled burns
of forests globally for thousands of years, shaping landscapes in order
to better fit their needs. They burned vegetation and forests to create
space for crops, sometimes resulting in higher levels of species
diversity. Today, in the absence of indigenous populations who once
practiced controlled burns (most notably in North America and Australia),
naturally ignited wildfires have increased. In addition, there has been
destabilization of "ecosystem after ecosystem, and there is good
documentation to suggest fire exclusion by Europeans has led to floral
and faunal extinctions."
Biological invasions and the spread of pathogens and diseases
are two mechanisms that spread both inadvertently and purposefully.
Biological invasions begin with introductions of foreign species or
biota into an already existing environment. They can be spread by
stowaways on ships or even as weapons in warfare.
In some cases a new species may wreak havoc on a landscape, causing the
loss of native species and destruction of the landscape. In other
cases, the new species may fill a previously empty niche, and play a
positive role. The spread of new pathogens, viruses, and diseases rarely
have any positive effects; new pathogens and viruses sometimes destroy
populations lacking immunities to those diseases. Some pathogens have
the ability to transfer from one species to another, and may be spread
as a secondary effect of a biological invasion.
Other mechanisms of human-mediated disturbances include water management and soil management. In Mediterranean Europe, these have been recognized as ways of landscape alteration since the Roman Empire. Cicero noted that through fertilization, irrigation, and other activities, humans had essentially created a second world. At present, fertilization
yields larger, more productive harvests of crops, but also has had
adverse effects on many landscapes, such as decreasing the diversity of
plant species and adding pollutants to soils.
Anthropogenic fire
Anthropogenic
fire is a mechanism of human-mediated disturbance, defined within
historical ecology as a means of altering the landscape in a way that
better suits human needs.
The most common form of anthropogenic fire is controlled burns, or
broadcast burning, which people have employed for thousands of years.
Forest fires and burning tend to carry negative connotations, yet
controlled burns can have a favorable impact on landscape diversity,
formation, and protection.
Broadcast burning alters the biota of a landscape. The immediate
effect of a forest fire is a decrease in diversity. This negative impact
associated with broadcast burning, however, is only temporary. Cycles
of burning will allow the landscape to gradually increase in diversity.
The time required for this change is dependent on the intensity,
frequency, timing, and size of the controlled burns. After a few cycles,
however, diversity increases. The adaptation to fire has shaped many of
Earth's landscapes.
A swidden fire, an example of a controlled burn
In addition to fostering diversity, controlled burns have helped
change landscapes. These changes can range from grasslands to woodlands,
from prairies or forest-steppes, to scrubland to forest. Whatever the
case, these transformations increase diversity and engender landscapes
more suitable to human needs, creating patches rich in utilitarian and
natural resources.
In addition to increasing diversity of landscapes, broadcast
burning can militate against catastrophic wildfires. Forest fires gained
a negative connotation because of cultural references to uncontrolled
fires that take lives and destroy homes and properties. Controlled burns
can decrease the risk of wildfires through the regular burning of
undergrowth that would otherwise fuel rampant burning. Broadcast burning
has helped to fireproof landscapes by burning off undergrowth and using
up potential fuel, leaving little or no chance for a wildfire to be
sparked by lightning.
Of all of the mechanisms of human-mediated disturbances,
anthropogenic fire has become one of great interest to ecologists,
geographers, soil scientists, and anthropologists alike. By studying the
effects of anthropogenic fires, anthropologists have been able to
identify landscape uses and requirements of past cultures. Ecologists
became interested in the study of anthropogenic fire as to utilize
methods from previous cultures to develop policies for regular burning.
Geographers and soil scientists are interested in the utility of
anthropic soils caused by burning in the past. The interest in
anthropogenic fire came about in the wake of the Industrial Revolution.
This time period included a mass migration from rural to urban areas,
which decreased controlled burning in the countryside. This led to an
increase in the frequency and strength of wildfires, thus initiating a
need to develop proper prevention methods.
Historical ecology focuses on the impact on landscapes through
human-mediated disturbances, once such being anthropogenic fire. It is a
fusion of ecological, geographical, anthropological, and pedological
interests.
Biological invasions
Lymantria dispar
Biological invasions are composed of exotic biota that enter a
landscape and replace species with which they share similarities in
structure and ecological function. Because they multiply and grow
quickly, invasive species can eliminate or greatly reduce existing flora
and fauna by various mechanisms, such as direct competitive exclusion.
Invasive species typically spread at a faster rate when they have no
natural predators or when they fill an empty niche. These invasions
often occur in a historical context and are classified as a type of
human-mediated disturbance called human-mediated invasions.
Invasive species can be transported intentionally or
accidentally. Many invasive species originate in shipping areas from
where they are unintentionally transported to their new location.
Sometimes human populations intentionally introduce species into new
landscapes to serve various purposes, ranging from decoration to erosion
control. These species can later become invasive and dramatically
modify the landscape. It is important to note that not all exotic
species are invasive; in fact, the majority of newly introduced species
never become invasive.
Humans have on their migrations through the ages taken along plants of
agricultural and medicinal value, so that the modern distribution of
such favored species is a clear mapping of the routes they have traveled
and the places they have settled.
One example of an invasive species that has had a significant impact on the landscape is the gypsy moth (Lymantria dispar). The foliage-feeding gypsy moth is originally from temperate Eurasia; it was intentionally brought to the United States by an entomologist
in 1869. Many specimens escaped from captivity and have since changed
the ecology of deciduous and coniferous forests in North America by
defoliation. This has led not only to the loss of wildlife habitat, but
also other forest services, such as carbon sequestration and nutrient
cycling. After its initial introduction, the continued accidental
transport of its larvae across North America has contributed to its
population explosion.
Regardless of the medium of introduction, biological invasions
have a considerable effect on the landscape. The goal of eliminating
invasive species is not new; Plato wrote about the benefits of biotic
and landscape diversity centuries ago. However, the notion of
eliminating invasive species is difficult to define because there is no
canonical length of time that a species must exist in a specific
environment until it is no longer classified as invasive. European
forestry defines plants as being archetypes if they existed in Europe
before 1500 and neophytes if they arrived after 1500. This
classification is still arbitrary and some species have unknown origins
while others have become such key components of their landscape that
they are best understood as keystone species. As a result, their removal
would have an enormous impact on the landscape, but not necessarily
cause a return to conditions that existed before the invasion.
Epidemic disease
A San Tribesman: Those living in dry climates have fewer intestinal parasites.
A clear relationship between nature and people is expressed through
human disease. Infectious disease can thus be seen as another example of
human-mediated disturbance as humans are hosts
for infectious diseases. Historically, evidence of epidemic diseases is
associated with the beginnings of agriculture and sedentary
communities. Previously, human populations were too small and mobile for
most infections to become established as chronic diseases.
Permanent settlements, due to agriculture, allowed for more
inter-community interaction, enabling infections to develop as
specifically human pathogens.
Holistic and interdisciplinary approaches to the study of human
disease have revealed a reciprocal relationship between humans and
parasites. The variety of parasites found within the human body often
reflects the diversity of the environment in which that individual
resides. For instance, Bushmen and Australian Aborigines have half as many intestinal parasites
as African and Malaysian hunter-gatherers living in a species-rich
tropical rainforest. Infectious diseases can be either chronic or acute,
and epidemic or endemic, impacting the population in any given
community to different extents. Thus, human-mediated disturbance can
either increase or decrease species diversity in a landscape, causing a
corresponding change in pathogenic diversity.
Transformation of waterways
Historical ecologists postulate that landscape transformations have occurred throughout history, even before the dawn of western civilization. Human-mediated disturbances are predated by soil erosion and animals damming waterways which contributed to waterway transformations. Landscapes, in turn, were altered by waterway transformation.
Historical ecology views the effects of human-mediated disturbances on
waterway transformation as both subtle and drastic occurrences.
Waterways have been modified by humans through the building of
irrigation canals, expanding or narrowing waterways, and multiple other
adjustments done for agricultural or transportation usage.
The evidence for past and present agricultural use of wetlands in Mesoamerica suggests an evolutionary sequence of landscape and waterway alteration. Pre-Columbian,
indigenous agriculturalists developed capabilities with which to raise
crops under a wide range of ecological conditions, giving rise to a
multiplicity of altered, cultivated landscapes. The effects of waterway
transformation were particularly evident in Mesoamerica, where
agricultural practices ranged from swiddening to multicropped
hydraulically transformed wetlands.
Manaus, the largest city on the Amazon, as seen from a NASA satellite image, surrounded by the muddy Amazon River and the dark Rio Negro
Historical ecologists view the Amazon basin landscape as cultural and embodying social labor. The Amazon River
has been altered by the local population for crop growth and water
transportation. Previous research failed to account for human
interaction with the Amazon landscape. Recent research, however, has
demonstrated that the landscape has been manipulated by its indigenous
population over time. The continual, natural shifting of rivers,
however, often masked the human disturbances in the course of rivers. As
a result, the indigenous populations in the Amazon are often overlooked for their ability to alter the land and the river.
However, waterway transformation has been successfully identified in the Amazon landscape. Clark Erickson observes that pre-Hispanic savanna peoples of the Bolivian Amazon built an anthropogenic
landscape through the construction of raised fields, large settlement
mounds, and earthen causeways. Erickson, on the basis of location, form,
patterning, associations and ethnographic analogy, identified a
particular form of earthwork, the zigzag structure, as fish weirs in the savanna of Baures,
Bolivia. The artificial zigzag structures were raised from the adjacent
savanna and served as a means to harvest the fish who used them to
migrate and spawn.
Further evidence of waterway transformation is found in Igarapé Guariba
in Brazil. It is an area in the Amazon basin where people have
intervened in nature to change rivers and streams with dramatic results.
Researcher Hugh Raffles notes that British naturalistsHenry Walter Bates and Alfred Russel Wallace noted waterway transformation as they sailed through a canal close to the town of Igarapé-Miri
in 1848. Archival materials identifies that it had been dug out by
slaves. In his studies he notes an abundance of documentary and
anecdotal evidence which supports landscape transformation by the
manipulation of waterways. Transformation continues in more recent times
as noted when in 1961, a group of villagers from Igarapé Guariba cut a
canal about two miles (3 km) long across fields thick with tall papyrus
grass and into dense tropical rain forest. The narrow canal and the
stream that flowed into it have since formed a full-fledged river more
than six hundred yards wide at its mouth, and the landscape in this part
of the northern Brazilian state of Amapá was dramatically transformed.
In general, with an increase in global population growth, comes an increase in the anthropogenic transformation of waterways. The Sumerians
had created extensive irrigations by 4000 BC. As the population
increased in the 3,000 years of agriculture, the ditches and canals
increased in number. By the early 1900s, ditching, dredging, and diking
had become common practice. This led to an increase in erosion which impacted the landscapes.
Human activities have affected the natural role of rivers and its
communal value. These changes in waterways have impacted the
floodplains, natural tidal patterns, and the surrounding land.
The importance of understanding such transformation is it
provides a more accurate understanding to long-standing popular and
academic insights of the Amazon, as well as other ecological settings, as places where indigenous populations have dealt with the forces of nature. Ecological landscapes have been portrayed as an environment, not a society.
Recent studies supported by historical ecologists, however, understand
that ecological landscape like the Amazon are biocultural, rather than
simply natural and provide for a greater understanding of anthropogenic transformation of both waterways and landscapes.
Soil management
Soil management,
or direct human interaction with the soil, is another mechanism of
anthropogenic change studied by historical ecologists. Soil management
can take place through rearranging soils, altering drainage patterns,
and building large earthen formations. Consistent with the basic
premises of historical ecology, it is recognized that anthropogenic soil
management practices can have both positive and negative effects on
local biodiversity.
Some agricultural practices have led to organically and chemically
impoverished soils. In the North American Midwest, industrial
agriculture has led to a loss in topsoil. Salinization of the Euphrates River
has occurred due to ancient Mesopotamian irrigation, and detrimental
amounts of zinc have been deposited in the New Caliber River of Nigeria.
Elsewhere, soil management practices may not have any effect on soil
fertility. The iconic mounds of the Hopewell Indians built in the Ohio
River valley likely served a religious or ceremonial purpose, and show
little evidence of changing soil fertility in the landscape.
The case of soil management in the Neotropics (including the
Amazon) is a classic example of beneficial results of human-mediated
disturbance. In this area, prehistoric peoples altered the texture and
chemical composition of natural soils. The altered black and brown
earths, known as Amazon Dark Earths, or Terra preta, are actually much more fertile than unaltered surrounding soils. Furthermore, the increased soil fertility improves the results of agriculture. Terra preta is characterized by the presence of charcoal
in high concentrations, along with pottery shards and organic residues
from plants, animal bones, and feces. It is also shows increased levels
of nutrients such as nitrogen, phosphorus, calcium, zinc, and manganese;
along with high levels of microorganic activity. It is now accepted that these soils are a product of a labor-intensive technique termed slash-and-char. In contrast to the commonly known slash-and-burn
technique, this uses a lower temperature burn that produces more
charcoal than ashes. Research shows these soils were created by human
activity between 9000 and 2500 years ago. Contemporary local farmers
actively seek out and sell this dark earth, which covers around 10% of
the Amazon basin. Harvesting Terra preta does not deplete it however,
for it has the ability to regenerate at the rate of one centimeter per
year by sequestering more carbon.
Scorched land resulting from slash-and-burn agriculture
Interest in and the study of Amazon dark earths was advanced with the
work of Wim Sombroek. Sombroek's interest in soil fertility came from
his childhood. He was born in the Netherlands and lived through the
Dutch famine of 1944. His family subsided on a small plot of land that
had been maintained and improved for generations. Sombroek's father, in
turn, improved the land by sowing it with the ash and cinders from their
home. Sombroek came across Terra preta in the 1950s and it reminded him
of the soil from his childhood, inspiring him to study it further. Soil
biologist from the University of Kansas William W. Woods is also a
major figure in Terra preta research. Woods has made several key
discoveries and his comprehensive bibliography on the subject doubles in
size every decade.
Globally, forests are well known for having greater biodiversity
than nearby savannas or grasslands. Thus, the creation of ‘forest
islands’ in multiple locations can be considered a positive result of
human activity. This is evident in the otherwise uniform savannas of
Guinea and central Brazil that are punctured by scattered clumps of
trees.
These clumps are the result of generations of intense resource
management. Earth works and mounds formed by humans, such as the Ibibate
mound complex in the Llanos de Mojos in Bolivia, are examples of built
environments that have undergone landscape transformation and provide
habitats for a greater number of species than the surrounding wetland
areas.
The forest islands in the Bolivian Amazon not only increase the local
plant species diversity, but also enhance subsistence possibilities for
the local people.
Applied historical ecology
Historical
ecology involves an understanding of multiple fields of study such as
archaeology and cultural history as well as ecological processes,
species diversity, natural variability, and the impact of human-mediated
disturbances. Having a broad understanding of landscapes allows
historical ecology to be applied to various disciplines. Studying past
relationships between humans and landscapes can successfully aid land
managers by helping develop holistic, environmentally rational, and
historically accurate plans of action. As summarized in the postulates
of historical ecology, humans play significant roles in the creation and
destruction of landscapes as well as in ecosystem function. Through
experience, many indigenous societies learned how to effectively alter
their landscapes and biotic distributions. Modern societies, seeking to
curtail the magnitude of their effects on the landscape, can use
historical ecology to promote sustainability by learning from the past.
Farmers in the Amazon region, for example, now utilize nutrient-rich
terra preta to increase crop yields much like the indigenous societies that lived long before them.
Historical ecology can also aid in the goals of other fields of study. Conservation biology
recognizes different types of land management processes, each
attempting to maintain the landscape and biota in their present form. Restoration ecology
restores sites to former function, structure, and components of
biological diversity through active modification of the landscapes.
Reclamation deals with shifting a degraded ecosystem back toward a
higher value or use, but not necessarily to its original state.
Replacement of an ecosystem would create an entirely new one.
Revegetation involves new additions of biota into a landscape, not
limited to the original inhabitants of an area.
Each method can be enriched by the application of historical ecology
and the past knowledge it supplies. The interdisciplinary nature of
historical ecology would permit conservation biologists to create more
effective and efficient landscape improvements. Reclamation and
revegetation can use a historical perspective to determine what biota
will be able to sustain large populations without threatening native
biota of the landscape.
A tropical forest in particular needs to be studied extensively
because it is a highly diverse, heterogeneous setting. Historical
ecology can use archaeological sites within this setting to study past
successes and failures of indigenous peoples. The use of swidden fires
in Laos is an example of historical ecology as used by current land
managers in policy-making. Swidden fires were originally considered a
source of habitat degradation. This conclusion led the Laos government
to discourage farmers from using swidden fires as a farming technique.
However, recent research has found that swidden fires were practiced
historically in Laos and were not, in fact, the source of degradation.
Similar research revealed that habitat degradation originated from a
population increase after the Vietnam War. The greater volume of people
compelled the government to put pressure on farmers for increased
agricultural production.
Land managers no longer automatically eliminate the use of swidden
fires, but rather the number of swidden fires that are set for
government-sponsored agricultural purposes.
The San Francisco Estuary Institute also uses historical ecology
to study human impacts on the California landscape to guide
environmental management. A study of the wetlands of Elkhorn Slough near Monterey, California,
sought to enhance conservation and restoration activities. By using
historical data such as maps, charts, and aerial photographs,
researchers were able to trace habitat change to built structures that
had negatively altered the tidal flow into the estuaries dating from the
early 1900s.
The study further suggested using techniques that "imitate the complex
structure of natural tidal wetlands and maintain connectivity with
intact wetland habitats as well as with adjoining subtidal and upland
habitats."
In mathematics, a permutation group is a groupG whose elements are permutations of a given setM and whose group operation is the composition of permutations in G (which are thought of as bijective functions from the set M to itself). The group of all permutations of a set M is the symmetric group of M, often written as Sym(M). The term permutation group thus means a subgroup of the symmetric group. If M = {1, 2, ..., n} then Sym(M) is usually denoted by Sn, and may be called the symmetric group on n letters.
The way in which the elements of a permutation group permute the elements of the set is called its group action. Group actions have applications in the study of symmetries, combinatorics and many other branches of mathematics, physics and chemistry.
The popular puzzle Rubik's cube invented in 1974 by Ernő Rubik has been used as an illustration of permutation groups. Each rotation of a layer of the cube results in a permutation of the surface colors and is a member of the group. The permutation group of the cube is called the Rubik's cube group.
Basic properties and terminology
Being a subgroup of a symmetric group, all that is necessary for a set of permutations to satisfy the group axioms and be a permutation group is that it contain the identity permutation, the inverse permutation of each permutation it contains, and be closed under composition of its permutations.
A general property of finite groups implies that a finite nonempty
subset of a symmetric group is again a group if and only if it is closed
under the group operation.
The degree of a group of permutations of a finite set is the number of elements in the set. The order of a group (of any type) is the number of elements (cardinality) in the group. By Lagrange's theorem, the order of any finite permutation group of degree n must divide n! since n-factorial is the order of the symmetric group Sn.
Since permutations are bijections of a set, they can be represented by Cauchy's two-line notation. This notation lists each of the elements of M in the first row, and for each element, its image under the permutation below it in the second row. If is a permutation of the set then,
For instance, a particular permutation of the set {1, 2, 3, 4, 5} can be written as
this means that σ satisfies σ(1) = 2, σ(2) = 5, σ(3) = 4, σ(4) = 3, and σ(5) = 1. The elements of M need not appear in any special order in the first row, so the same permutation could also be written as
Permutations are also often written in cycle notation (cyclic form) so that given the set M = {1, 2, 3, 4}, a permutation g of M with g(1) = 2, g(2) = 4, g(4) = 1 and g(3)
= 3 will be written as (1, 2, 4)(3), or more commonly, (1, 2, 4) since 3
is left unchanged; if the objects are denoted by single letters or
digits, commas and spaces can also be dispensed with, and we have a
notation such as (124). The permutation written above in 2-line notation
would be written in cycle notation as
Composition of permutations–the group product
The product of two permutations is defined as their composition as functions, so is the function that maps any element x of the set to . Note that the rightmost permutation is applied to the argument first, because of the way function composition is written. Some authors prefer the leftmost factor acting first, but to that end permutations must be written to the right of their argument, often as a superscript, so the permutation acting on the element results in the image . With this convention, the product is given by . However, this gives a different
rule for multiplying permutations. This convention is commonly used in
the permutation group literature, but this article uses the convention
where the rightmost permutation is applied first.
Since the composition of two bijections always gives another
bijection, the product of two permutations is again a permutation. In
two-line notation, the product of two permutations is obtained by
rearranging the columns of the second (leftmost) permutation so that its
first row is identical with the second row of the first (rightmost)
permutation. The product can then be written as the first row of the
first permutation over the second row of the modified second
permutation. For example, given the permutations,
the product QP is:
The composition of permutations, when they are written in cycle
notation, is obtained by juxtaposing the two permutations (with the
second one written on the left) and then simplifying to a disjoint cycle
form if desired. Thus, the above product would be given by:
Since function composition is associative, so is the product operation on permutations: .
Therefore, products of two or more permutations are usually written
without adding parentheses to express grouping; they are also usually
written without a dot or other sign to indicate multiplication (the dots
of the previous example were added for emphasis, so would simply be
written as ).
Neutral element and inverses
The
identity permutation, which maps every element of the set to itself, is
the neutral element for this product. In two-line notation, the
identity is
In cycle notation, e = (1)(2)(3)...(n) which by convention is also denoted by just (1) or even ().
Since bijections have inverses, so do permutations, and the inverse σ−1 of σ is again a permutation. Explicitly, whenever σ(x)=y one also has σ−1(y)=x.
In two-line notation the inverse can be obtained by interchanging the
two lines (and sorting the columns if one wishes the first line to be in
a given order). For instance
To obtain the inverse of a single cycle, we reverse the order of its elements. Thus,
To obtain the inverse of a product of cycles, we first reverse the
order of the cycles, and then we take the inverse of each as above.
Thus,
Having an associative product, an identity element, and inverses for all its elements, makes the set of all permutations of M into a group, Sym(M); a permutation group.
Examples
Consider the following set G1 of permutations of the set M = {1, 2, 3, 4}:
e = (1)(2)(3)(4) = (1)
This is the identity, the trivial permutation which fixes each element.
a = (1 2)(3)(4) = (1 2)
This permutation interchanges 1 and 2, and fixes 3 and 4.
b = (1)(2)(3 4) = (3 4)
Like the previous one, but exchanging 3 and 4, and fixing the others.
ab = (1 2)(3 4)
This permutation, which is the composition of the previous two, exchanges simultaneously 1 with 2, and 3 with 4.
G1 forms a group, since aa = bb = e, ba = ab, and abab = e. This permutation group is, as an abstract group, the Klein groupV4.
As another example consider the group of symmetries of a square.
Let the vertices of a square be labeled 1, 2, 3 and 4 (counterclockwise
around the square starting with 1 in the top left corner). The
symmetries are determined by the images of the vertices, that can, in
turn, be described by permutations. The rotation by 90°
(counterclockwise) about the center of the square is described by the
permutation (1234). The 180° and 270° rotations are given by (13)(24)
and (1432), respectively. The reflection about the horizontal line
through the center is given by (12)(34) and the corresponding vertical
line reflection is (14)(23). The reflection about the 1,3−diagonal line
is (24) and reflection about the 2,4−diagonal is (13). The only
remaining symmetry is the identity (1)(2)(3)(4). This permutation group
is known, as an abstract group, as the dihedral group of order 8.
In the above example of the symmetry group of a square, the
permutations "describe" the movement of the vertices of the square
induced by the group of symmetries. It is common to say that these group
elements are "acting" on the set of vertices of the square. This idea
can be made precise by formally defining a group action.
Let G be a group and M a nonempty set. An action of G on M is a function f: G × M → M such that
f(1, x) = x, for all x in M (1 is the identity (neutral) element of the group G), and
f(g, f(h, x)) = f(gh, x), for all g,h in G and all x in M.
This pair of conditions can also be expressed as saying that the action induces a group homomorphism from G into Sym(M). Any such homomorphism is called a (permutation) representation of G on M.
For any permutation group, the action that sends (g, x) → g(x) is called the natural action of G on M. This is the action that is assumed unless otherwise indicated.
In the example of the symmetry group of the square, the group's action
on the set of vertices is the natural action. However, this group also
induces an action on the set of four triangles in the square, which are:
t1 = 234, t2 = 134, t3 = 124 and t4 = 123. It also acts on the two diagonals: d1 = 13 and d2 = 24.
Group element
Action on triangles
Action on diagonals
(1)
(1)
(1)
(1234)
(t1t2t3t4)
(d1d2)
(13)(24)
(t1t3)(t2t4)
(1)
(1432)
(t1t4t3t2)
(d1d2)
(12)(34)
(t1t2)(t3t4)
(d1d2)
(14)(23)
(t1t4)(t2t3)
(d1d2)
(13)
(t1t3)
(1)
(24)
(t2t4)
(1)
Transitive actions
The action of a group G on a set M is said to be transitive if, for every two elements s, t of M, there is some group element g such that g(s) = t. Equivalently, the set M forms a single orbit under the action of G. Of the examples above,
the group {e, (1 2), (3 4), (1 2)(3 4)} of permutations of {1, 2, 3, 4}
is not transitive (no group element takes 1 to 3) but the group of
symmetries of a square is transitive on the vertices.
A permutation group G acting transitively on a non-empty finite set M is imprimitive if there is some nontrivial set partition of M that is preserved by the action of G, where "nontrivial" means that the partition isn't the partition into singleton sets nor the partition with only one part. Otherwise, if G is transitive but does not preserve any nontrivial partition of M, the group G is primitive.
For example, the group of symmetries of a square is imprimitive
on the vertices: if they are numbered 1, 2, 3, 4 in cyclic order, then
the partition {{1, 3}, {2, 4}} into opposite pairs is preserved by every
group element. On the other hand, the full symmetric group on a set M is always primitive.
Any group G can act on itself (the elements of the group being thought of as the set M) in many ways. In particular, there is a regular action given by (left) multiplication in the group. That is, f(g, x) = gx for all g and x in G. For each fixed g, the function fg(x) = gx is a bijection on G and therefore a permutation of the set of elements of G. Each element of G can be thought of as a permutation in this way and so G is isomorphic to a permutation group; this is the content of Cayley's theorem.
For example, consider the group G1 acting on the set {1, 2, 3, 4} given above. Let the elements of this group be denoted by e, a, b and c = ab = ba. The action of G1 on itself described in Cayley's theorem gives the following permutation representation:
fe ↦ (e)(a)(b)(c)
fa ↦ (ea)(bc)
fb ↦ (eb)(ac)
fc ↦ (ec)(ab).
Isomorphisms of permutation groups
If G and H are two permutation groups on sets X and Y with actions f1 and f2 respectively, then we say that G and H are permutation isomorphic (or isomorphic as permutation groups) if there exists a bijective mapλ : X → Y and a group isomorphismψ : G → H such that
λ(f1(g, x)) = f2(ψ(g), λ(x)) for all g in G and x in X.
If X = Y this is equivalent to G and H being conjugate as subgroups of Sym(X). The special case where G = H and ψ is the identity map gives rise to the concept of equivalent actions of a group.
In the example of the symmetries of a square given above, the
natural action on the set {1,2,3,4} is equivalent to the action on the
triangles. The bijection λ between the sets is given by i ↦ ti. The natural action of group G1
above and its action on itself (via left multiplication) are not
equivalent as the natural action has fixed points and the second action
does not.
Oligomorphic groups
When a group G acts on a setS, the action may be extended naturally to the Cartesian productSn of S, consisting of n-tuples of elements of S: the action of an element g on the n-tuple (s1, ..., sn) is given by
g(s1, ..., sn) = (g(s1), ..., g(sn)).
The group G is said to be oligomorphic if the action on Sn has only finitely many orbits for every positive integer n. (This is automatic if S is finite, so the term is typically of interest when S is infinite.)
The study of groups originally grew out of an understanding of permutation groups. Permutations had themselves been intensively studied by Lagrange
in 1770 in his work on the algebraic solutions of polynomial equations.
This subject flourished and by the mid 19th century a well-developed
theory of permutation groups existed, codified by Camille Jordan in his book Traité des Substitutions et des Équations Algébriques of 1870. Jordan's book was, in turn, based on the papers that were left by Évariste Galois in 1832.
When Cayley introduced the concept of an abstract group,
it was not immediately clear whether or not this was a larger
collection of objects than the known permutation groups (which had a
definition different from the modern one). Cayley went on to prove that
the two concepts were equivalent in Cayley's theorem.
Another classical text containing several chapters on permutation groups is Burnside's Theory of Groups of Finite Order of 1911.
The first half of the twentieth century was a fallow period in the
study of group theory in general, but interest in permutation groups was
revived in the 1950s by H. Wielandt whose German lecture notes were reprinted as Finite Permutation Groups in 1964.
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