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Darwin made the important discovery that species originated from a single location and spead from there rather then the idea that they had been created at differnt locations[E]. Infact species can be found over large geographical areas which was the consequence of dispersal, spreading form their ancestral original location to further widespread locations. There are two differnt types of dispersal - jump dispersal (the movement accros barriers) and range expansion- which is dispersal or movement accros favourable habitats[E]. Range expansion has occurred in the history of many species as evident from current observations such as the presentce of plants and animals on islands which are simmilar to those on nearby mainlands. Range expansion can also be found in the fossil record which also gives good insights into continental drift and other such events in the history of life on earth[E]. There can be many reasons for range expansion, and exapmle is climate changes such as global warming or ice ages leading to periods of directional growth and of contractions and re-expansions of plants and animals. Other factors could be invasive species being introduced to new and ideal habitats which allows the invasive species to collonise and spread from the initial site of introduction. Range expansion has yielded distinct genetic diversity patterns on a population, that has led to the (understanding of phenominom with the aid of the )formation of models, a few of which will be discussed bellow.
Before a discussion of the models it is important to establish the two different types of genetic diversity which include neutral and adaptive.
There are two different types of genetic diversity, neutral and adaptive.
Neutral genetic diversity
Neutral genetic variation refers to genes (or DNA segments) that do not affect the fitness of an organism. For example when looking at an alleles, a and b, whether the organism inherits homozygous (aa or bb) or heterozygous (ab) alleles, it won't have an effect on the survival (and reproductive success) of that organism. Mutations for example do not effect fitness, they are usually in non coding regions of the DNA or in the replacemtn of old alleles by new ones resulkting in non-adaptive evolution. This essentially means neutral genetic variation is not effected by selection and is affect by both genetic drift and gene flow (migration -only those that sucessfuly repoduce in the new population contriburte to gene flow).
Adaptive genetic diverstiy
Adaptive genetic variation on the other hand is determined by natural selection. This refers to genes that do contribute to the fitness or survival of the organism. Unlike neutral genes, genes alleles, for example a or b do matter to the fitness of the organism, be it homozygouse ( aa or bb) or heterozygous (ab). Natural selection will act these genotype and favour one over the others ( aa vs ab vs bb). The favoured gene will tend to accumulate in the population while the unfavoured are removed as they less fit. These genes, just as neutral ones, are affected by genetic drift and gene flow but selection is acting above the other processes. It is important to note that genetic drift is not responsibe for changes in anatomical, physiological or behanvioral features of a species that may increase their survival or repoductive sucess, instead it refers to the more molecular level, in particular the differnce in DNA sequences between and among species[E]. Consequencly, all allele are potentialy subject to random genetic drift however not all are subject to natural selection[E].
Coalescence theory is a model used in population genetics to predict genetic diversity patterns. It is based on tarcing back the geneologies of (species??) back to their Most Recent Common Ancestor(MRCA) . It is used to work out for example the probability of two gene lineages coalescing. The probability of these genes coalescing is inversly proprtional to the size of the population, where it takes a longer time for them to coalesc in a larger population than in a smaller one. In this case we can use this theory to predict the genetic diverstiy of expanding populations and the time scale in which they occured. Previose studies comparing differnt pairs of DNA sequences have yeilded conclusions that differences between them is proprtional the the expansion time.
One of the patters observed during range expansion is the initial decrease of genetic diversity due to a bottleneck because of successive founder events. This is because range expansion usualy origionates from a small population of ansestral species. More so at the marginal populations of the range expansion experience a reduced genetic diversity. Overall the range expansion causes a decreased neutral genetic diversity, pheotypic diversity and quaothntitative genetic diversity. Although the bottleneck affect caused reduced diveristy it does on the other hand increase genetic differentiation. However if there is gene flow the differentation between the population will be decreased.
During range expansion there is an observed star-shaped gene genelogy observed, meaning an exces of rare mutations( as will be explained later) This causes an increased genetic distance from the ancestor.
Pattern/model 1-Surfing phenomenon
During the range expansion mutations in the DNA can occur and they can either be 'carried with the wave' and travel large distances or ( the majority of mutations) can be lost or stay at low frequencies due to genetic drift.  The successful mutations (known as 'surfing mutations in this scenario) can on the other hand reach high frequencies and can be studied using computer simulations to understand and estimate the fate of such mutations.
Klopfstein et al(year) used a simulating program -SPLATCHE to simulate the fate of mutations during range expansion in haploid individuals (on a two-dimentional stepping stone grid). From this they outline two important observations from this surfing mutation phenominom. One that that this phenomenon happens at any population size, from small to large. This is important so there is no discrimination in the consequence of gentic diversity because of population size. The second is that the survival of a new mutation is dependent on where it occurred, where being at the edge of the range expansion increases its chance of survival, and decrease if not at the edge of the range expansion. This implies that mutations occurring during range expansion contribute significantly to evolution as these mutations could arise, persist and accumulate.
When looking at the consequences between neutral and adaptive genetic diversity, we see that both accumulate mutations. Firstly with neutral mutations (i.e. not selected oppon) the surfing phenomenon suggests that there is a 'reduced rate of loss of mutations' and that mutations could accumulate even after a speciasion event. Therefore after a speciation event and during range expansion there is an accelerated rate of neutral mutations and so accepelerating the evolution of the species at the edge of the range expansion. However two processes affect the succese of neutral mutations- genetic drift and gene flow. If there is high genetic drift it is hard for the mutation to spread during range expansion, the mutations therefore leading to and increased probability that the mutation will become extinct if it does not reach a high enough frequency within the deme. However if there is a lot of migration ( high gene flow) then we see and increased proportion of mutations persisting over a large range of demes. If on the other hand, if there is a combination of large deme size and a large number of migrating individuals, then it becomes harder for the mutations to reach a high local frequency. [due to this the behaviour of a mutauton is dependent on deme size and migrations onf ao cant be used to distinguish neutral mutations that have arisen during range expansion of large or small populations.
Although these neutral mutations are independed of the adaptive mutations linked to the speciation even, it is also thought that the surfing pnenimon also speeds up these also? Although the differences the surfing phenominom has between positively and negatively selected genes is not well studied. However if a recessive disadvantageous allele occurs during the range expansion it could be carried over a over a large area but it cannot reach high frequencies due to negative selection.
Factors affecting genetic diversity
The shape of the environment also add another factor that affects genetic diversity of a species during and after range expansion. Geographical barriers are well known to favour the formation of races and species(i.e. there is greater genetic drift where individuals are physically unable to migrate with other deems). However, as proposed in the stepping stone model, even if there is no physical barriers, the sheer size of the environment can cause a similar affect because migration distances would be too large(isolation by distance). This model suggests that during range expansion there are a series of bottlenecks or founder events in which individuals living nearby tend to be more alike then those living further apart[3.10].
The simulating model used above SPLATCHE does take into account spatial environmental heterogeneity, instead it assumes that the environment is uniformly occupied. This means that the model doesn't take into account that a species may in fact populate the environment in a patch like manner. A patch distribution could occur by change or by certain factors such as nutrition availabitily, pray, preditors, sunlight, temperature or humidity resulting in difference in population densities at different locations.
[[maybe, due to this maybe there is an increased selective pressure in some patches more hten others, afftecting the adaptive genetic diversity, where the distances between populations and their ability or migrate would affect the neutral genetic diversity and potentially the adaptive]]
Also in this patchy distrubution, migrants from favourable environments to recipeint populations in unfavourable enviroments may prevent the recipeint population from adapting locally at the range margin. This procces of gene flow essentually counteracts the natual selection for the recipient population in this case.[E]
Extonction and recolinisation
It is also important to take into account that during range expansion there is a difference in both the size of deems and their migration rates over time. Which also intertwines with the population dynamics of extinction and re-colonisation. These factors result in complex genetic diversity patterns, where extinction acts as another form of genetic drift and re-colonisation acts as another form of the founder effect. These both have opsite effects, extinction on one hand increases the differentiation between deems where the recolinsation acts like gene flow ( and new colonies originate form nabouring colonies) , decreasing differentiation between deems.
sThe interplay between neutral and adaptive prosses during range expansion can be one that is still under controversy. The proses of genetic drift is the key link between neutral and adaptive genetics. Before it was thought that almost all alleils differences affected the fitness of an organism. However it is now better understood that evolution can occure from just random genetic drift of selectively neutral allies. This discovery was made due to the amount of enzyme loci that are polymorphic which was argued that natural selection could not account for and maintain the quantity of genetic variation. This 'mnuetralist-selectionist debatee is still unresolved' but in the case of this discusion, it is clear that genetic drift plays a role in both the formation of nuetral and adaptive mutations accounting for the variarion during range expansion. Simmilary gene flow between the population can decrease the variation and even the evolution of populations during range expansion. Acting on the reducetion of nuetral mutations(check) and even possible reducing the fitness of other populations. And so gene flow is another process that interplays between nutral and adaptive genetics.
The prosses that is not shared in range expansion or any other conditions is ofcourse selection. Natural selection is the only prosses that effect adaptive mutations, acting either positivily or negitivly on them. Where non beninficial mutation are removed from the equation, and positive mutation are kept. Although as explained in the surfing phenominom, even recesive negative mutaion may sucessed due to the range expansion event. Natural selection does not account for nuetral mution, however because of this nuetral mutations are the most effective for viewing and understanding population genetics of range expansion. Unlike adaptive prosses, mutation can be eliminated from the population and not be observed, nuetral pose more of an accurate account of the range expansion as they are not acted upon by selection (so gentic drift and gene flow) provodonmg an insight int o the past movents and history of a species and their distribution.
[E] -evo book