5,784 research outputs found

### How to read probability distributions as statements about process

Probability distributions can be read as simple expressions of information.
Each continuous probability distribution describes how information changes with
magnitude. Once one learns to read a probability distribution as a measurement
scale of information, opportunities arise to understand the processes that
generate the commonly observed patterns. Probability expressions may be parsed
into four components: the dissipation of all information, except the
preservation of average values, taken over the measurement scale that relates
changes in observed values to changes in information, and the transformation
from the underlying scale on which information dissipates to alternative scales
on which probability pattern may be expressed. Information invariances set the
commonly observed measurement scales and the relations between them. In
particular, a measurement scale for information is defined by its invariance to
specific transformations of underlying values into measurable outputs.
Essentially all common distributions can be understood within this simple
framework of information invariance and measurement scale.Comment: v2: added table of contents, adjusted section numbers v3: minor
editing, updated referenc

### Receptor uptake arrays for vitamin B12, siderophores and glycans shape bacterial communities

Molecular variants of vitamin B12, siderophores and glycans occur. To take up
variant forms, bacteria may express an array of receptors. The gut microbe
Bacteroides thetaiotaomicron has three different receptors to take up variants
of vitamin B12 and 88 receptors to take up various glycans. The design of
receptor arrays reflects key processes that shape cellular evolution.
Competition may focus each species on a subset of the available nutrient
diversity. Some gut bacteria can take up only a narrow range of carbohydrates,
whereas species such as B.~thetaiotaomicron can digest many different complex
glycans. Comparison of different nutrients, habitats, and genomes provide
opportunity to test hypotheses about the breadth of receptor arrays. Another
important process concerns fluctuations in nutrient availability. Such
fluctuations enhance the value of cellular sensors, which gain information
about environmental availability and adjust receptor deployment. Bacteria often
adjust receptor expression in response to fluctuations of particular
carbohydrate food sources. Some species may adjust expression of uptake
receptors for specific siderophores. How do cells use sensor information to
control the response to fluctuations? That question about regulatory wiring
relates to problems that arise in control theory and artificial intelligence.
Control theory clarifies how to analyze environmental fluctuations in relation
to the design of sensors and response systems. Recent advances in deep learning
studies of artificial intelligence focus on the architecture of regulatory
wiring and the ways in which complex control networks represent and classify
environmental states. I emphasize the similar design problems that arise in
cellular evolution, control theory, and artificial intelligence. I connect
those broad concepts to testable hypotheses for bacterial uptake of B12,
siderophores and glycans.Comment: Added many new references, edited throughou

### Microbial metabolism: optimal control of uptake versus synthesis

Microbes require several complex organic molecules for growth. A species may
obtain a required factor by taking up molecules released by other species or by
synthesizing the molecule. The patterns of uptake and synthesis set a flow of
resources through the multiple species that create a microbial community. This
article analyzes a simple mathematical model of the tradeoff between uptake and
synthesis. Key factors include the influx rate from external sources relative
to the outflux rate, the rate of internal decay within cells, and the cost of
synthesis. Aspects of demography also matter, such as cellular birth and death
rates, the expected time course of a local resource flow, and the associated
lifespan of the local population. Spatial patterns of genetic variability and
differentiation between populations may also strongly influence the evolution
of metabolic regulatory controls of individual species and thus the structuring
of microbial communities. The widespread use of optimality approaches in recent
work on microbial metabolism has ignored demography and genetic structure

### Simple unity among the fundamental equations of science

The Price equation describes the change in populations. Change concerns some
value, such as biological fitness, information or physical work. The Price
equation reveals universal aspects for the nature of change, independently of
the meaning ascribed to values. By understanding those universal aspects, we
can see more clearly why fundamental mathematical results in different
disciplines often share a common form. We can also interpret more clearly the
meaning of key results within each discipline. For example, the mathematics of
natural selection in biology has a form closely related to information theory
and physical entropy. Does that mean that natural selection is about
information or entropy? Or do natural selection, information and entropy arise
as interpretations of a common underlying abstraction? The Price equation
suggests the latter. The Price equation achieves its abstract generality by
partitioning change into two terms. The first term naturally associates with
the direct forces that cause change. The second term naturally associates with
the changing frame of reference. In the Price equation's canonical form, total
change remains zero because the conservation of total probability requires that
all probabilities invariantly sum to one. Much of the shared common form for
the mathematics of different disciplines may arise from that seemingly trivial
invariance of total probability, which leads to the partitioning of total
change into equal and opposite components of the direct forces and the changing
frame of reference.Comment: arXiv admin note: text overlap with arXiv:1810.0926

### Universal expressions of population change by the Price equation: natural selection, information, and maximum entropy production

The Price equation shows the unity between the fundamental expressions of
change in biology, in information and entropy descriptions of populations, and
in aspects of thermodynamics. The Price equation partitions the change in the
average value of a metric between two populations. A population may be composed
of organisms or particles or any members of a set to which we can assign
probabilities. A metric may be biological fitness or physical energy or the
output of an arbitrarily complicated function that assigns quantitative values
to members of the population. The first part of the Price equation describes
how directly applied forces change the probabilities assigned to members of the
population when holding constant the metrical values of the members---a fixed
metrical frame of reference. The second part describes how the metrical values
change, altering the metrical frame of reference. In canonical examples, the
direct forces balance the changing metrical frame of reference, leaving the
average or total metrical values unchanged. In biology, relative reproductive
success (fitness) remains invariant as a simple consequence of the conservation
of total probability. In physics, systems often conserve total energy.
Nonconservative metrics can be described by starting with conserved metrics,
and then studying how coordinate transformations between conserved and
nonconserved metrics alter the geometry of the dynamics and the aggregate
values of populations. From this abstract perspective, key results from
different subjects appear more simply as universal geometric principles for the
dynamics of populations subject to the constraints of particular conserved
quantitiesComment: v2: Complete rewrite, new title and abstract. Changed focus to Price
equation as basis for universal expression of changes in populations. v3:
Cleaned up usage of terms virtual and reversible displacements and virtual
work and usage of d'Alembert's principle. v4: minor editing and correction

### d'Alembert's direct and inertial forces acting on populations: the Price equation and the fundamental theorem of natural selection

I develop a framework for interpreting the forces that act on any population
described by frequencies. The conservation of total frequency, or total
probability, shapes the characteristics of force. I begin with Fisher's
fundamental theorem of natural selection. That theorem partitions the total
evolutionary change of a population into two components. The first component is
the partial change caused by the direct force of natural selection, holding
constant all aspects of the environment. The second component is the partial
change caused by the changing environment. I demonstrate that Fisher's
partition of total change into the direct force of selection and the forces
from the changing environmental frame of reference is identical to d'Alembert's
principle of mechanics, which separates the work done by the direct forces from
the work done by the inertial forces associated with the changing frame of
reference. In d'Alembert's principle, there exist inertial forces from a change
in the frame of reference that exactly balance the direct forces. I show that
the conservation of total probability strongly shapes the form of the balance
between the direct and inertial forces. I then use the strong results for
conserved probability to obtain general results for the change in any system
quantity, such as biological fitness or energy. Those general results derive
from simple coordinate changes between frequencies and system quantities.
Ultimately, d'Alembert's separation of direct and inertial forces provides deep
conceptual insight into the interpretation of forces and the unification of
disparate fields of study.Comment: version 2: New Methods section, revised throughout for minor
corrections and clarity, version 3: minor editing, publication informatio

### Hierarchical Selection Theory And Sex Ratios. Ii. On Applying The Theory, And A Test With Fig Wasps

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/137439/1/evo00440.pd

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