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Engineering receptors and antibodies for biosensors.

Biosensor sensitivity and selectivity depend essentially on the properties of the biorecognition elements to be used for analyte binding. Two principally different applications are considered, (1) effects monitoring with biological components as targets for bioeffective substances, among them endocrine disruptors; and (2) immunochemical analysis employing antibodies as binding proteins for a wide variety of analytes such as pesticides. Genetic engineering provides an elegant way not only for providing unlimited amounts of biorecognition molecules but also for the alteration of existing properties and the supplementation with additional functions. Instrumental applications were carried out with the optical sensor BIAcore. The first example deals with the characterization of receptors. For this purpose, the human estrogen receptor alpha was used. Binding studies were carried out with natural as well as xenoestrogens. An equilibrium dissociation constant K(d) of 2.3x10(-10) (M) was derived for 17beta-estradiol. A competition assay was performed with a bovine serum albumin (BSA)-17beta-estradiol conjugate, immobilized at the optical sensor surface, and the free estrogen. The signals obtained represent estradiol equivalents. This format was transferred to a microplate-based enzyme-linked receptor assay. It reached a detection limit of 0.02 microg l(-1) 17beta-estradiol and proved suitable for the detection of natural and synthetic estrogens as well as xenoestrogens in field studies. The second example is targeted at kinetic and affinity measurements of recombinant antibody fragments derived from antibody libraries with s-triazine selectivities. Different strategies for the synthesis of antibody fragment libraries, followed by the selection of specific antibody variants, were examined. An antibody library was derived from a set of B cells. Chain shuffling of the heavy and light chains provided the best binders. An enzyme linked immunosorbent assay (ELISA) was achieved for atrazine with an IC(50) of 0.9 microg l(-1) and a detection limit of 0.2 microg l(-1). The close relations between the optimization of recombinant antibodies by evolutionary strategies and genetic algorithms are considered.

Algorithms↗

Charles Darwin and other great men in correspondence with Carl Wilhelm von Naegeli.

The great Swiss-German botanist Carl Wilhelm von Naegeli (1817-1891) was a student of Lorenz Oken, A.P. de Candolle, and Matthias Jacob Schleiden and became a key figure in "genetic" (i.e., evolutionary-developmental) biology in the mid-late 19th century. He was an expert on the hawk-weed, Hieracium and also made important contributions to microbiology. One of his many outstanding students was Carl Correns, one of the 3 rediscoverers of Mendel's work. Naegeli was an early proponent and defender of Darwin. The correspondence preserved in the Naegeli family contains many important letters between Naegeli and his contemporaries. Those from Mendel to Naegeli have passed out of the Naegeli family and were published by Correns earlier in the century. However, exceptionally notable items still in the archives of the Naegeli family include 4 surviving letters from Darwin, 2 letters from Virchow, and 10 from Justus von Liebig. In spite of a lack of appreciation of Mendel's work, we call attention to the importance of those surviving documents from an era in which very few of the greatest naturalists and founders of modern biology--including Goethe, Darwin, Galton, Agassiz, von Humboldt, von Baer--were without "blind spots."

Botany↗

Haplotype block structure is conserved across mammals.

Genetic variation in genomes is organized in haplotype blocks, and species-specific block structure is defined by differential contribution of population history effects in combination with mutation and recombination events. Haplotype maps characterize the common patterns of linkage disequilibrium in populations and have important applications in the design and interpretation of genetic experiments. Although evolutionary processes are known to drive the selection of individual polymorphisms, their effect on haplotype block structure dynamics has not been shown. Here, we present a high-resolution haplotype map for a 5-megabase genomic region in the rat and compare it with the orthologous human and mouse segments. Although the size and fine structure of haplotype blocks are species dependent, there is a significant interspecies overlap in structure and a tendency for blocks to encompass complete genes. Extending these findings to the complete human genome using haplotype map phase I data reveals that linkage disequilibrium values are significantly higher for equally spaced positions in genic regions, including promoters, as compared to intergenic regions, indicating that a selective mechanism exists to maintain combinations of alleles within potentially interacting coding and regulatory regions. Although this characteristic may complicate the identification of causal polymorphisms underlying phenotypic traits, conservation of haplotype structure may be employed for the identification and characterization of functionally important genomic regions.

Animals↗

Detecting natural selection on cis-regulatory DNA.

Changes in transcriptional regulation play an important role in the genetic basis for evolutionary change. Here I review a growing body of literature that seeks to determine the forces governing the non-coding regulatory sequences underlying these changes. I address the challenges present in studying natural selection without the familiar structure and regularity of protein-coding sequences, but show that most tests of neutrality that have been used for coding regions are applicable to non-coding regions, albeit with some caveats. While some experimental investment is necessary to identify heritable regulatory variation, the most basic inferences about selection require very little functional information. A growing body of research on cis-regulatory variation has uncovered all the forms of selection common to coding regions, in addition to novel forms of selection. An emerging pattern seems to be the ubiquity of local adaptation and balancing selection, possibly due to the greater freedom organisms have to fine-tune gene expression without changing protein function. It is clear from multiple single locus and whole genome studies of non-coding regulatory DNA that the effects of natural selection reach far beyond the start and stop codons.

Animals↗

Nonneutral evolution at the mitochondrial NADH dehydrogenase subunit 3 gene in mice.

The neutral theory of molecular evolution asserts that while many mutations are deleterious and rapidly eliminated from populations, those that we observe as polymorphisms within populations are functionally equivalent to each other and thus neutral with respect to fitness. Mitochondrial DNA (mtDNA) is widely used as a genetic marker in evolutionary studies and is generally assumed to evolve according to a strictly neutral model of molecular evolution. One prediction of the neutral theory is that the ratio of replacement (nonsynonymous) to silent (synonymous) nucleotide substitutions will be the same within and between species. We tested this prediction by measuring DNA sequence variation at the mitochondrially encoded NADH dehydrogenase subunit 3 (ND3) gene among 56 individual house mice, Mus domesticus. We also compared ND3 sequence from M. domesticus to ND3 sequence from Mus musculus and Mus spretus. A significantly greater number of replacement polymorphisms were observed within M. domesticus than expected based on comparisons to either M. musculus or M. spretus. This result challenges the conventional view that mtDNA evolves according to a strictly neutral model. However, this result is consistent with a nearly neutral model of molecular evolution and suggests that most amino acid polymorphisms at this gene may be slightly deleterious.

Amino Acid Sequence↗

Mitochondrial DNA diversity in the Llanos de Moxos: Moxo, Movima and Yuracare Amerindian populations from Bolivia lowlands.

BACKGROUND: Movima, Yuracare, Ignaciano and Trinitario are Amerindian populations living in the Bolivian lowlands of the Amazonian basin. The cultural and genetic affinity of the peoples living in this area is poorly known, despite many archaeological studies demonstrating its importance in pre-Columbian times. Densely populated Amerindian groups occupied the region, both in the Llanos and along the river streams of the Amazonian basin, practising intense agricultural activities and exchange of goods. The historical and linguistic records indicate that the land was occupied through successive migrations that gave rise to complex socio-economic communities. Genetic information suggests that the colonization of the American continent was fairly simple from a emigrational point of view, but other evolutionary processes, such as genetic drift or natural selection, could have also shaped the genetic background of present day populations in the Beni region. AIM: The objective of this study is to characterize the genetic diversity of these populations by analysing the sequence variability of the HVR-I control region in the mitochondrial DNA (mtDNA). The Amerindian origin of these populations suggests that close genetic similarities should be evident between the Beni samples studied here and other Amerindian groups. However, complex processes of population interactions and/or isolation in the Beni region might result in non-expected genetic affinities. SUBJECTS AND METHODS: DNA was extracted from pulled-out hairs obtained in situ from non-closely related individuals living in the Beni Department in Bolivia. DNA was extracted using a standard Chelex 100 method and a 401 bp DNA fragment of the HVR-I region was amplified using specific primers (L-15978 and H-16412). DNA amplicons were purified by centrifugation using Microspin S-300 HR columns and both SNA strands were sequenced after asymmetric PCR using direct Dye-Terminator 2 sequencing kit (Perkin-Elmer). Two independent 401 and 328 bp DNA fragments were sequenced separately for each sample. The sequence analyses includes mismatch distributions and mean pairwise differences, median network analysis, and neighbour joining, maximum likelihood phylogenetic comparisons. Genetic diversity of DNA sequences was also measured in various ways for the sample studied and UPGMA trees were drawn, including a large number of South Amerindian sequences. RESULTS: The genetic diversity of 401 nucleotide long mtDNA sequences in the hypervariable control region, from positions 16,000-16,400, was characterized in a sample of 54 Amerindians living in the Llanos de Moxos. A total of 34 distinct lineages were observed, defined by 41 variable nucleotide positions, and 70.6% of all lineages were single sequences. All four major Amerindian haplogroups were detected (A 18.5%, n=10; B 24.1%, n=13, C 50.0% n=27; and D 5.6%, n=3). The median network analysis observed suggests that processes of population expansion took place in the Beni region. However, no clear haplotype differentiation by population could be detected. High levels of molecular variability and a bimodal pair-wise mismatch distribution were seen within the sample. The analyses of molecular variance (AMOVA) showed that most of the variance observed was due to intrapopulation variability, and that the highest among-groups variance was obtained when a linguistic classification criteria was used. The phylogenetic comparison revealed unique lineages in the Beni areas, not reported for other Amerindian populations. CONCLUSIONS: The genetic diversity observed in the Beni area is higher than that observed in other American populations living in much larger areas and with a long, known evolutionary history, despite the reduced area of Moxos. This could result from processes of reproductive isolation between groups, followed by population expansions and migration, where genetic drift might have be a major evolutionary force in population differentiation.

Bolivia↗

Population genetic evidence for rapid changes in intraspecific diversity and allelic cycling of a specialist defense gene in Zea.

Two patterns of plant defense gene evolution are emerging from molecular population genetic surveys. One is that specialist defenses experience stronger selection than generalist defenses. The second is that specialist defenses are more likely to be subject to balancing selection, i.e., evolve in a manner consistent with balanced-polymorphism or trench-warfare models of host-parasite coevolution. Because most of the data of specialist defenses come from Arabidopsis thaliana, we examined the genetic diversity and evolutionary history of three defense genes in two outcrossing species, the autotetraploid Zea perennis and its most closely related extant relative the diploid Z. diploperennis. Intraspecific diversity at two generalist defenses, the protease inhibitors wip1 and mpi, were consistent with a neutral model. Like previously studied genes in these taxa, wip1 and mpi harbored similar levels of diversity in Z. diploperennis and Z. perennis. In contrast, the specialist defense hm2 showed strong although distinctly different departures from a neutral model in the two species. Z. diploperennis appears to have experienced a strong and recent selective sweep. Using a rejection-sampling coalescent method, we estimate the strength of selection on Z. diploperennis hm2 to be approximately 3.0%, which is approximately equal to the strength of selection on tb1 during maize domestication. Z. perennis hm2 harbors three highly diverged alleles, two of which are found at high frequency. The distinctly different patterns of diversity may be due to differences in the phase of host-parasite coevolutionary cycles, although higher hm2 diversity in Z. perennis may also reflect reduced efficacy of selection in the autotetraploid relative to its diploid relative.

Alleles↗

Genetic structure and origin of t haplotypes of mice, analyzed with H-2 cDNA probes.

We investigated the genetic organization and evolutionary origin of t chromosomes of mice by examining the restriction fragment patterns of DNA from t haplotypes and normal chromosomes with cDNA probes to H-2 class I genes. On genomic DNA blots, the restriction fragments containing H-2-related sequences were highly variable among different inbred strains of mice, whereas they were very similar among different t haplotypes even when the t haplotypes carried serologically different H-2 haplotypes. These observations suggest that all t haplotypes have a common origin and are not products of independent mutational events. We also mapped the position of several restriction fragments characteristic of t DNA by using a battery of recombinant t haplotypes, defined with respect to their t-lethal factors and H-2 haplotypes. We thus show that restriction fragments containing H-2-related sequences map to the left of the H-2 class I genes in t chromosomes, a region in which the tw32 b-lethal factor also maps. The cloning of these fragments can be expected to provide an entry for the structural analysis of t DNA.

Animals↗

Clinical Impact and Genetic Analysis of Enteric Viruses Associated With Acute Gastroenteritis in Greater Accra, Ghana: A Comprehensive Study of Five Viruses.

Enteric viruses are significantly associated with acute gastroenteritis globally. Despite a decrease in severe rotavirus associated diarrhoea, Ghana still records high diarrhoea burden. Meanwhile aetiological investigations in hospital settings do not routinely include viral testing. Rotavirus vaccination is thought to alter enteric viral populations and impact evolution. To better understand virus-specific effects in acute gastroenteritis in both children and adults, we tested fecal samples from 228 patients at two hospitals in Accra from January to December 2019, using multiplex and singleplex PCR assays. The clinical impact of detected viruses was assessed using a modified Vesikari score system. Partial viral genome sequences were obtained by Sanger Sequencing and their genetic diversity and evolutionary history, traced by phylogenetic analyses. At least one enteric virus was found in 86 (37.7%) patient samples, with 36.9% of the population under five infected. Single infections of rotavirus, norovirus, adenovirus, sapovirus and astrovirus were 33, 14, 8, 6, and 1, respectively, while coinfections were 24. Rotavirus accounted for 33.3% of 24 clinically severe cases (modified Vesikari score > 7). Three out of 10 rotavirus cases with evidence of vaccination experienced severe gastroenteritis. Diverse genotypes, including RVA G2P[4], G1P[8], G12P[8] and G12P[6]; AdV F40 and F41; NoV GII.4 Sydney 2012, GII.6 and GI.3, several of which clustered with contemporary strains from the Americas, Europe and Asia, were detected. This study also provides the first report of SaV GI.1, GI.7 and GII.8 detection in humans in Ghana. RVA G2P[4] and AdV F were associated with higher proportions of hospitalizations. While RVA continues to have a profound clinical impact on gastroenteritis, AdV and SaV produce an equally severe disease. In contrast, NoV and AstV showed a generally mild to moderate impact on clinical disease severity.

Humans↗

Genetic variation of Cordyceps sinensis, a fruit-body-producing entomopathogenic species from different geographical regions in China.

Cordyceps sinensis is one of the most valuable medicinal fungi in the Orient. It is naturally distributed in the eastern extension area of the Qinghai-Tibet plateau, at an altitude over 4000 m high. In order to investigate genetic variation and evolutionary relationships of C. sinensis from different geographical regions, 17 isolates of C. sinensis were collected from different provinces and the complete sequences of rDNA ITS were determined. On the basis of 5.8S rDNA and ITS region analysis, it was clearly shown that the ITS sequences within C. sinensis are highly homologous regardless of geographical origin. The distance values between the sequences in this study were lower than 0.03. This implied that C. sinensis from different geographic regions are the same species; they are not different species or a species complex. The results also showed that distance values between C. sinensis and Hirsutella sinensis are of the same order as those within C. sinensis from different geographic regions. This confirmed our previous results that C. sinensis should only have H. sinensis as its asexual stage whatever the geographic region from which the samples were collected. An rDNA ITS clone library was established to obtain further evidence for the interpretation of the fungal community structure from C. sinensis and to confirm the accuracy of the taxonomic identities produced by directly sequencing the rDNA ITS region. The discrimination between intraspecies of C. sinensis might provide additional data for the authentication of medicinal material at the species or intraspecies level.

Animals↗

Determination of relatedness between individuals using DNA fingerprinting.

Relatedness between individuals is an important element of genetic-epidemiological and evolutionary investigations in the context of anthropological research. In general, data on relationships between individuals are gathered from personal interviews or from examination of vital records. When blood samples are collected, such information can be validated from genotypic similarities of individuals. Although genotype data may offer opportunities to exclude certain types of relationships, inclusionary statements are necessarily only probabilistic in nature. The limitations of such probabilistic statements depend on the number of segregating alleles and the extent of polymorphisms at the loci employed. With the advent of DNA technology, several hypervariable single-locus probes (SLPs) and multilocus probes (MLPs) are now available for many organisms. These can be used to circumvent limitations of unequivocal assignment of relationships from genotype data. In this article we describe analytical principles for such investigations. In particular, we propose summary measures of DNA fingerprinting data (e.g., number of different alleles and number of shared alleles) that can be used to describe kinship relationships between individuals. We derive the expected distributions of number of alleles in individuals and of number of shared alleles between individuals of known relationships in a population. These distributions can be used in hypothesis testing to determine relatedness between individuals. We also derive the number of SLPs, each detecting a hypervariable polymorphism, needed to determine a specified relationship for given ranges of errors of prediction. Illustrations of the theory with data on several short tandem repeat loci and variable number of tandem repeat (VNTR) loci indicate that with 6 to 12 SLPs the parent-offspring pairs can be reliably distinguished from random pairs of individuals. This theory also serves the purpose of detecting inbreeding levels in a natural population.

Alleles↗

The conversion of variance and the evolutionary potential of restricted recombination.

Genetic recombination is usually considered to facilitate adaptive evolution. However, recombination prevents the reliable cotransmission of interacting gene combinations and can disrupt complexes of coadapted genes. If interactions between genes have important fitness effects, restricted recombination may lead to evolutionary responses that are different from those predicted from a purely additive model and could even aid adaptation. Theory and data have demonstrated that phenomena that limit the effectiveness of recombination via increasing homozygosity, such as inbreeding and population subdivision and bottlenecks, can temporarily increase the additive genetic variance available to these populations. This effect has been attributed to the conversion of nonadditive to additive genetic variance. Analogously, phenomena such as chromosomal inversions and apomictic parthenogenesis that physically restrict recombination in part or all of the genome may also result in a release of additive variance. Here, we review and synthesize literature concerning the evolutionary potential of populations with effectively or physically restricted recombination. Our goal is to emphasize the common theme of increased short-term access to additive genetic variance in all of these situations and to motivate research directed towards a more complete characterization of the relevance of the conversion of variance to the evolutionary process.

Animals↗

Genotypic analysis at multiple loci across Kaposi's sarcoma herpesvirus (KSHV) DNA molecules: clustering patterns, novel variants and chimerism.

BACKGROUND: The genomes of human Kaposi's sarcoma-associated herpesvirus (KSHV) display several levels of DNA sequence heterogeneity and subgrouping that show distinctive clustering patterns in related human populations. The four major subtype patterns for the hypervariable ORF-K1 protein correlate closely with the principal diasporas resulting from the migration of modern humans out of East Africa and suggest that KSHV is an ancient human virus that is transmitted primarily in a familial fashion with consequent very low recombination rates. However, chimeric genomes have also been detected, especially with regard to the presence of P versus M alleles of the ORF-K15 gene. OBJECTIVES: To understand further the genetic organization and evolutionary history of KSHV, especially with regard to possible new subtypes, recombinant genomes, constant region loci and clustering in particular ethnic groups or among classic versus epidemic cases in the same geographic area. STUDY DESIGN: Direct PCR DNA sequencing was carried out on the ORF-K1 and ORF-K15 genes at the extreme left and right hand sides, as well as on six other internal loci of diagnostic samples collected from 70 new KSHV-positive patients in Israel, South Korea, Sicily, Scandinavia, Brazil, Uganda, South Africa and the US. RESULTS AND CONCLUSIONS: Our overall results from more than 135 KSHV genomes from many different human population groups now provides evidence for seven distinct subtypes of KSHV genomes (referred to as A/P, B/P, C/P, D/P, M, N and Q). However, the two most closely related subtypes (A/P and C/P) are only differentiated at the LHS side of the genome, and the three most distantly related forms (M, N and Q) appear to exist only as small chimeric segments that are remnants from the RHS of more ancient forms of the virus. By analyzing multiple conserved loci across the B subtype genomes that predominate in sub-Saharan Africa, we can also now recognize three to four distinct B genome subgroups with varying patterns of inter and intratypic mosaicism. Analysis of classic KS genomes from Israel has revealed that the ORF-K1 clade referred to as A1' predominates in Ashkenazi Jewish immigrants from Russia, whereas C2 and C6 variants predominate in North African Sephardi Jews. A variety of chimeric genomes containing C2 or C3 ORF-K1 genes are disseminated among classic KS cases throughout Europe and Asia including Israel, Sicily, Scandinavia, South Korea, and Taiwan. Comparison of the genomes from classic versus AIDS-associated KSHV in the US indicates that it was derived originally by reactivation and spread of a subset of the endogenous viruses carried by descendants of immigrants from endemic areas of Northern and Eastern Europe, the Mediterranean and sub-Saharan Africa.

Acquired Immunodeficiency Syndrome↗

Evolutionary dental changes.

In the evolution of primates there has been a tendency towards reduction in jaw length and prognathism, mandibular canine size and first molar cusp number, and third molar presence. These oral structures were contrasted, and compared with cranial size, body height and weight, and finger length in 118 males and 102 females of the Burlington Growth Centre. Body weight was significantly related to canine width and to jaw length and prognathism. These relationships were stronger in the males than in the females. The evolutionary reduction in these dental dimensions may result from an evolutionary reduction in genetically determined body size. In the males the number of molar cusps was related to finger length and cranial height. Agenesis of third molars was related to the length of the maxilla in both sexes. In the females, canine width was related to the number of cusps of the first molars, agenesis of third molars, and length of a finger. Simultaneous reductions in dental structures were more frequent in the females.

Adolescent↗

Deciduous dental morphology and the biological affinities of a late Chalcolithic skeletal series from western India.

Morphological variations of the dental crown and roots provide valuable data for determining the genetic affinities and evolutionary adaptedness of prehistoric human skeletal populations. This paper documents morphological variations of a sample of deciduous teeth from the late Chalcolithic farming village of Inamgaon (1600-700 B.C.) in western India. Hanihara's (1963) grading system of deciduous dental traits was employed in assessing the degree of expression of shovel-shape of incisors, cusp number of upper and lower first molars, hypocone variation, Carabelli's trait, cusp number of lower second molars and the protostylid. Turner's (1970) classification was used to determine presence and size of accessory cusps: entoconulid (C-6) and metaconulid (C-7). Comparative evaluation of the Inamgaon deciduous dental data is hampered by the absence of data for dental features of living and prehistoric South Asian populations. Many of the traits observed in the Inamgaon series exhibit a frequency of occurrence intermediate between figures characteristic of the "Mongoloid" dental complex and the "Caucasoid" dental complex.

Animals↗

Mhc-DRB genes and the origin of New World monkeys.

The major histocompatibility complex (Mhc) is a family of loci characterized by its relatively rapid evolutionary turnover, large genetic distances between genes, and long persistence of allelic lineages effected by balancing selection. These features render the Mhc highly suitable for answering questions concerning speciation and adaptive radiation. The aim of the present study was to use Mhc-DRB genes to make inferences about the founding population of the Platyrrhini. Three segments, each approximately 300 base pairs in length, of the platyrrhine DRB genes were amplified by the polymerase chain reaction and sequenced. The segments were derived from intron 2, exon 3, and exon 6 of DRB genes from different species of New World monkeys. The results of the study have revealed that on a phylogenetic tree, all of the tested platyrrhine genes appear to form a single cluster, while all catarrhine DRB genes form a distinct cluster, although the bootstrap values fail to provide statistically significant support for the separation of these two clades. This observation suggests that the multiple platyrrhine genes originated from a single ancestral gene after the divergence of the Platyrrhini and Catarrhini and thus contradicts the results of an earlier study in which some exon 2 DRB sequences appeared to predate the split of the two primate groups. The inconsistency in the DRB gene phylogeny can be explained by postulating convergent evolution for the peptide-binding region of the DRB exon 2 sequences. The phylogeny of the platyrrhine DRB genes (except for exon 2) is relatively "shallow"; the distances between genes are relatively short (in comparison to the catarrhine DRB genes), and there is a tendency for sequences of individual species to cluster together. The phylogeny of the platyrrhine DRB genes is consistent with the postulate that a small population founded the group and that there is an ongoing adaptive radiation from small, relatively isolated founding populations.

Amino Acid Sequence↗

Reevaluation of phylogeny in the Drosophila obscura species group based on combined analysis of nucleotide sequences.

The Drosophila obscura species group has served as an important model system in many evolutionary and population genetic studies. Despite the amount of study this group has received, some phylogenetic relationships remain unclear. While individual analysis of different nuclear, mitochondrial, allozyme, restriction fragment, and morphological data partitions are able to discern relationships among closely related species, they are unable to resolve relationships among the five obscura species subgroups. A combined analysis of several nucleotide data sets is able to provide resolution and support for some nodes not seen or well supported in analyses of individual loci. A phylogeny of the obscura species group based on combined analysis of nucleotide sequences from six mitochondrial and five nuclear loci is presented here. The results of several different combined analyses indicate that the Old World obscura and subobscura subgroups form a monophyletic clade, although they are unable to resolve the relationships among the major lineages within the obscura species group.

Animals↗

A generalization of Pontryagin's maximum principle for dynamic evolutionary games among relatives.

We present two theorems that generalize Pontryagin's maximum principle to the setting of dynamic evolutionary games between genetically related individuals. The two theorems correspond to two types of interactions among individuals: patch-structured populations in which individuals locally "play the field" and pairwise interactions. These generalizations can be used in the same way that Pontryagin's maximum principle is used and they are valid for diploid organisms under a single locus, diallelic genetic model. These generalizations involve an interesting, dynamic version of Hamilton's Rule from inclusive fitness theory. We illustrate how these theoretical results can be applied by modeling the evolution of lifetime resource allocation to growth and reproduction in an annual plant when there is competition for resources among related individuals.

Biological Evolution↗