Correction to: Adaptive dynamics of saturated polymorphisms

Journal of Mathematical Biology - In the original publication, Proposition 4 is mistaken.     

Adaptive superparasitism and host-parasitoid dynamics

We consider a host-solitary parasitoid system with three categories of individuals: parasitoids, healthy hosts and parasitized hosts. Parasitoids are assumed to discriminate perfectly between the two kinds of hosts and they can reject those which are already parasitized. If parasitoids systematically accept or reject superparasitism or behave randomly, the system is always unstable. Using an optimal foraging model, we determine the behavior of parasitoids which leads to maximization of the instantaneous reproductive rate. When following this adaptive decision rule, parasitoids accept or refuse superparasitism according to the densities of both healthy and parasitized hosts. We study the dynamics of the system when parasitoids follow the optimal rule and show that under certain conditions it possesses a locally stable equilibrium point. In addition, our model predicts that at equilibrium parasitoids show partial preferences for superparasitism.     

Adaptive behavior with protozoa-inspired dynamics

A protozoa-inspired system for controlling autonomous robots is explained. The proposed system uses the nonlinear dynamics of the molecule concentrations in the cytoplasm of a protozoan. The model includes many parameters which are optimized using the genetic algorithm. A mobile robot obstacle avoidance example is shown with simulation results. The proposed protozoa-inspired system opens interesting possibilities to create new species by combining individual models by symbiotic or colony relationships. Received: 13 March 1996 / Accepted in revised form: 17 July 1998     

Adaptive dynamics of cuticular hydrocarbons in Drosophila

Cuticular hydrocarbons (CHCs) are hydrophobic compounds deposited on the arthropod cuticle that are of functional significance with respect to stress tolerance, social interactions and mating dynamics. We characterized CHC profiles in natural populations of Drosophila melanogaster at five levels: across a latitudinal transect in the eastern United States, as a function of developmental temperature during culture, across seasonal time in replicate years, and as a function of rapid evolution in experimental mesocosms in the field. Furthermore, we also characterized spatial and temporal changes in allele frequencies for SNPs in genes that are associated with the production and chemical profile of CHCs. Our data demonstrate a striking degree of parallelism for clinal and seasonal variation in CHCs in this taxon; CHC profiles also demonstrate significant plasticity in response to rearing temperature, and the observed patterns of plasticity parallel the spatiotemporal patterns observed in nature. We find that these congruent shifts in CHC profiles across time and space are also mirrored by predictable shifts in allele frequencies at SNPs associated with CHC chain length. Finally, we observed rapid and predictable evolution of CHC profiles in experimental mesocosms in the field. Together, these data strongly suggest that CHC profiles respond rapidly and adaptively to environmental parameters that covary with latitude and season, and that this response reflects the process of local adaptation in natural populations of D. melanogaster.     

Adaptive dynamics for physiologically structured population models

We develop a systematic toolbox for analyzing the adaptive dynamics of multidimensional traits in physiologically structured population models with point equilibria (sensu Dieckmann et al. in Theor. Popul. Biol. 63:309–338, 2003). Firstly, we show how the canonical equation of adaptive dynamics (Dieckmann and Law in J. Math. Biol. 34:579–612, 1996), an approximation for the rate of evolutionary change in characters under directional selection, can be extended so as to apply to general physiologically structured population models with multiple birth states. Secondly, we show that the invasion fitness function (up to and including second order terms, in the distances of the trait vectors to the singularity) for a community of N coexisting types near an evolutionarily singular point has a rational form, which is model-independent in the following sense: the form depends on the strategies of the residents and the invader, and on the second order partial derivatives of the one-resident fitness function at the singular point. This normal form holds for Lotka–Volterra models as well as for physiologically structured population models with multiple birth states, in discrete as well as continuous time and can thus be considered universal for the evolutionary dynamics in the neighbourhood of singular points. Only in the case of one-dimensional trait spaces or when N = 1 can the normal form be reduced to a Taylor polynomial. Lastly we show, in the form of a stylized recipe, how these results can be combined into a systematic approach for the analysis of the (large) class of evolutionary models that satisfy the above restrictions.      

Adaptive dynamics: Modelling Darwin's divergence principle

A model illustrating Darwin's divergence principle is presented. It shows how competition for resources can explain evolutionary branching. It is based on an assumption of degenerate competition. Mathematically, it is a partial differential equation with an integral term, and it describes a new mechanism of self-organization.     

Investigation of phase transitions of saturated phosphocholine lipid bilayers via molecular dynamics simulations

Lipid bilayers play an important role in biological systems as they protect cells against unwanted chemicals and provide a barrier for material inside a cell from leaking out. In this paper, nearly 30 μs of molecular dynamics (MD) simulations were performed to investigate phase transitions of 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) and 1,2-dipalmitoyl-sn-glycero-phosphocholine (DPPC) lipid bilayers from the liquid crystalline (L_α) to the ripple (P_β) and to the gel phase (L_β). Our MD simulations accurately predict the main transition temperature for the single-component bilayers. A key focus of this work is to quantify the structure of the P_β phase for DMPC and compare with measures from x-ray experiments. The P_β major arm has similar structure to that of the L_β, while the thinner minor arm has interdigitated chains and the transition region between these two regions has large chain splay and disorder. At lower temperatures, our MD simulations predict the formation of the L_β phase with tilted fatty acid chains. The P_β and L_β phases are studied for mixtures of DMPC and DPPC and compare favorably with experiment. Overall, our MD simulations provide evidence for the relevancy of the CHARMM36 lipid force field for structures and add to our understanding of the less-defined P_β phase.     

Adaptive host preference and the dynamics of host-parasitoid interactions

Models of two independent host populations and a common parasitoid are investigated. The hosts have density-dependent population growth and only interact indirectly by their effects on parasitoid behavior and population dynamics. The parasitoid is assumed to experience a trade-off in its ability to exploit the two hosts. Three alternative types of parasitoid are investigated: (i) fixed generalists whose consumption rates are those that maximize fitness; (ii) "ideal free" parasitoids, which modify their behavior to maximize their rate of finding unparasitized hosts within a generation; and (iii) "evolving" parasitoids, whose capture rates change between generations based on quantitative genetic determination of the relative attack rates on the two hosts. The primary questions addressed are: (1) Do the different types of adaptive processes stabilize or destabilize the population dynamics? (2) Do the adaptive processes tend to equalize or to magnify differences in host densities? The models show that adaptive behavior and evolution frequently destabilize population dynamics and frequently increase the average difference between host densities.     

Effects of single nucleotide polymorphisms on human N-acetyltransferase 2 structure and dynamics by molecular dynamics simulation

Background

Arylamine N-acetyltransferase 2 (NAT2) is an important catalytic enzyme that metabolizes the carcinogenic arylamines, hydrazine drugs and chemicals. This enzyme is highly polymorphic in different human populations. Several polymorphisms of NAT2, including the single amino acid substitutions R64Q, I114T, D122N, L137F, Q145P, R197Q, and G286E, are classified as slow acetylators, whereas the wild-type NAT2 is classified as a fast acetylator. The slow acetylators are often associated with drug toxicity and efficacy as well as cancer susceptibility. The biological functions of these 7 mutations have previously been characterized, but the structural basis behind the reduced catalytic activity and reduced protein level is not clear.

Methodology/Principal Findings

We performed multiple molecular dynamics simulations of these mutants as well as NAT2 to investigate the structural and dynamical effects throughout the protein structure, specifically the catalytic triad, cofactor binding site, and the substrate binding pocket. None of these mutations induced unfolding; instead, their effects were confined to the inter-domain, domain 3 and 17-residue insert region, where the flexibility was significantly reduced relative to the wild-type. Structural effects of these mutations propagate through space and cause a change in catalytic triad conformation, cofactor binding site, substrate binding pocket size/shape and electrostatic potential.

Conclusions/Significance

Our results showed that the dynamical properties of all the mutant structures, especially in inter-domain, domain 3 and 17-residue insert region were affected in the same manner. Similarly, the electrostatic potential of all the mutants were altered and also the functionally important regions such as catalytic triad, cofactor binding site, and substrate binding pocket adopted different orientation and/or conformation relative to the wild-type that may affect the functions of the mutants. Overall, our study may provide the structural basis for reduced catalytic activity and protein level, as was experimentally observed for these polymorphisms.     

A model for the evolutionary dynamics of cross-feeding polymorphisms in microorganisms

 Understanding mechanisms of evolutionary diversification is central to evolutionary biology. Microbes constitute promising model systems for observing processes of diversification directly in the laboratory. One of the main existing paradigms for microbial diversification is the evolution of cross-feeding polymorphisms, in which a strain specializing on a primary resource coexists with a cross-feeding strain that specializes on a waste product resulting from consumption of the primary resource. Here I propose a theoretical model for the evolutionary dynamics through which cross-feeding polymorphisms can gradually emerge from a single ancestral strain. The model is based on the framework of adaptive dynamics, which has proved to be very useful for studying adaptive processes of divergence under sympatric conditions. In particular, the phenomenon of evolutionary branching serves as a general paradigm for diversification. I show that evolutionary branching naturally occurs in evolutionary models of cross-feeding if (1) there is a trade-off between uptake efficiencies on the primary and secondary resources, and (2) this trade-off has positive curvature. The model also suggests that the evolution of cross-feeding should be more likely in chemostat cultures than in serial batch cultures, which conforms with empirical observations. Overall, the model provides a theoretical metaphor for the evolution of cross-feeding polymorphisms. Received: February 19, 2002 / Accepted: May 8, 2002     

Adaptive plasticity in ontogenetic niche shifts stabilizes consumer-resource dynamics

Ontogenetic niche shifts, changes in the diet or habitats of organisms during their ontogeny, are widespread among various animal taxa. Ontogenetic niche shifts introduce stage structure in a population with different stages interacting with different communities and can substantially affect their dynamics. In this article, I use mathematical models to test the hypothesis that adaptive plasticity in the timing of ontogenetic niche shifts has a stabilizing effect on consumer-resource dynamics. Adaptive plasticity allows consumers in one ontogenetic niche to perform an early shift to the next ontogenetic niche if the resource density of the first niche is low. The early shift will reduce predation by the consumer on the scarce resource. On the other hand, adaptive plasticity allows consumers to delay their shift to the next niche if the resource density of the first niche is high. The delayed shift will increase the predation on the abundant resource. As a result, the scarce resource will tend to increase, and the abundant resource will tend to decrease. This causes density-dependent negative feedback in the resource dynamics, which stabilizes the consumer-resource dynamics. To test this hypothesis, I compare three consumer-resource models differing in terms of mechanisms controlling the timing of the ontogenetic niche shift: the fixed-age model assumes that the age at which the ontogenetic niche shift occurs is fixed; the fixed-size model assumes that the size at the shift is fixed; and the adaptive plasticity model assumes that the timing of the shift is such that the individual fitness of the consumer is maximized. I show that only the adaptive plasticity model has a locally stable equilibrium and that the stabilizing effect is due to the density-dependent negative feedback in the resource dynamics. I discuss the ontogenetic niche shifts of lake fish in light of the obtained result.     

Adaptive dispersal strategies and the dynamics of a range expansion

In species undergoing range expansion, newly established populations are often more dispersive than older populations. Because dispersal phenotypes are complex and often costly, it is unclear how highly dispersive phenotypes are maintained in a species to enable their rapid expression during periods of range expansion. Here I test the idea that metapopulation dynamics of local extinction and recolonization maintain distinct dispersal strategies outside the context of range expansion. Western bluebirds display distinct dispersal phenotypes where aggressive males are more dispersive than nonaggressive males, resulting in highly aggressive populations at the edge of their expanding range. I experimentally created new habitat interior to the range edge to show that, as on the range front, it was colonized solely by aggressive males. Moreover, fitness consequences of aggression depended on population age: aggressive males had high fitness when colonizing new populations, while nonaggressive males performed best in an older population. These results suggest that distinct dispersal strategies were maintained before range expansion as an adaptation for the continual recolonization of new habitat. These results emphasize similarities between range expansion and metapopulation dynamics and suggest that preexisting adaptive dispersal strategies may explain rapid changes in dispersal phenotypes during range expansion.     

Adaptive evolution of cooperation through Darwinian dynamics in Public Goods games

The linear or threshold Public Goods game (PGG) is extensively accepted as a paradigmatic model to approach the evolution of cooperation in social dilemmas. Here we explore the significant effect of nonlinearity of the structures of public goods on the evolution of cooperation within the well-mixed population by adopting Darwinian dynamics, which simultaneously consider the evolution of populations and strategies on a continuous adaptive landscape, and extend the concept of evolutionarily stable strategy (ESS) as a coalition of strategies that is both convergent-stable and resistant to invasion. Results show (i) that in the linear PGG contributing nothing is an ESS, which contradicts experimental data, (ii) that in the threshold PGG contributing the threshold value is a fragile ESS, which cannot resist the invasion of contributing nothing, and (iii) that there exists a robust ESS of contributing more than half in the sigmoid PGG if the return rate is relatively high. This work reveals the significant effect of the nonlinearity of the structures of public goods on the evolution of cooperation, and suggests that, compared with the linear or threshold PGG, the sigmoid PGG might be a more proper model for the evolution of cooperation within the well-mixed population.     

Adaptive feeding across environmental gradients and its effect on population dynamics

This paper analyzes a consumer's adaptive feeding response to environmental gradients. We consider a consumer-resource system where resources are distributed among many discrete resource patches. Each consumer exhibits a feeding morphology allowing it to remove resources from a patch down to some threshold density (or level) before having to seek resources elsewhere. Assuming consumers trade off resource extraction with patch access and predation, we show that for a given environment there often exists a single evolutionarily stable feeding threshold and it is an evolutionary attractor. We then investigate how the population dynamics of the resource and the consumer change as the environment changes. Two cases are considered: (i) all consumers exhibit a fixed feeding threshold that is adaptive for an intermediate environment; and (ii) the consumer population adapts and adopts the evolutionarily stable feeding threshold associated with the current environment. In less harsh environments (i.e., environments where consumers experience a lower risk of predation, or environments where resource patches are more abundant) the adaptive consumer population is predicted to evolve so that resources within a patch are depleted to lower densities. We show that the change in consumer density due to environmental change can be rather different depending on whether or not the population can adapt. In some situations we observe that when the consumer's environment becomes harsher, the consumer population may increase in density before a rapid crash to extinction. This result has implications for monitoring and managing a population.     

Identification of mitochondrial DNA polymorphisms that alter mitochondrial matrix pH and intracellular calcium dynamics

Mitochondrial DNA (mtDNA) is highly polymorphic, and its variations in humans may contribute to individual differences in function as well as susceptibility to various diseases such as Parkinson disease, Alzheimer disease, bipolar disorder, and cancer. However, it is unclear whether and how mtDNA polymorphisms affect intracellular function, such as calcium signaling or pH regulation. Here we searched for mtDNA polymorphisms that have intracellular functional significance using transmitochondrial hybrid cells (cybrids) carrying ratiometric Pericam (RP), a fluorescent calcium indicator, targeted to the mitochondria and nucleus. By analyzing the entire mtDNA sequence in 35 cybrid lines, we found that two closely linked nonsynonymous polymorphisms, 8701A and 10398A, increased the basal fluorescence ratio of mitochondria-targeted RP. Mitochondrial matrix pH was lower in the cybrids with 8701A/10398A than it was in those with 8701G/10398G, suggesting that the difference observed by RP was mainly caused by alterations in mitochondrial calcium levels. Cytosolic calcium response to histamine also tended to be higher in the cybrids with 8701A/10398A. It has previously been reported that 10398A is associated with an increased risk of Parkinson disease, Alzheimer disease, bipolar disorder, and cancer, whereas 10398G associates with longevity. Our findings suggest that these mtDNA polymorphisms may play a role in the pathophysiology of these complex diseases by affecting mitochondrial matrix pH and intracellular calcium dynamics.     

Adaptive dynamics in diploid, sexual populations and the evolution of reproductive isolation

Evolutionary branching is the process whereby an initially monomorphic population evolves to a point where it undergoes disruptive selection and splits up into two phenotypically diverging lineages. We studied evolutionary branching in three models that are ecologically identical but that have different genetic systems. The first model is clonal, the second is sexual diploid with additive genetics on a single locus and the third is like the second but with an additional locus for mate choice. Evolutionary branching occurred under exactly the same ecological circumstances in all three models. After branching the evolutionary dynamics may be qualitatively different. In particular, in the diploid, sexual models there can be multiple evolutionary outcomes whereas in the corresponding clonal model there is only one. We showed that evolutionary branching favours the evolution of (partial) assortative mating and that this in turn effectively restores the results from the clonal model by rendering the alternative outcomes unreachable except for the one that also occurs in the clonal model. The evolution of assortative mating during evolutionary branching can be interpreted as the initial phase of sympatric speciation with phenotypic divergence and partial reproductive isolation.