Computational neuroscience

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Computational_neuroscience

Computational neuroscience (also known as theoretical neuroscience or mathematical neuroscience) is a branch of neuroscience which employs mathematics, computer science, theoretical analysis and abstractions of the brain to understand the principles that govern the development, structure, physiology and cognitive abilities of the nervous system.

Computational neuroscience employs computational simulations to validate and solve mathematical models, and so can be seen as a sub-field of theoretical neuroscience; however, the two fields are often synonymous. The term mathematical neuroscience is also used sometimes, to stress the quantitative nature of the field.

Computational neuroscience focuses on the description of biologically plausible neurons (and neural systems) and their physiology and dynamics. It is therefore not directly concerned with biologically unrealistic models used in connectionism, control theory, cybernetics, quantitative psychology, machine learning, artificial neural networks, artificial intelligence and computational learning theory; although mutual inspiration exists and sometimes there is no strict limit between fields, with model abstraction in computational neuroscience depending on research scope and the granularity at which biological entities are analyzed.

Models in theoretical neuroscience are aimed at capturing the essential features of the biological system at multiple spatial-temporal scales, from membrane currents, and chemical coupling via network oscillations, columnar and topographic architecture, nuclei, all the way up to psychological faculties like memory, learning and behavior. These computational models frame hypotheses that can be directly tested by biological or psychological experiments.

History

The term 'computational neuroscience' was introduced by Eric L. Schwartz, who organized a conference, held in 1985 in Carmel, California, at the request of the Systems Development Foundation to provide a summary of the current status of a field which until that point was referred to by a variety of names, such as neural modeling, brain theory and neural networks. The proceedings of this definitional meeting were published in 1990 as the book Computational Neuroscience. The first of the annual open international meetings focused on Computational Neuroscience was organized by James M. Bower and John Miller in San Francisco, California in 1989. The first graduate educational program in computational neuroscience was organized as the Computational and Neural Systems Ph.D. program at the California Institute of Technology in 1985.

The early historical roots of the field can be traced to the work of people including Louis Lapicque, Hodgkin & Huxley, Hubel and Wiesel, and David Marr. Lapicque introduced the integrate and fire model of the neuron in a seminal article published in 1907, a model still popular for artificial neural networks studies because of its simplicity (see a recent review).

About 40 years later, Hodgkin and Huxley developed the voltage clamp and created the first biophysical model of the action potential. Hubel and Wiesel discovered that neurons in the primary visual cortex, the first cortical area to process information coming from the retina, have oriented receptive fields and are organized in columns. David Marr's work focused on the interactions between neurons, suggesting computational approaches to the study of how functional groups of neurons within the hippocampus and neocortex interact, store, process, and transmit information. Computational modeling of biophysically realistic neurons and dendrites began with the work of Wilfrid Rall, with the first multicompartmental model using cable theory.

Major topics

Research in computational neuroscience can be roughly categorized into several lines of inquiry. Most computational neuroscientists collaborate closely with experimentalists in analyzing novel data and synthesizing new models of biological phenomena.

Single-neuron modeling

Main article: Biological neuron models

Even a single neuron has complex biophysical characteristics and can perform computations (e.g.). Hodgkin and Huxley's original model only employed two voltage-sensitive currents (Voltage sensitive ion channels are glycoprotein molecules which extend through the lipid bilayer, allowing ions to traverse under certain conditions through the axolemma), the fast-acting sodium and the inward-rectifying potassium. Though successful in predicting the timing and qualitative features of the action potential, it nevertheless failed to predict a number of important features such as adaptation and shunting. Scientists now believe that there are a wide variety of voltage-sensitive currents, and the implications of the differing dynamics, modulations, and sensitivity of these currents is an important topic of computational neuroscience.

The computational functions of complex dendrites are also under intense investigation. There is a large body of literature regarding how different currents interact with geometric properties of neurons.

There are many software packages, such as GENESIS and NEURON, that allow rapid and systematic in silico modeling of realistic neurons. Blue Brain, a project founded by Henry Markram from the École Polytechnique Fédérale de Lausanne, aims to construct a biophysically detailed simulation of a cortical column on the Blue Gene supercomputer.

Modeling the richness of biophysical properties on the single-neuron scale can supply mechanisms that serve as the building blocks for network dynamics. However, detailed neuron descriptions are computationally expensive and this computing cost can limit the pursuit of realistic network investigations, where many neurons need to be simulated. As a result, researchers that study large neural circuits typically represent each neuron and synapse with an artificially simple model, ignoring much of the biological detail. Hence there is a drive to produce simplified neuron models that can retain significant biological fidelity at a low computational overhead. Algorithms have been developed to produce faithful, faster running, simplified surrogate neuron models from computationally expensive, detailed neuron models.

Modeling Neuron-glia interactions

Glial cells participate significantly in the regulation of neuronal activity at both the cellular and the network level. Modeling this interaction allows to clarify the potassium cycle, so important for maintaining homeostasis and to prevent epileptic seizures. Modeling reveals the role of glial protrusions that can penetrate in some cases the synaptic cleft to interfere with the synaptic transmission and thus control synaptic communication.

Development, axonal patterning, and guidance

Computational neuroscience aims to address a wide array of questions, including: How do axons and dendrites form during development? How do axons know where to target and how to reach these targets? How do neurons migrate to the proper position in the central and peripheral systems? How do synapses form? We know from molecular biology that distinct parts of the nervous system release distinct chemical cues, from growth factors to hormones that modulate and influence the growth and development of functional connections between neurons.

Theoretical investigations into the formation and patterning of synaptic connection and morphology are still nascent. One hypothesis that has recently garnered some attention is the minimal wiring hypothesis, which postulates that the formation of axons and dendrites effectively minimizes resource allocation while maintaining maximal information storage.

Sensory processing

Early models on sensory processing understood within a theoretical framework are credited to Horace Barlow. Somewhat similar to the minimal wiring hypothesis described in the preceding section, Barlow understood the processing of the early sensory systems to be a form of efficient coding, where the neurons encoded information which minimized the number of spikes. Experimental and computational work have since supported this hypothesis in one form or another. For the example of visual processing, efficient coding is manifested in the forms of efficient spatial coding, color coding, temporal/motion coding, stereo coding, and combinations of them.

Further along the visual pathway, even the efficiently coded visual information is too much for the capacity of the information bottleneck, the visual attentional bottleneck. A subsequent theory, V1 Saliency Hypothesis (V1SH), has been developed on exogenous attentional selection of a fraction of visual input for further processing, guided by a bottom-up saliency map in the primary visual cortex.

Current research in sensory processing is divided among a biophysical modeling of different subsystems and a more theoretical modeling of perception. Current models of perception have suggested that the brain performs some form of Bayesian inference and integration of different sensory information in generating our perception of the physical world.

Motor control

Many models of the way the brain controls movement have been developed. This includes models of processing in the brain such as the cerebellum's role for error correction, skill learning in motor cortex and the basal ganglia, or the control of the vestibulo ocular reflex. This also includes many normative models, such as those of the Bayesian or optimal control flavor which are built on the idea that the brain efficiently solves its problems.

Memory and synaptic plasticity

Main article: Synaptic plasticity

Earlier models of memory are primarily based on the postulates of Hebbian learning. Biologically relevant models such as Hopfield net have been developed to address the properties of associative (also known as "content-addressable") style of memory that occur in biological systems. These attempts are primarily focusing on the formation of medium- and long-term memory, localizing in the hippocampus.

One of the major problems in neurophysiological memory is how it is maintained and changed through multiple time scales. Unstable synapses are easy to train but also prone to stochastic disruption. Stable synapses forget less easily, but they are also harder to consolidate. It is likely that computational tools will contribute greatly to our understanding of how synapses function and change in relation to external stimulus in the coming decades.

Behaviors of networks

Biological neurons are connected to each other in a complex, recurrent fashion. These connections are, unlike most artificial neural networks, sparse and usually specific. It is not known how information is transmitted through such sparsely connected networks, although specific areas of the brain, such as the visual cortex, are understood in some detail. It is also unknown what the computational functions of these specific connectivity patterns are, if any.

The interactions of neurons in a small network can be often reduced to simple models such as the Ising model. The statistical mechanics of such simple systems are well-characterized theoretically. Some recent evidence suggests that dynamics of arbitrary neuronal networks can be reduced to pairwise interactions. It is not known, however, whether such descriptive dynamics impart any important computational function. With the emergence of two-photon microscopy and calcium imaging, we now have powerful experimental methods with which to test the new theories regarding neuronal networks.

In some cases the complex interactions between inhibitory and excitatory neurons can be simplified using mean-field theory, which gives rise to the population model of neural networks. While many neurotheorists prefer such models with reduced complexity, others argue that uncovering structural-functional relations depends on including as much neuronal and network structure as possible. Models of this type are typically built in large simulation platforms like GENESIS or NEURON. There have been some attempts to provide unified methods that bridge and integrate these levels of complexity.

Visual attention, identification, and categorization

Visual attention can be described as a set of mechanisms that limit some processing to a subset of incoming stimuli. Attentional mechanisms shape what we see and what we can act upon. They allow for concurrent selection of some (preferably, relevant) information and inhibition of other information. In order to have a more concrete specification of the mechanism underlying visual attention and the binding of features, a number of computational models have been proposed aiming to explain psychophysical findings. In general, all models postulate the existence of a saliency or priority map for registering the potentially interesting areas of the retinal input, and a gating mechanism for reducing the amount of incoming visual information, so that the limited computational resources of the brain can handle it. An example theory that is being extensively tested behaviorally and physiologically is the V1 Saliency Hypothesis that a bottom-up saliency map is created in the primary visual cortex to guide attention exogenously. Computational neuroscience provides a mathematical framework for studying the mechanisms involved in brain function and allows complete simulation and prediction of neuropsychological syndromes.

Cognition, discrimination, and learning

Computational modeling of higher cognitive functions has only recently begun. Experimental data comes primarily from single-unit recording in primates. The frontal lobe and parietal lobe function as integrators of information from multiple sensory modalities. There are some tentative ideas regarding how simple mutually inhibitory functional circuits in these areas may carry out biologically relevant computation.

The brain seems to be able to discriminate and adapt particularly well in certain contexts. For instance, human beings seem to have an enormous capacity for memorizing and recognizing faces. One of the key goals of computational neuroscience is to dissect how biological systems carry out these complex computations efficiently and potentially replicate these processes in building intelligent machines.

The brain's large-scale organizational principles are illuminated by many fields, including biology, psychology, and clinical practice. Integrative neuroscience attempts to consolidate these observations through unified descriptive models and databases of behavioral measures and recordings. These are the bases for some quantitative modeling of large-scale brain activity.

The Computational Representational Understanding of Mind (CRUM) is another attempt at modeling human cognition through simulated processes like acquired rule-based systems in decision making and the manipulation of visual representations in decision making.

Consciousness

One of the ultimate goals of psychology/neuroscience is to be able to explain the everyday experience of conscious life. Francis Crick, Giulio Tononi and Christof Koch made some attempts to formulate consistent frameworks for future work in neural correlates of consciousness (NCC), though much of the work in this field remains speculative.

Computational clinical neuroscience

Computational clinical neuroscience is a field that brings together experts in neuroscience, neurology, psychiatry, decision sciences and computational modeling to quantitatively define and investigate problems in neurological and psychiatric diseases, and to train scientists and clinicians that wish to apply these models to diagnosis and treatment.

Predictive computational neuroscience

Predictive computational neuroscience is a recent field that combines signal processing, neuroscience, clinical data and machine learning to predict the brain during coma or anesthesia. For example, it is possible to anticipate deep brain states using the EEG signal. These states can be used to anticipate hypnotic concentration to administrate to the patient.

Computational Psychiatry

Computational psychiatry was originally conceived in the late-2000s as the application of computational models to psychiatric disorders. It quickly developed throughout the 2010s with research into schizophrenia, addiction, and major depression among other disorders. There were also attempts to develop computationally inspired diagnostic criteria via the subfield of computational nosology. More recent work seeks to apply Bayesian models of cognition to explain the symptomatology and phenomenology of psychiatric disorders.

Technology

Neuromorphic computing

Main article: Neuromorphic engineering

A neuromorphic computer/chip is any device that uses physical artificial neurons (made from silicon) to do computations (See: neuromorphic computing, physical neural network). One of the advantages of using a physical model computer such as this is that it takes the computational load of the processor (in the sense that the structural and some of the functional elements don't have to be programmed since they are in hardware). In recent times, neuromorphic technology has been used to build supercomputers which are used in international neuroscience collaborations. Examples include the Human Brain Project SpiNNaker supercomputer and the BrainScaleS computer.

Psychophysics

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Psychophysics 

Psychophysics is the field of psychology which quantitatively investigates the relationship between physical stimuli and the sensations and perceptions they produce. Psychophysics has been described as "the scientific study of the relation between stimulus and sensation" or, more completely, as "the analysis of perceptual processes by studying the effect on a subject's experience or behaviour of systematically varying the properties of a stimulus along one or more physical dimensions".

Psychophysics also refers to a general class of methods that can be applied to study a perceptual system. Modern applications rely heavily on threshold measurement, ideal observer analysis, and signal detection theory.

Psychophysics has widespread and important practical applications. For instance, in the realm of digital signal processing, insights from psychophysics have guided the development of models and methods for lossy compression. These models help explain why humans typically perceive minimal loss of signal quality when audio and video signals are compressed using lossy techniques.

History

Many of the classical techniques and theories of psychophysics were formulated in 1860 when Gustav Theodor Fechner in Leipzig published Elemente der Psychophysik (Elements of Psychophysics). He coined the term "psychophysics", describing research intended to relate physical stimuli to the contents of consciousness such as sensations (Empfindungen). As a physicist and philosopher, Fechner aimed at developing a method that relates matter to the mind, connecting the publicly observable world and a person's privately experienced impression of it. His ideas were inspired by experimental results on the sense of touch and light obtained in the early 1830s by the German physiologist Ernst Heinrich Weber in Leipzig, most notably those on the minimum discernible difference in intensity of stimuli of moderate strength (just noticeable difference; jnd) which Weber had shown to be a constant fraction of the reference intensity, and which Fechner referred to as Weber's law. From this, Fechner derived his well-known logarithmic scale, now known as Fechner scale. Weber's and Fechner's work formed one of the bases of psychology as a science, with Wilhelm Wundt founding the first laboratory for psychological research in Leipzig (Institut für experimentelle Psychologie). Fechner's work systematised the introspectionist approach (psychology as the science of consciousness), that had to contend with the Behaviorist approach in which even verbal responses are as physical as the stimuli.

Fechner's work was studied and extended by Charles S. Peirce, who was aided by his student Joseph Jastrow, who soon became a distinguished experimental psychologist in his own right. Peirce and Jastrow largely confirmed Fechner's empirical findings, but not all. In particular, a classic experiment of Peirce and Jastrow rejected Fechner's estimation of a threshold of perception of weights. In their experiment, Peirce and Jastrow in fact invented randomized experiments: They randomly assigned volunteers to a blinded, repeated-measures design to evaluate their ability to discriminate weights. On the basis of their results they argued that the underlying functions were continuous, and that there is no threshold below which a difference in physical magnitude would be undetected. Peirce's experiment inspired other researchers in psychology and education, which developed a research tradition of randomized experiments in laboratories and specialized textbooks in the 1900s.

The Peirce–Jastrow experiments were conducted as part of Peirce's application of his pragmaticism program to human perception; other studies considered the perception of light, etc. Jastrow wrote the following summary: "Mr. Peirce's courses in logic gave me my first real experience of intellectual muscle. Though I promptly took to the laboratory of psychology when that was established by Stanley Hall, it was Peirce who gave me my first training in the handling of a psychological problem, and at the same time stimulated my self-esteem by entrusting me, then fairly innocent of any laboratory habits, with a real bit of research. He borrowed the apparatus for me, which I took to my room, installed at my window, and with which, when conditions of illumination were right, I took the observations. The results were published over our joint names in the Proceedings of the National Academy of Sciences. The demonstration that traces of sensory effect too slight to make any registry in consciousness could none the less influence judgment, may itself have been a persistent motive that induced me years later to undertake a book on The Subconscious." This work clearly distinguishes observable cognitive performance from the expression of consciousness.

Modern approaches to sensory perception, such as research on vision, hearing, or touch, measure what the perceiver's judgment extracts from the stimulus, often putting aside the question what sensations are being experienced. One leading method is based on signal detection theory, developed for cases of very weak stimuli. However, the subjectivist approach persists among those in the tradition of Stanley Smith Stevens (1906–1973). Stevens revived the idea of a power law suggested by 19th century researchers, in contrast with Fechner's log-linear function (cf. Stevens' power law). He also advocated the assignment of numbers in ratio to the strengths of stimuli, called magnitude estimation. Stevens added techniques such as magnitude production and cross-modality matching. He opposed the assignment of stimulus strengths to points on a line that are labeled in order of strength. Nevertheless, that sort of response has remained popular in applied psychophysics. Such multiple-category layouts are often misnamed Likert scaling after the question items used by Likert to create multi-item psychometric scales, e.g., seven phrases from "strongly agree" through "strongly disagree".

Omar Khaleefa has argued that the medieval scientist Alhazen should be considered the founder of psychophysics. Although al-Haytham made many subjective reports regarding vision, there is no evidence that he used quantitative psychophysical techniques and such claims have been rebuffed.

Thresholds

Psychophysicists usually employ stimuli that can be objectively measured, such as pure tones varying in intensity, or lights varying in luminance. All the canonical senses have been studied: vision, hearing, touch (including skin and enteric perception), taste, smell, and the sense of time. Regardless of the sensory domain, there are three main areas of investigation: absolute thresholds, discrimination thresholds (e.g. the just-noticeable difference), and scaling.

A threshold (or limen) is the point of intensity at which the participant can just detect the presence of a stimulus (absolute threshold) or the difference between two stimuli (difference threshold). Stimuli with intensities below this threshold are not detectable and are considered subliminal. Stimuli at values close to a threshold may be detectable on some occasions; therefore, a threshold is defined as the point at which a stimulus or change in a stimulus is detected on a certain proportion p of trials.

Detection

An absolute threshold is the level of intensity at which a subject can detect the presence of a stimulus a certain proportion of the time; a p level of 50% is commonly used. For example, consider the absolute threshold for tactile sensation on the back of one's hand. A participant might not feel a single hair being touched, but might detect the touch of two or three hairs, as this exceeds the threshold. The absolute threshold is also often referred to as the detection threshold. Various methods are employed to measure absolute thresholds, similar to those used for discrimination thresholds (see below).

Discrimination

A difference threshold (or just-noticeable difference, JND) is the magnitude of the smallest difference between two stimuli of differing intensities that a participant can detect a certain proportion of the time, with the specific percentage depending on the task. Several methods are employed to test this threshold. For instance, the subject may be asked to adjust one stimulus until it is perceived as identical to another (method of adjustment), to describe the direction and magnitude of the difference between two stimuli, or to decide whether the intensities in a pair of stimuli are the same or different (forced choice). The just-noticeable difference is not a fixed quantity; rather, it varies depending on the intensity of the stimuli and the specific sense being tested. According to Weber's Law, the just-noticeable difference for any stimulus is a constant proportion, regardless of variations in intensity.

In discrimination experiments, the experimenter seeks to determine at what point the difference between two stimuli, such as two weights or two sounds, becomes detectable. The subject is presented with one stimulus, for example, a weight, and is asked to say whether another weight is heavier or lighter. In some experiments, the subject may also indicate that the two weights are the same. At the point of subjective equality (PSE), the subject perceives both weights as identical. The just-noticeable difference, or difference limen (DL), is the magnitude of the difference in stimuli that the subject notices some proportion p of the time; typically, 50% is used for p in the comparison task. To reduce the biasing effects of a subject preferring a particular response, researchers often use a two-alternative forced choice (2AFC) paradigm. In the case of discriminating weights, this can be done by randomly varying which of two simultaneously-presented stimuli is heavier and requiring the participant to choose which one they think is heavier.

Absolute and difference thresholds are sometimes considered similar in principle because background noise always interferes with our ability to detect stimuli.

Experimentation

In psychophysics, experiments seek to determine whether the subject can detect a stimulus, identify it, differentiate between it and another stimulus, or describe the magnitude or nature of this difference. Software for psychophysical experimentation is overviewed by Strasburger.

Classical psychophysical methods

Psychophysical experiments have traditionally used three methods for testing subjects' perception in stimulus detection and difference detection experiments: the method of limits, the method of constant stimuli and the method of adjustment.

Method of limits

In the ascending method of limits, some property of the stimulus starts out at a level so low that the stimulus could not be detected, then this level is gradually increased until the participant reports that they are aware of it. For example, if the experiment is testing the minimum amplitude of sound that can be detected, the sound begins too quietly to be perceived, and is made gradually louder. In the descending method of limits, this is reversed. In each case, the threshold is considered to be the level of the stimulus property at which the stimuli are just detected.

In experiments, the ascending and descending methods are used alternately and the thresholds are averaged. A possible disadvantage of these methods is that the subject may become accustomed to reporting that they perceive a stimulus and may continue reporting the same way even beyond the threshold (the error of habituation). Conversely, the subject may also anticipate that the stimulus is about to become detectable or undetectable and may make a premature judgment (the error of anticipation).

To avoid these potential pitfalls, Georg von Békésy introduced the staircase procedure in 1960 in his study of auditory perception. In this method, the sound starts out audible and gets quieter after each of the subject's responses, until the subject does not report hearing it. At that point, the sound is made louder at each step, until the subject reports hearing it, at which point it is made quieter in steps again. This way the experimenter is able to "zero in" on the threshold.

Method of constant stimuli

Instead of being presented in ascending or descending order, in the method of constant stimuli the levels of a certain property of the stimulus are not related from one trial to the next, but presented randomly. This prevents the subject from being able to predict the level of the next stimulus, and therefore reduces errors of habituation and expectation. For 'absolute thresholds' again the subject reports whether they are able to detect the stimulus. For 'difference thresholds' there has to be a constant comparison stimulus with each of the varied levels. Friedrich Hegelmaier described the method of constant stimuli in an 1852 paper. This method allows for full sampling of the psychometric function, but can result in a lot of trials when several conditions are interleaved.

Method of adjustment

In the method of adjustment, the subject is asked to control the level of the stimulus and to alter it until it is just barely detectable against the background noise, or is the same as the level of another stimulus. The adjustment is repeated many times. This is also called the method of average error. In this method, the observers themselves control the magnitude of the variable stimulus, beginning with a level that is distinctly greater or lesser than a standard one and vary it until they are satisfied by the subjective equality of the two. The difference between the variable stimuli and the standard one is recorded after each adjustment, and the error is tabulated for a considerable series. At the end, the mean is calculated giving the average error which can be taken as a measure of sensitivity.

Adaptive psychophysical methods

The classic methods of experimentation are often argued to be inefficient. This is because, in advance of testing, the psychometric threshold is usually unknown and most of the data are collected at points on the psychometric function that provide little information about the parameter of interest, usually the threshold. Adaptive staircase procedures (or the classical method of adjustment) can be used such that the points sampled are clustered around the psychometric threshold. Data points can also be spread in a slightly wider range, if the psychometric function's slope is also of interest. Adaptive methods can thus be optimized for estimating the threshold only, or both threshold and slope. Adaptive methods are classified into staircase procedures (see below) and Bayesian, or maximum-likelihood, methods. Staircase methods rely on the previous response only, and are easier to implement. Bayesian methods take the whole set of previous stimulus-response pairs into account and are generally more robust against lapses in attention. Practical examples are found here.

Staircase procedures

Main article: Up-and-Down Designs

Diagram showing a specific staircase procedure: Transformed Up/Down Method (1 up/ 2 down rule). Until the first reversal (which is neglected) the simple up/down rule and a larger step size is used.

Staircases usually begin with a high intensity stimulus, which is easy to detect. The intensity is then reduced until the observer makes a mistake, at which point the staircase 'reverses' and intensity is increased until the observer responds correctly, triggering another reversal. The values for the last of these 'reversals' are then averaged. There are many different types of staircase procedures, using different decision and termination rules. Step-size, up/down rules and the spread of the underlying psychometric function dictate where on the psychometric function they converge. Threshold values obtained from staircases can fluctuate wildly, so care must be taken in their design. Many different staircase algorithms have been modeled and some practical recommendations suggested by Garcia-Perez.

One of the more common staircase designs (with fixed-step sizes) is the 1-up-N-down staircase. If the participant makes the correct response N times in a row, the stimulus intensity is reduced by one step size. If the participant makes an incorrect response the stimulus intensity is increased by the one size. A threshold is estimated from the mean midpoint of all runs. This estimate approaches, asymptotically, the correct threshold.

Bayesian and maximum-likelihood procedures

Bayesian and maximum-likelihood (ML) adaptive procedures behave, from the observer's perspective, similar to the staircase procedures. The choice of the next intensity level works differently, however: After each observer response, from the set of this and all previous stimulus/response pairs the likelihood is calculated of where the threshold lies. The point of maximum likelihood is then chosen as the best estimate for the threshold, and the next stimulus is presented at that level (since a decision at that level will add the most information). In a Bayesian procedure, a prior likelihood is further included in the calculation. Compared to staircase procedures, Bayesian and ML procedures are more time-consuming to implement but are considered to be more robust. Well-known procedures of this kind are Quest, ML-PEST, and Kontsevich & Tyler's method.

Magnitude estimation

In the prototypical case, people are asked to assign numbers in proportion to the magnitude of the stimulus. This psychometric function of the geometric means of their numbers is often a power law with stable, replicable exponent. Although contexts can change the law & exponent, that change too is stable and replicable. Instead of numbers, other sensory or cognitive dimensions can be used to match a stimulus and the method then becomes "magnitude production" or "cross-modality matching". The exponents of those dimensions found in numerical magnitude estimation predict the exponents found in magnitude production. Magnitude estimation generally finds lower exponents for the psychophysical function than multiple-category responses, because of the restricted range of the categorical anchors, such as those used by Likert as items in attitude scales.

Convergent evolution

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Convergent_evolution 

 

Two succulent plant genera, Euphorbia and Astrophytum, are only distantly related, but the species within each have converged on a similar body form.

Convergent evolution is the independent evolution of similar features in species of different lineages. Convergent evolution creates analogous structures that have similar form or function but were not present in the last common ancestor of those groups. The cladistic term for the same phenomenon is homoplasy. The recurrent evolution of flight is a classic example, as flying insects, birds, pterosaurs, and bats have independently evolved the useful capacity of flight. Functionally similar features that have arisen through convergent evolution are analogous, whereas homologous structures or traits have a common origin but can have dissimilar functions. Bird, bat, and pterosaur wings are analogous structures, but their forelimbs are homologous, sharing an ancestral state despite serving different functions.

The opposite of convergent evolution is divergent evolution, where related species evolve different traits. Convergent evolution is similar to parallel evolution, which occurs when two independent species evolve in the same direction and thus independently acquire similar characteristics; for instance, gliding frogs have evolved in parallel from multiple types of tree frog.

Many instances of convergent evolution are known in plants, including the repeated development of C₄ photosynthesis, seed dispersal by fleshy fruits adapted to be eaten by animals, and carnivory.

Overview

Homology and analogy in mammals and insects: on the horizontal axis, the structures are homologous in morphology, but different in function due to differences in habitat. On the vertical axis, the structures are analogous in function due to similar lifestyles but anatomically different with different phylogeny.

Further information: List of examples of convergent evolution

In morphology, analogous traits arise when different species live in similar ways and/or a similar environment, and so face the same environmental factors. When occupying similar ecological niches (that is, a distinctive way of life) similar problems can lead to similar solutions. The British anatomist Richard Owen was the first to identify the fundamental difference between analogies and homologies.

In biochemistry, physical and chemical constraints on mechanisms have caused some active site arrangements such as the catalytic triad to evolve independently in separate enzyme superfamilies.

In his 1989 book Wonderful Life, Stephen Jay Gould argued that if one could "rewind the tape of life [and] the same conditions were encountered again, evolution could take a very different course." Simon Conway Morris disputes this conclusion, arguing that convergence is a dominant force in evolution, and given that the same environmental and physical constraints are at work, life will inevitably evolve toward an "optimum" body plan, and at some point, evolution is bound to stumble upon intelligence, a trait presently identified with at least primates, corvids, and cetaceans.

Distinctions

Cladistics

Further information: Cladistics

In cladistics, a homoplasy is a trait shared by two or more taxa for any reason other than that they share a common ancestry. Taxa which do share ancestry are part of the same clade; cladistics seeks to arrange them according to their degree of relatedness to describe their phylogeny. Homoplastic traits caused by convergence are therefore, from the point of view of cladistics, confounding factors which could lead to an incorrect analysis.

Atavism

Further information: Atavism

It can be difficult to tell whether a trait has been lost and then re-evolved convergently, or whether a gene has simply been switched off and then re-enabled later. Such a re-emerged trait is called an atavism. From a mathematical standpoint, an unused gene (selectively neutral) has a steadily decreasing probability of retaining potential functionality over time. The time scale of this process varies greatly in different phylogenies; in mammals and birds, there is a reasonable probability of a gene's remaining in the genome in a potentially functional state for around 6 million years.

Parallel vs. convergent evolution

Evolution at an amino acid position. In each case, the left-hand species changes from having alanine (A) at a specific position in a protein in a hypothetical ancestor, and now has serine (S) there. The right-hand species may undergo divergent, parallel, or convergent evolution at this amino acid position relative to the first species.

When two species are similar in a particular character, evolution is defined as parallel if the ancestors were also similar, and convergent if they were not. Some scientists have argued that there is a continuum between parallel and convergent evolution, while others maintain that despite some overlap, there are still important distinctions between the two.

When the ancestral forms are unspecified or unknown, or the range of traits considered is not clearly specified, the distinction between parallel and convergent evolution becomes more subjective. For instance, the striking example of similar placental and marsupial forms is described by Richard Dawkins in The Blind Watchmaker as a case of convergent evolution, because mammals on each continent had a long evolutionary history prior to the extinction of the dinosaurs under which to accumulate relevant differences.

At molecular level

Evolutionary convergence of serine and cysteine protease towards the same catalytic triads organisation of acid-base-nucleophile in different protease superfamilies. Shown are the triads of subtilisin, prolyl oligopeptidase, TEV protease, and papain.

Proteins

Tertiary structures

Many proteins share analogous structural elements that arose independently across different genomes. There are several examples of convergent protein motifs sharing similar arrangements of structural elements. Whole protein structures too have arisen through convergent evolution.

Protease active sites

The enzymology of proteases provides some of the clearest examples of convergent evolution. These examples reflect the intrinsic chemical constraints on enzymes, leading evolution to converge on equivalent solutions independently and repeatedly.

Serine and cysteine proteases use different amino acid functional groups (alcohol or thiol) as a nucleophile. To activate that nucleophile, they orient an acidic and a basic residue in a catalytic triad. The chemical and physical constraints on enzyme catalysis have caused identical triad arrangements to evolve independently more than 20 times in different enzyme superfamilies.

Threonine proteases use the amino acid threonine as their catalytic nucleophile. Unlike cysteine and serine, threonine is a secondary alcohol (i.e. has a methyl group). The methyl group of threonine greatly restricts the possible orientations of triad and substrate, as the methyl clashes with either the enzyme backbone or the histidine base. Consequently, most threonine proteases use an N-terminal threonine in order to avoid such steric clashes. Several evolutionarily independent enzyme superfamilies with different protein folds use the N-terminal residue as a nucleophile. This commonality of active site but difference of protein fold indicates that the active site evolved convergently in those families.

Cone snail and fish insulin

Conus geographus produces a distinct form of insulin that is more similar to fish insulin protein sequences than to insulin from more closely related molluscs, suggesting convergent evolution, though with the possibility of horizontal gene transfer.

Ferrous iron uptake via protein transporters in land plants and chlorophytes

Distant homologues of the metal ion transporters ZIP in land plants and chlorophytes have converged in structure, likely to take up Fe²⁺ efficiently. The IRT1 proteins from Arabidopsis thaliana and rice have extremely different amino acid sequences from Chlamydomonas's IRT1, but their three-dimensional structures are similar, suggesting convergent evolution.

Na⁺,K⁺-ATPase and Insect resistance to cardiotonic steroids

Many examples of convergent evolution exist in insects in terms of developing resistance at a molecular level to toxins. One well-characterized example is the evolution of resistance to cardiotonic steroids (CTSs) via amino acid substitutions at well-defined positions of the α-subunit of Na⁺,K⁺-ATPase (ATPalpha). Variation in ATPalpha has been surveyed in various CTS-adapted species spanning six insect orders. Among 21 CTS-adapted species, 58 (76%) of 76 amino acid substitutions at sites implicated in CTS resistance occur in parallel in at least two lineages. 30 of these substitutions (40%) occur at just two sites in the protein (positions 111 and 122). CTS-adapted species have also recurrently evolved neo-functionalized duplications of ATPalpha, with convergent tissue-specific expression patterns.

Nucleic acids

Convergence occurs at the level of DNA and the amino acid sequences produced by translating structural genes into proteins. Studies have found convergence in amino acid sequences in echolocating bats and the dolphin; among marine mammals; between giant and red pandas; and between the thylacine and canids. Convergence has also been detected in a type of non-coding DNA, cis-regulatory elements, such as in their rates of evolution; this could indicate either positive selection or relaxed purifying selection.

In animals

Dolphins and ichthyosaurs converged on many adaptations for fast swimming.

Bodyplans

Swimming animals including fish such as herrings, marine mammals such as dolphins, and ichthyosaurs (of the Mesozoic) all converged on the same streamlined shape. A similar shape and swimming adaptations are even present in molluscs, such as Phylliroe. The fusiform bodyshape (a tube tapered at both ends) adopted by many aquatic animals is an adaptation to enable them to travel at high speed in a high drag environment. Similar body shapes are found in the earless seals and the eared seals: they still have four legs, but these are strongly modified for swimming.

The marsupial fauna of Australia and the placental mammals of the Old World have several strikingly similar forms, developed in two clades, isolated from each other. The body, and especially the skull shape, of the thylacine (Tasmanian tiger or Tasmanian wolf) converged with those of Canidae such as the red fox, Vulpes vulpes.

• Convergence of marsupial and placental mammals
• 
  Red fox skeleton
   
• 
  Skulls of thylacine (left), timber wolf (right)
   
• 
  Thylacine skeleton

Echolocation

As a sensory adaptation, echolocation has evolved separately in cetaceans (dolphins and whales) and bats, but from the same genetic mutations.

Electric fishes

The Gymnotiformes of South America and the Mormyridae of Africa independently evolved passive electroreception (around 119 and 110 million years ago, respectively). Around 20 million years after acquiring that ability, both groups evolved active electrogenesis, producing weak electric fields to help them detect prey.

• Convergence of weakly electric fishes
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  A gymnotiform electrolocation waveform
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  A gymnotiform electric fish of South America
   
• 
  A mormyrid electric fish of Africa
   
• 
  A mormyrid electrolocation waveform

Eyes

Main article: Eye evolution

The camera eyes of vertebrates (left) and cephalopods (right) developed independently and are wired differently; for instance, optic nerve ⁽³⁾ fibres ⁽²⁾ reach the vertebrate retina ⁽¹⁾ from the front, creating a blind spot ⁽⁴⁾.

One of the best-known examples of convergent evolution is the camera eye of cephalopods (such as squid and octopus), vertebrates (including mammals) and cnidarians (such as jellyfish). Their last common ancestor had at most a simple photoreceptive spot, but a range of processes led to the progressive refinement of camera eyes—with one sharp difference: the cephalopod eye is "wired" in the opposite direction, with blood and nerve vessels entering from the back of the retina, rather than the front as in vertebrates. As a result, vertebrates have a blind spot.

Sex organs

Hydrostatic penises have convergently evolved at least six times in male amniotes. In these species, males copulate with females and internally fertilize their eggs. Similar intromittent organs have evolved in invertebrates such as octopuses and gastropods.

Flight

Further information: Flying and gliding animals § Evolution and ecology of aerial locomotion

Vertebrate wings are partly homologous (from forelimbs), but analogous as organs of flight in (1) pterosaurs, (2) bats, (3) birds, evolved separately.

Birds and bats have homologous limbs because they are both ultimately derived from terrestrial tetrapods, but their flight mechanisms are only analogous, so their wings are examples of functional convergence. The two groups have independently evolved their own means of powered flight. Their wings differ substantially in construction. The bat wing is a membrane stretched across four extremely elongated fingers and the legs. The airfoil of the bird wing is made of feathers, strongly attached to the forearm (the ulna) and the highly fused bones of the wrist and hand (the carpometacarpus), with only tiny remnants of two fingers remaining, each anchoring a single feather. So, while the wings of bats and birds are functionally convergent, they are not anatomically convergent. Birds and bats also share a high concentration of cerebrosides in the skin of their wings. This improves skin flexibility, a trait useful for flying animals; other mammals have a far lower concentration. The extinct pterosaurs independently evolved wings from their fore- and hindlimbs, while insects have wings that evolved separately from different organs.

Flying squirrels and sugar gliders are much alike in their mammalian body plans, with gliding wings stretched between their limbs, but flying squirrels are placentals while sugar gliders are marsupials, widely separated within the mammal lineage from the placentals.

Hummingbird hawk-moths and hummingbirds have evolved similar flight and feeding patterns.

Insect mouthparts

Insect mouthparts show many examples of convergent evolution. The mouthparts of different insect groups consist of a set of homologous organs, specialised for the dietary intake of that insect group. Convergent evolution of many groups of insects led from original biting-chewing mouthparts to different, more specialised, derived function types. These include, for example, the proboscis of flower-visiting insects such as bees and flower beetles, or the biting-sucking mouthparts of blood-sucking insects such as fleas and mosquitos.

Intelligence

Further information: Cephalopod intelligence

Advanced intelligence has evolved independently in cephalopods and vertebrates. Octopus have demonstrated mammalian levels of problem-solving, cognition, and learning behaviors. One aquarium director even claimed his octopus specimen to have developed a sense of personal taste as to the arrangement of its tank. Unlike other highly intelligent animals, cephalopods typically live short lives with varying levels of sociality, with the bulk of the nervous system divided between the head and limbs.

Opposable thumbs

Opposable thumbs allowing the grasping of objects are most often associated with primates, like humans and other apes, monkeys, and lemurs. Opposable thumbs also evolved in giant pandas, but these are completely different in structure, having six fingers including the thumb, which develops from a wrist bone entirely separately from other fingers.

Primate phenotypes

Further information: Human skin color § Genetics of skin color variation

 

Convergent evolution in humans includes blue eye colour and light skin colour. When humans migrated out of Africa, they moved to more northern latitudes with less intense sunlight. It was beneficial to them to have reduced skin pigmentation. It appears certain that there was some lightening of skin colour before European and East Asian lineages diverged, as there are some skin-lightening genetic differences that are common to both groups. However, after the lineages diverged and became genetically isolated, the skin of both groups lightened more, and that additional lightening was due to different genetic changes.

Humans		Lemurs
Despite the similarity of appearance, the genetic basis of blue eyes is different in humans and lemurs.

Lemurs and humans are both primates. Ancestral primates had brown eyes, as most primates do today. The genetic basis of blue eyes in humans has been studied in detail and much is known about it. It is not the case that one gene locus is responsible, say with brown dominant to blue eye colour. However, a single locus is responsible for about 80% of the variation. In lemurs, the differences between blue and brown eyes are not completely known, but the same gene locus is not involved.

In plants

In myrmecochory, seeds such as those of Chelidonium majus have a hard coating and an attached oil body, an elaiosome, for dispersal by ants.

The annual life-cycle

While most plant species are perennial, about 6% follow an annual life cycle, living for only one growing season. The annual life cycle independently emerged in over 120 plant families of angiosperms. The prevalence of annual species increases under hot-dry summer conditions in the four species-rich families of annuals (Asteraceae, Brassicaceae, Fabaceae, and Poaceae), indicating that the annual life cycle is adaptive.

Carbon fixation

C₄ photosynthesis, one of the three major carbon-fixing biochemical processes, has arisen independently up to 40 times. About 7,600 plant species of angiosperms use C₄ carbon fixation, with many monocots including 46% of grasses such as maize and sugar cane, and dicots including several species in the Chenopodiaceae and the Amaranthaceae.

Fruits

Fruits with a wide variety of structural origins have converged to become edible. Apples are pomes with five carpels; their accessory tissues form the apple's core, surrounded by structures from outside the botanical fruit, the receptacle or hypanthium. Other edible fruits include other plant tissues; the fleshy part of a tomato is the walls of the pericarp. This implies convergent evolution under selective pressure, in this case the competition for seed dispersal by animals through consumption of fleshy fruits.

Seed dispersal by ants (myrmecochory) has evolved independently more than 100 times, and is present in more than 11,000 plant species. It is one of the most dramatic examples of convergent evolution in biology.

Carnivory

Molecular convergence in carnivorous plants

Carnivory has evolved multiple times independently in plants in widely separated groups. In three species studied, Cephalotus follicularis, Nepenthes alata and Sarracenia purpurea, there has been convergence at the molecular level. Carnivorous plants secrete enzymes into the digestive fluid they produce. By studying phosphatase, glycoside hydrolase, glucanase, RNAse and chitinase enzymes as well as a pathogenesis-related protein and a thaumatin-related protein, the authors found many convergent amino acid substitutions. These changes were not at the enzymes' catalytic sites, but rather on the exposed surfaces of the proteins, where they might interact with other components of the cell or the digestive fluid. The authors also found that homologous genes in the non-carnivorous plant Arabidopsis thaliana tend to have their expression increased when the plant is stressed, leading the authors to suggest that stress-responsive proteins have often been co-opted in the repeated evolution of carnivory.

Methods of inference

Angiosperm phylogeny of orders based on classification by the Angiosperm Phylogeny Group. The figure shows the number of inferred independent origins of C₃-C₄ photosynthesis and C₄ photosynthesis in parentheses.

Phylogenetic reconstruction and ancestral state reconstruction proceed by assuming that evolution has occurred without convergence. Convergent patterns may, however, appear at higher levels in a phylogenetic reconstruction, and are sometimes explicitly sought by investigators. The methods applied to infer convergent evolution depend on whether pattern-based or process-based convergence is expected. Pattern-based convergence is the broader term, for when two or more lineages independently evolve patterns of similar traits. Process-based convergence is when the convergence is due to similar forces of natural selection.

Pattern-based measures

Earlier methods for measuring convergence incorporate ratios of phenotypic and phylogenetic distance by simulating evolution with a Brownian motion model of trait evolution along a phylogeny. More recent methods also quantify the strength of convergence. One drawback to keep in mind is that these methods can confuse long-term stasis with convergence due to phenotypic similarities. Stasis occurs when there is little evolutionary change among taxa.

Distance-based measures assess the degree of similarity between lineages over time. Frequency-based measures assess the number of lineages that have evolved in a particular trait space.

Process-based measures

Methods to infer process-based convergence fit models of selection to a phylogeny and continuous trait data to determine whether the same selective forces have acted upon lineages. This uses the Ornstein–Uhlenbeck process to test different scenarios of selection. Other methods rely on an a priori specification of where shifts in selection have occurred.