BIOL 4160

Evolution

Phil Ganter

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Looking up at a Redwood (Sequoia sempervirens)

08 - Phylogenetics I (Background)

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Classification is the process of subdividing large collections of items, living or not, into identifiable groups based on a rule or set of rules

  • The need for this comes out of the power of organization to allow a person to think about large groups of things
    • Libraries must classify their holdings so that an individual can find a particular item without a piece-by-piece search
  • Biological Classification arises from the same need because there are so many different kinds of organisms -- too many to think about without resorting to grouping them

Taxonomy

  • Any system of organizing things based on shared characteristics is a taxonomy
  • taxonomy does not have to reflect common ancestry, only similarity
    • One can construct a taxonomy of buttons based on size, number of holes, materials used, shape, etc. but this taxonomy would not reflect anything about the "ancestry" of buttons

Systematics is the classification of biological diversity through the use of shared ancestry (relatedness - see Lecture 01)

  • Why base biological classification on shared ancestry
    • Biologists desire a natural system of classification
      • Natural systems are those whose existence does not depend on the presence of humans - we discover these systems but we do not invent them
      • Artificial systems are those that do depend on our presence - we invent these systems but we can not discover them
    • Classification can be either natural or artificial but natural classifications tell us more about the biological world than do artificial ones
  • A Darwinian view of evolution, whether by natural selection or not, involves the application of the idea of ancestry (originally used to describe the relation of parent to offspring) to groups of organisms - from populations to species and larger groups
    • Just as a genealogy branches out over time from a single individual, relationships between groups of organism branch out from a Common Ancestor
  • For any three or more groups of organisms, the two with the most recent common ancestor are the most closely related
    • Primitive - occurring or originating long ago
    • Derived - occurring or originating more recently

Phylogenetics is the study of relationships among groups of organisms based on relatedness (common ancestry)

  • Phylogenetics can also be seen as the study of the evolutionary history of organisms, assuming the Darwinian view of evolution

Branching versus Hierarchical classification

  • Hierarchy is a classification scheme in which there is a "vertical" component, an idea of higher and lower, usually an outcome of inclusiveness in the sense that higher group in the hierarchy is composed of one or more groups from the next lower level
    • Domain-Kingdom-Phylum-Class-Order-Family-Genus-Species system is a hierarchical system
    • This is an artificial system because it requires the same number of levels to describe each organism but that may not be an accurate reflection of their evolutionary history
    • The inadequacy of this approach becomes obvious when you compare two species
      • Drosophila mauritiana is a member of the large, polyphyletic genus Drosophila (>1450 species) that occurs on the island of Mauritius in the Indian Ocean.  Its closest relative is D. simulans, from which it diverged about 250,000 MYA (McDermott SR, Kliman RM  2008  Estimation of Isolation Times of the Island Species in the Drosophila simulans Complex from Multilocus DNA Sequence Data.   PLoS ONE 3(6): e2442. doi:10.1371/journal.pone.0002442)
        • According to Uniprot (a large database of protein  sequences from all organisms), the classification of D. mauritiana is as follows:  Arthropod (Phylum)-Mandible (Class)-Dicondylia-Pterygota-Neoptera-Endopterygota-Diptera (Order)-Brachycera-Muscomorpha-Eremoneura-Cyclorrhapha-Schizophora-Acalyptratae-Ephydroidea-Drosophilidae (Family)- Drosophilinae-Drosophilini-Drosophilina-Drosophiliti-Drosophila (Genus)-Sophophora-melanogaster group-melanogaster subgroup
      • Gingko biloba's closest living relative, probably a cycad, is a member of a different phylum, according to the USDA's hierarchical classification of plants, and from which it diverged at least 270 MYA (during the Permian - divergence time over a billion times longer than for D. mauritiana and its closest relative)
        • In order to adhere to the biological taxonomic hierarchy, we need to make a phylum, class, order, family and genus with only one member (Ginkgophyta-Ginkgoopsida-Ginkgoales-Ginkgoaceae-Ginkgo) to classify this one species
      • D. mauritiana classification involves adding many additional levels not seen in the classification of Ginkgo biloba
        • D. mauritana has 26 levels (3 below the level of the genus) and G. biloba has 5 levels (and it's the only member of its group on any level)
      • Thus, one hierarchy does not fit all organisms
  • A Branching system is one in which earlier groups divide to produce new groups and so they reflect time and do not necessitate have a hierarchical structure
    • The metaphor of a tree as a branching system is apt here (the trunk of the tree precedes -- or is more primitive than -- any branches that originate from it)
    • Branching classifications can be natural if the branches reflect the true evolutionary history
      • We are in a transition period between the common use of hierarchical classification and a more natural branching classification of life
    • Go to the "TREE OF LIFE" [http://www.tolweb.org] website to see a branching history of life
  • Phylogeneticists do not use hierarchical systems
    • Phylogenetic change can occur as a branching event (Cladeogenesis) or as change along a branch without a division (Anagenesis)
      • A Clade is an ancestor and all of its descendent lineages
      • Phylogenies are presented as Tree Diagrams
        • Cladograms - show only the branching (can be Rooted or Unrooted)
        • Phenograms - show the branching and the length of the branch indicates the distance between a taxon and its most recent ancestor (rooted trees) or between taxa (unrooted trees)
    • Will we do away with the hierarchical classification schemes?
      • As of now, the answer is no because:
        • the professional taxonomy societies have not abandoned hierarchies
        • databases (protein, nucleotide sequence, etc.) need the hierarchical system because they need to organize their data just like librarians need to organize theirs and the available computer algorithms for such tasks use hierarchies

Inferring Phylogenetic History

We will never know with certainty any phylogenetic history prior to today

  • No one recorded the data
  • So, we must infer the history from the existing data

The first systemetists had several kinds of data:   morphology, anatomy, behavior, habitat

  • They made an assumption in order to derive an evolutionary history from the data:
    • Organisms that are closely related are more likely to share a trait than are less closely related organisms
  • Many recognized the faults in the assumption of similarity = relation

Phylogenies are based on ancestry but they are still constructed on the assumption that degree of similarity directly indicated degree of relatedness

  • Some definitions
    • Taxon (Taxa pl.) is a group of organisms classified into a single group -
      • a phylogenetic tree normally has all terminal taxa with similar taxonomic rank (all species or all populations within a species, etc.) although many trees drawn to illustrate particular points violate this
    • Characters (Traits) are features of an organism
      • Characters may take on values (Character States) and these may be:
        • Continuous - the character state may be one of an infinite set of states within the total range
        • Discrete - character states can have only certain values within the total range of values
      • Ancestral states are those present in the ancestor of any set of taxa
      • Derived states are those character states found only in a subset of the descendents of a single ancestral taxon
      • The ancestral state is an Plesiomorphy (pronounced Please-e-o-morphy) and the descendent (=derived) state is an Apomorphy
    • Terminal Taxa are those taxa at the tips of a tree's branches (that have no descendent taxa) and, for most trees, they are the living taxa
    • Other taxa all are made of an ancestral taxon and its descendents and there are three types:
      • Monophyletic - a taxon is monophyletic if it includes an ancestral taxon and all of the taxa that are descendents of the thet ancestral taxon
      • Paraphyletic - a taxon is paraphyletic if it includes an ancestral taxon and some, but not all, of its descendent taxa
      • Polyphyletic - a taxon is polyphyletic if it includes an ancestral taxon and at least one other taxon that is not a descendant of the ancestral taxon
  • Hennig formalized these ideas about similarity and relatedness when he proposed that there are three reasons for two organisms to share a character state
    • Ancestral Inheritance - the character state was in the ancestral taxon
      • Therefore, it should be in all of the ancestral taxon's descendents
        • If it is missing, it has been lost or altered
      • The tree on the left in the figure below illustrates this
        • Taxa 1 and 3 share a guanine in the second position in the short DNA sequence that is not shared by taxon 2
        • They do so because the ancestor of the group (the sequence in red) has a G
    • Inheritance of Shared Derived Character States (also called Synapomorphies) - the character state was not present in the ancestor for the entire lineage but is found in two or  more taxa because they chare a recent ancestor with that trait
      • The tree in the middle in the figure below illustrates this
        • Taxa 1 and 2 share a guanine in the second position in the short DNA sequence that is not shared by taxon 3, as on the tree to the left
          • They do so because their most recent ancestor has that state (G) but the ancestor did not
        • The state of "G" is derived because it is no- t found in the more distant ancestor but is found in a more recent ancestor
        • Thus, the "G" is a shared, derived character
    • For the sake of completeness, I should mention that an apomorphy that is not shared (i. e. it is found only in one taxon) is called an Autapomorphy and is useless when constructing a phylogeny
    • Homoplasy
      • Two or more taxa share a state because the state arose more than once.  There are two reasons for this
        • Convergence - the state arose in different lineages within the tree
        • Reversal - the state arose twice in the same lineage
      • Homology is the older term and was used to describe convergence of phenotypic character states
        • Reversals are very rare for complex phenotypic characters
        • Sequence data contains more reversals (e. g. A mutates to T and back to A again) and homoplasy is now the more acceptable term
      • The tree to the right in the figure below illustrates this
      • Taxa 1 and 3 share a guanine in the second position in the short DNA sequence that is not shared by taxon 2
        • They do so not because their most recent ancestor has that state (the ancestor in red is their most recent common ancestor and it has) but because the state has arisen twice through mutation

  • Hennig drew the logical conclusion that, of the three reasons for shared states, only shared, derived states give any information about relatedness
    • Homoplasy is a false indicator as it indicates an  ancestral condition that was never so
      • The similarity between Taxa 1 and 3  in the tree to the right is not a reliable indicator of relatedness
      • the homoplasy arises because the mutation has occurred twice since the most recent ancestor to all three taxa
    • Ancestral States can also give a false indication of relatedness, as taxa 1 and 3 are most similar in the tree on the left but are not most closely related

Constructing a Phylogenetic Tree

  • Given a set of taxa and the character states of multiple characters, the problem is to draw a tree which reflects the phylogeny of the group
    • Phylogenetic Since we have seen that the only information useful in this is that found in shared, derived character states, we need to separate them from changes that reflect homoplasy or similarities due to shared, ancestral states
    • If you know what the ancestors' character states were, this would be a snap but it is exceedingly rare to know this
  • Several methodologies have been developed to do this (we will mention only four)
    • Distance methods (also called similarity methods)
      • a formula is applied to the data to calculate the distances (or similarities) among all of the taxa and a procedure (there are many) is used to take the matrix of distances (or similarities) an construct the tree
    • Maximum Parsimony - here trees are compared directly
      • Each tree is given a "length" - the total number of evolutionary events that have to occur for the data to fit the tree
      • The tree with the least number of events is most probably shows the true relationships
      • Parsimony is the empirical principle that the explanation with the fewest number of assumptions is most likely to be correct
      • In this case, each evolutionary event needed to fit the data onto a tree is an assumption about the evolutionary history of the taxa, so the tree with the fewest number of events is most parsimonious
    • Maximum Likelihood - these methods use a model of evolution to calculate the likelihood of the data given a particular tree
      • The tree with the largest likelihood is the one that reflects the true relationships among the taxa
      • The evolutionary model is crucial - if it is wrong, then a false tree may have the greatest likelihood
    • Bayesian Probability - this method is based on Bayes Theorem and uses a model of evolution to compute the probability of a particular tree given the data
      • The most probable tree is the best guess of the real relationships, given the data
      • the model of evolution must be explicit about the chance of particular mutations occurring (only models of sequence evolution are explicit enough to be used in this approach)
  • Performance
    • Various tests have been devised to test the performance of these methods
      • Many involve simulated data (so that the true tree is known)
      • If applied correctly (a big if in many cases), then
        • Distance Methods are very good and require the fewest number of calculations
        • Maximum Parsimony is excellent but takes more effort than distance methods
        • Maximum Likelihood methods are even more excellent and require even more effort
        • Bayesian Probability is as good as maximum likelihood and is more efficient (and, although last to be developed, is becoming the standard)
    • Distance methods differ in a very important way from the other three
      • Although there is more than one method for drawing a tree from a matrix of distances, each method yields only one tree (there are some minor exceptions to this rule)
      • The other methods must be applied to every possible tree that can be drawn from the set of taxa and the best tree is known only after all of them have been evaluated
        • This rapidly becomes a Herculean task
          • Given a set of taxa, the number of rooted or unrooted trees that can be drawn that connects all taxa becomes astronomically large as the number of taxa goes up (more rooted than unrooted trees for the same number of taxa)
            • for 20 taxa, the number of rooted trees is 8.2 x 1021 or 8 thousand trillion trillion trees
              • If the fastest supercomputer could examine a tree in the time it takes it to perform one calculation (called a FLOP), it would take a year to examine all of the trees (in actuality, thousands of calculations are needed to evaluate a tree of that size, so a the fastest computer would take thousands of years!!)
            • for 57 taxa, the number of rooted trees is 3.85 x 1090 trees, or about 4 trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion trees
              • there are only about 1 x 1089 protons in the universe
      • Heruistic Search
        • Thus, we cannot really compare all trees when the number of taxa gets beyond the teens
        • The accepted approach is to search for the best tree without trying out all of them (we haven't time to discuss how this is done) - called a heuristic search
        • The performance evaluation above is based on heuristic methods

Molecular Clocks

A molecular clock is the ability to measure time by measuring change to a DNA or protein sequence

  • By comparing orthologous sequences in two taxa, we could then tell how long ago they shared a common ancestor
    • Requires several assumptions
      • constant rate of change all along the sequence and between the two lineages
      • no homoplasy (reversals, etc.)
    • If we know the rate of single changes, we can get an absolute time since their common ancestor
  • A tree with tree branch lengths that reflects the distances between taxa presents a view of the relative time since divergence but absolute time since divergence is possible if the clock can be calibrated
    • Two ways to calibrate the clock
      • fossil data on a common ancestor
      • measuring the rate of neutral change in the sequence
  • Molecular clocks are popular but still controversial
    • It is known that some lineages violate the constant rate assumption
    • Relative Rates Test
      • Since the amount of time that has elapsed since any two taxa shared a common ancestor is the same for both taxa (no matter how many splits into new taxa have occurred during that time), the number of changes should be the same for both taxa with random chance explaining any differences found
      • Relative Rate Test tests the assumption of equal number of changes in two lineages (first a tree must be constructed and the number of evolutionary events counted on the tree)
        • For closely related species, the relative rate test often finds no difference
        • For distantly related species, the relative rate test finds many more cases of different rates of evolution in the two lineages compared
      • This is a direct test of the most important assumption behind molecular clocks: constant rates of evolution

Phylogenetic Problems

There are recognized problems in tree construction, some are theoretical and some are practical

  • Practical Problems
    • Early in  the "Sequencing Era", a single gene was sequenced in several species or populations and a phylogeny of the species, not the gene, was inferred from the data
      • This assumes that all genes in an organism have the same evolutionary history, so all reflect the history of the species
    • However, as sequencing became easier and more common, multiple genes were often sequenced and combined in a single phylogeny
      • This is done in two ways:
        1. All data is combined into a single analysis
        2. A tree is constructed for each gene sequence and the species tree is the consensus among the different gene trees
        • Method 1 forces a consensus from the data by assuming that all gene histories are those of the species and deviations are due to undetected homoplasy or simply error in data collection
        • Method 2 does not make the same assumption and has discovered that genes in the same individual may have different ancestries due to such evolutionary events as horizontal transfer of genes, hybridization, gene duplication, and confusion due to polymorphic characters inherited by descendents (this confusion is generally said to be caused by "Lineage Sorting"
          • Lineage sorting is the result of the presence of polymorphic loci that persist over one or more speciation events. 
            • Suppose Species A splits into Species B and C and Species C further splits in to Species D and F. 
              • B, D, and F are the extant species and you collect data on the same gene from all three. 
                • Locus W (for fuzziness, say) is polymorphic in species A (W1W2, W1 produces fuzz, W2 does not)
              • The polymorphism persists in both Species B and C
              • Over time, W1 become fixed in species B
                • When Species C splits into Species D and F, W2 becomes fixed in Species D, but W1 is fixed in Species F
              • Your data now shows that Species B and F share W1 and Species D has a different allele, even though the true tree places D closer to F and has B as the outgroup
          • Notice that this problem arose  without any convergent evolution or mutation and can arise from any locus that is polymorphic at the time of speciation
        • The use of method 2 has, in fact, been key to uncovering instances of horizontal gene transfer (see below) and hybrid species formation (see below)
    • Problems with Character Scoring
      • Phenotypic characters
        • How to score multiple changes (and even deciding how many changes actually took place!) can be difficult and, if you don't get it right the resulting tree may be incorrect
      • Sequence characters
        • How to deal with indels and multiple point mutations at the same site
        • Indels are problems when multiple lineages have indels at the same site but the indels are not identical (impossible to decide which came first!)
        • If more than one change occurs at a site, the second change may restore the original base
          • The second occurance of the base at the site is not phylogenetically equal to the first (the second occurance is not the descendent of the first), although it is biochemically identical to the first and  may be undetectable
  • Theoretical Problems
    • Homoplasy is common so you need to gather enough data that the true history is supported by many characters (homoplasies tend to be unique and supported by only one or a few characters)
    • Radiations occur so quickly that some divergences have no synapomorphies and, thus, leave no evolutionary record
    • Long-Branch Attraction
      • If a phylogeny has unequal rates of evolution, such that some branches leading to terminal taxa are long (many changes) and some very short (few changes) then tree construction methods will tend to place the long branches as sister taxa, even if they are not closely related (this bias occurs in all methods of tree construction)
        • It is a problem that can't be solved with more data because that usually just makes the long branches longer, which worsens the problem
          • When long branch attraction occurs, the analysis is said to have entered the "Felsenstein Zone", a kind of Twilight Zone (from the TV scifi series) where the normal rules are turned on their heads (named after Joe Felsenstein, who first described long branch attraction along with many other innovations in phylogenetic analysis)
    • Base Composition Bias and differences in the probability of Transitions versus Tranversions
      • both of these biases, if undetected, can constrain evolution and, if the model of evolution used to score a tree does not take them into consideration, they may result in the acceptance of an incorrect tree

Hybridization, Horizontal Gene Transfer, and Gene Duplication

These three process all violate the model of evolution behind phylogenetic tree construction, specifically the basic tenet that says a taxon splits into daughter taxa (in the strictest sense, this splitting is only into two daughter taxa

  • This results in a bifurcating tree in which all branching events have two descendent branches
  • Trees often result from analyses of particular data sets that have trifurcations or more branches from one Node (a branching event) but the strict model assumes that this is a result of insufficient data and more data would resolve all branching events into bifurcations (not always true!)
  • Evolution that can't be depicted as bifurcations (or tri- etc. furcations) is called Reticulate Evolution

Horizontal Gene Transfer

  • This is the transfer of genes between different lineages outside of sexual reproduction (reproduction is seen as vertical gene transfer between generations)
    • Bacterial parasexual recombination is considered HGT when the gene is transferred by transduction, transformation, or conjugation if the recipient is an unrelated lineage (another species or another subspecies)
    • Thus, a gene with a completely different ancestry is suddenly found in a species and, if you are using that gene to understand the lineage, you will draw the wrong conclusions
  • Sequence analysis has shown that this is not a rare event for prokaryotes and, although less common, is found in eukaryotes as well
    • Eukaryotic processes of transfer are not as well understood but may involve eukaryotic parallels to both transduction and transformation
  • Most HGT involves environmental genes
      • Housekeeping genes - those with products that function in basic cellular processes like DNA replication, protein synthesis, etc.
      • Environmental genes - those with products that are important only in particular environments like genes for assimilation of particular nutrients, genes for disease resistance, etc.
    • Housekeeping genes are optimized for interaction among themselves as the basic cell functions are all interconnected and transfer of these genes disrupts the optimization (usually)
    • Environmental genes are optimized for performance in particular situations and may lose value when the environment changes but, if HGT brings them at the right time, may be very valuable additions to the genome

Hybridization

  • When hybrids form, two lineages are merged into one,  exactly the opposite of a bifurcation
  • The resulting linage may lose some of the duplicated loci but for those loci that are not lost, the effect is the same as a gene duplication (discussed below)

Gene Duplication

  • When segments of a chromosome are duplicated (a hybridization event is only one way for this to occur and duplication of portions of a chromosome appear to be more common) it complicates the idea of ancestry because related sequences are now found at different loci
    • Orthologs - these are two different variants at the same locus (these are what we commonly refer to as alleles when they occur in the same species)
    • Paralogs - these are two different copies of a gene that are now at different loci due to the duplication (I don't want to call them alleles)
  • Because recombination occurs only for sequences at the same locus, two mutations in different positions on orthologs can eventually be in the same sequence
    • Two mutations, each on a different paralog, will never be in the same sequence as there can be no recombination
  • Thus, the evolutionary history of duplicated genes is sundered at the time of duplication, although they continue to reflect a common history from the time prior to the duplication

Parallelisms, Convergences and Reversals

Although sequence data is commonly used to infer phylogenetics, we should not let it obscure the patterns found in phenotypic evolution that are illuminated though phylogenetic analysis and we will, in this and the next section, investigate some of those patterns

Homoplasy is not uncommon in sequence or phenotypic evolution and Convergence, Parallelism, and Reversals are all sources of phenotypic homoplasy

  • Convergence is the development of similar phenotypes in response to similar environmental pressures (opportunities? - the phenotypes are said to converge from two different ancestral phenotypes to a single phenotype)
    • Camera eyes have arisen twice and are an example of convergent evolution
    • Note that, because the convergence may involve different parts of the bodies, that the final product, the convergent phenotypes, can have significant differences (note the smart way that the mollusc eye is innervated and the stupid way that the vertebrate eye is innervated)
  • Parallelisms differ from Convergences
    • Parallel phenotypes are those that have arisen more than once in a phenotypic tree and are essentially the same change that arises in different lineages
    • This means that a parallel phenotypes share very similar developmental pathways and that the changes may be mutations to the same genes that occurred in different lineages
      • What Convergence and Parallelism share is that each phenotype arises as an adaptation to the same environmental challenge
      • What they do not share is their origins
    • Example - both pandas and humans have opposable digits on their anterior limbs but the human thumb is one of the ancestral five digits while the panda uses an extension of a bone found in both the panda and human wrist
      • This is a convergence as the opposition is useful for manipulation of objects but is not a parallelism because the developmental pathways differ
    • However, it must be said that, in many cases we do not know enough about the genetics of complex phenotypes to separate convergences from parallels
  • Reversals
    • This is the re-acquisition of a primitive character from a derived character
      • Molecular reversals are not uncommon for point mutations or for amino acid substitutions because the number of options for the phenotype are very limited
      • Reversals of complex characters may not truly be reversals but may be convergences or parallels that occur over time in the same lineage
    • The book notes the re-acquisition of lower-jaw teeth in a species of frog
      • If the genetic mechanism and phenotype of the "reacquired" phenotype are similar to those in the primitive condition, then it is a reversal
      • If the new lower-jaw teeth differ in the genes and developmental pathway such that the teeth are not really the same as those present in the ancestral phenotype, then this is a case of convergence or reversal

Allometry, Heterochrony and Heterotrophy

  • Phenotypic evolution depends on development of the organism but this obvious truism has some subtle and interesting outcomes
    • Modular development
      • Many animals and plants are modular in that the overall body is composed of a series of modules that are basically all the same
        • In old fashioned zoology, this phenomenon is known as metamerism and the modules are called metameres (the book does not use these terms)
      • Although the modules start out similar, many modules have independent developmental pathways so that, when fully grown, they acquire specialized functions and are much modified in the adult organism
        • Due to the extensive modification modules may undergo, modules are often most easily seen early in development
      • This process of independent developmental fates for modules is called Individualization (the term does not refer to each organism developing into an individual but each module having an individual developmental fate)
        • This means of building a complex organism (similar to building a complex molecule, n'est-ce pas?) allows for small changes in the developmental pathways of individual modules to greatly alter the overall phenotype of an organism

Patterns in development

Heterochrony

  • Phenotypic change can be effected by heterochrony: alterations to the timing of developmental events
    • One example is when the development of the reproductive system is altered relative to the rest of the organism so that the organism still has many juvenile features when it attains maturity, a process called Paedomorphosis (remember, maturity in biology is when an organism becomes reproductively competent)
    • The opposite example occurs when the development of the reproductive system is altered relative to the rest of the organism such that the rest of the organism develops past where it would otherwise be when the reproductive system matures, a process called Peramorphosis

Allometry

  • Allometric growth is produced by different parts of the body growing at different rates (our heads grow more slowly than our legs, for instance)
  • Many evolutionary changes to phenotypes are the result of alterations of the growth rate of individual body parts
    • We often detect allometry by relating the size of two body parts in several related species and looking for a line or curve that passes through the points (each species provides a point)
    • Many relationships are not linear but are described well by using a power curve (often called the allometric function):
      • If y is the size of one body part and x is the size of another, then the allometric function is

y = bxa

      • This equation is a curve but it can be linearized (turned into a linear equation of the form y = mx + b) by taking the log of each side (linear equations are easier to analyze)

log(y) = log(b) + a(log(x)) - a is the slope and log(b) is the y-intercept

    • If there is no allometry, then the growth of the body parts relative to one another is the same in each species (even though the overall size may differ) and the linearized allometric relationship has a slope of 1
      • Departures from this line are evidence of allometric growth
      • If one structure is doubled in size, the other is also doubled (allometry occurs when one structure is doubled but the other is changes by a ratio greater than or less than, but not equal to, 2)
  • Allometric change can involve changes in the rate of development, the duration of development, or the time of initiation of development of particular body parts or systems
    • Because growth is not linear, these changes can produce a great range of possible phenotypes from a very similar set of genes
      • For instance, Paedomorphosis can result from the slowing of the body's development relative to the reproductive system (Neoteny) or by halting growth early (Progenesis)
      • Neoteny is the reduction of the growth rate of a character
      • Peramorphosis may be the result of allowing growth to proceed for a longer period
      • Those structures growing fastest will become very much larger than other, more slowly growing, structures

 

Heterogtrophy

  • This is the repositioning of body parts or a change in the place in which a gene is expressed
  • Many genes are expressed only in certain places (the gene for crystallin, the protein found in the eye's lens, has undergone heterotrophy as the gene products have gained new functions in the body)

Adaptive Radiation

  • This topic will be treated in several places but it refers to a burst of speciation within a lineage when that lineage colonizes a new habitat
  • Often seen on islands (land snails in the South Pacific) and in deep lakes ( Gammarid amphipods in Lake Biakal)
Last updated March 18, 2009