Population trajectories for single locus additive fecundity selection and related selection models

A selection model which comprises models of additive fecundities as well as models of viability, fecundity, or differential mating selection acting only in one sex, is investigated for an autosomal gene locus in a population reproducing in nonoverlapping generations. The recurrence equations and basic properties of the genotypic population trajectories and equilibrium points are formulated for the multiallelic case. For the diallelic case, the trajectory development is discussed in more detail, and it is proven that every population trajectory converges to a Hardy-Weinberg equilibrium point.     

Deep inference of seabird dives from GPS-only records: Performance and generalization properties

At-sea behaviour of seabirds have received significant attention in ecology over the last decades as it is a key process in the ecology and fate of these populations. It is also, through the position of top predator that these species often occupy, a relevant and integrative indicator of the dynamics of the marine ecosystems they rely on. Seabird trajectories are recorded through the deployment of GPS, and a variety of statistical approaches have been tested to infer probable behaviours from these location data. Recently, deep learning tools have shown promising results for the segmentation and classification of animal behaviour from trajectory data. Yet, these approaches have not been widely used and investigation is still needed to identify optimal network architecture and to demonstrate their generalization properties. From a database of about 300 foraging trajectories derived from GPS data deployed simultaneously with pressure sensors for the identification of dives, this work has benchmarked deep neural network architectures trained in a supervised manner for the prediction of dives from trajectory data. It first confirms that deep learning allows better dive prediction than usual methods such as Hidden Markov Models. It also demonstrates the generalization properties of the trained networks for inferring dives distribution for seabirds from other colonies and ecosystems. In particular, convolutional networks trained on Peruvian boobies from a specific colony show great ability to predict dives of boobies from other colonies and from distinct ecosystems. We further investigate accross-species generalization using a transfer learning strategy known as ‘fine-tuning’. Starting from a convolutional network pre-trained on Guanay cormorant data reduced by two the size of the dataset needed to accurately predict dives in a tropical booby from Brazil. We believe that the networks trained in this study will provide relevant starting point for future fine-tuning works for seabird trajectory segmentation.     

Virtual trajectory and stiffness ellipse during multijoint arm movement predicted by neural inverse models

We predict the virtual trajectories and stiffness ellipses during multijoint arm movements by computer simulations. A two-link manipulator with four single-joint muscles and two double-joint muscles is used as a model of the human arm. Physical parameters of the model are derived from several experimental data. Among them, special emphasis is put on low values of the dynamic hand stiffness recently measured during single joint and multijoint movements. The feedback-error-learning scheme to acquire the inverse dynamics model and the inverse statics model is utilized for this prediction. The virtual trajectories are much more complex than the actual trajectories. This indicates that planning the virtual trajectory is as difficult as solving the inverse dynamics problem for medium and fast movements, and simply falsifies the advocated computational advantage of the virtual trajectory control hypothesis. Thus, we conclude that learning inverse models is essential even in the virtual trajectory control framework. Finally, we propose a new computational model to learn the complicated shape of the virtual trajectories by integrating the virtual trajectory control and the feedback-error-learning scheme.     

Examination of the λ equilibrium point hypothesis when applied to single degree of freedom movements performed with different inertial loads

 One of the theories of human motor control is the λ Equilibrium Point Hypothesis. It is an attractive theory since it offers an easy control scheme where the planned trajectory shifts monotionically from an initial to a final equilibrium state. The feasibility of this model was tested by reconstructing the virtual trajectory and the stiffness profiles for movements performed with different inertial loads and examining them. Three types of movements were tested: passive movements, targeted movements, and repetitive movements. Each of the movements was performed with five different inertial loads. Plausible virtual trajectories and stiffness profiles were reconstructed based on the λ Equilibrium Point Hypothesis for the three different types of movements performed with different inertial loads. However, the simple control strategy supported by the model, where the planned trajectory shifts monotonically from an initial to a final equilibrium state, could not be supported for targeted movements performed with added inertial load. To test the feasibility of the model further we must examine the probability that the human motor control system would choose a trajectory more complicated than the actual trajectory to control. Received: 20 June 1995 / Accepted in revised form: 6 August 1996     

Optimal temperature control for a structured model of plant cell culture

This article calculates optimal open-loop temperature trajectories that maximize the average rate of product synthesis of a plant cell culture. It uses a previously published five-state mathematical model which describes the growth and product synthesis of a batch plant cell suspension culture of Catharanthus roseus under temperature control. The optimal open-loop temperatures maximize the final product concentration for predefined fermentation periods. A single switch in temperature is shown by computer simulation to be near optimal, with a 22% increase in final product yield over that obtained at the optimal constant temperature. Examination of the achieved final product yield as a function of fermentation period allows this period also to be chosen optimally. This time is reduced from 16 days in the constant temperature case to 12 days in the switched temperature case.     

Variational principles in evolution

For a one-locus selection model, Svirezhev introduced an integral variational principle by defining a Lagrangian which remained stationary on the trajectory followed by the population undergoing selection. It is shown here (i) that this principle can be extended to multiple loci in some simple cases and (ii) that the Lagrangian is defined by a straightforward generalization of the one-locus case, but (iii) that in two-locus or more general models there is no straightforward extension of this principle if linkage and epistasis are present. The population trajectories can be constructed as trajectories of steepest ascent in a Riemannian metric space. A general method is formulated to find the metric tensor and the surface in the metric space on which the trajectories, which characterize the variations in the gene structure of the population, lie. The local optimality principle holds good in such a space. In the special case when all possible linkage disequilibria are zero, the phase point of then-locus genetic system moves on the surface of the product space ofn higher dimensional unit spheres in a certain Riemannian metric space of gene frequencies so that the rate of change of mean fitness is maximum along the trajectory. In the two-locus case the corresponding surface is a hyper-torus.     

Modulation of the electron redistribution in mixed valence cytochrome C oxidase by protein conformational changes

The redistribution of two electrons in the four redox centers of cytochrome c oxidase following photodissociation of CO from the CO-bound mixed valence species has been examined by resonance Raman spectroscopy. To account for both the kinetic data, obtained from 5 micros to 2 ms, and the equilibrium results, a model is proposed in which the electron redistribution is modulated by a protein conformation transition from a nascent P(1) state to a relaxed P(2) state in a time window longer than 2 ms. In this model, all six possible two-electron reduced species are considered. The high population of species with a one-electron reduced binuclear center, in which the spectrum of heme a(3) is perturbed by the redox state of Cu(B), accounts for the significant residuals in the fitting of the kinetic data with four standard spectra derived from redox species with either zero or two electrons in the binuclear center. Under equilibrium conditions, the conformational change to the P(2) state destabilizes the redox states with only one electron in the binuclear center with respect to those with either zero or two electrons. As a result, the redox equilibrium is perturbed, and the electrons are redistributed. A simulation based on the new kinetics scheme, in which the electron redistribution is modulated by the protein conformation, gives reasonable agreement with both the equilibrium and the kinetic data, demonstrating the validity of this model.     

Grape powdery mildew as a food source for generalist predatory mites occurring in vineyards: effects on life-history traits

In several perennial cropping systems, generalist or omnivorous species represent important biocontrol agents. They can persist on plants by feeding on alternative foods when prey is scarce and potentially limit pest outbreaks. Among beneficials characterised by a wide food range, those belonging to the acarine family Phytoseiidae represent important biocontrol agents. Generalist predatory mites can develop and reproduce using various food sources as alternatives to their tetranychid prey. The presence of alternative food sources can also induce switching feeding behaviour of generalist predators from prey to alternative foods. We evaluated in the laboratory the role of the grape powdery mildew (GPM) for the survival, development and reproduction of Amblyseius andersoni and Typhlodromus pyri , two important beneficial phytoseiid mites, in European and North-American vineyards. We also compared life-history parameters obtained when feeding on GPM with those obtained feeding on tetranychids mite prey or cattail pollen. Results indicated that GPM is an adequate food source for generalist mite survival and development. Results suggest that GPM can sustain mite populations in the absence of higher quality food sources. Based on optimal foraging theory, comparison of life-history parameters on GPM and mite prey suggests that the disruption of phytophagous mite control by these predatory mites in the presence of GPM appears unlikely. Implications for biological control in vineyards are discussed.     

Maladaptive choice behaviour by pigeons: an animal analogue and possible mechanism for gambling (sub-optimal human decision-making behaviour)

Consistent with human gambling behaviour but contrary to optimal foraging theory, pigeons showed maladaptive choice behaviour in experiment 1 by choosing an alternative that provided on average two food pellets over an alternative that provided a certain three food pellets. On 20 per cent of the trials, choice of the two-pellet alternative resulted in a stimulus that always predicted ten food pellets; on the remaining 80 per cent of the trials, the two-pellet alternative resulted in a different stimulus that always predicted zero food pellets. Choice of the three-pellet alternative always resulted in three food pellets. This choice behaviour mimics human monetary gambling in which the infrequent occurrence of a stimulus signalling the winning event (10 pellets) is overemphasized and the more frequent occurrence of a stimulus signalling the losing event (zero pellets) is underemphasized, compared with the certain outcome associated with not gambling (the signal for three pellets). In experiment 2, choice of the two-pellet alternative resulted in ten pellets with a probability of 20 per cent following presentation of either stimulus. Choice of the three-pellet alternative continued to result in three food pellets. In this case, the pigeons reliably chose the alternative that provided a certain three pellets over the alternative that provided an average of two pellets. Thus, in experiment 1, the pigeons were responding to obtain the discriminative stimuli signalling reinforcement and the absence of reinforcement, rather than to obtain the variability in reinforcement.     

Automatic determination of the transition between successive control mechanisms in upright stance assessed by modelling of the centre of pressure.

A recently introduced concept models the trajectory of the centre of pressure as a fractional Brownian motion and reveals that two successive scaling regimes, acting hypothetically as open and closed loop mechanisms, are implicated in posture control. Objectivity is obviously required in the determination of the transition point, i.e. the point at which an open-loop control mechanism would switch to a closed-loop one, in order to provide reproducibility and automatism in the processing of data. In the method proposed herein, the transition point corresponds to the maximal distance separating a diffusion curve in a double logarithmic plot (mean square distances MSD calculated on each axis versus increasing time intervals Deltat) from a straight line characterising a pure stochastic behaviour. In closed eye conditions, the switch appears medio-laterally in a 0. 26-0.52 s range for Deltat, the corresponding MSD being in the range of 1.86-10.50 mm(2). In the forward-backward direction, the transition is in a 0.28-0.42 s range and the corresponding MSD is between 3.60 and 15.17 mm(2). Finally, these co-ordinates induce scaling exponents over 0.50 for the shortest Deltat, thus suggesting open-loop control, whereas those of longest Deltat, ranged between 0 and 0.20, give evidence of close-loop control. This data is compared to previous data based upon empirical methods.     

Prediction of titration properties of structures of a protein derived from molecular dynamics trajectories.

This paper explores the dependence of the molecular dynamics (MD) trajectory of a protein molecule on the titration state assigned to the molecule. Four 100-ps MD trajectories of bovine pancreatic trypsin inhibitor (BPTI) were generated, starting from two different structures, each of which was held in two different charge states. The two starting structures were the X-ray crystal structure and one of the solution structures determined by NMR, and the charge states differed only in the ionization state of N terminus. Although it is evident that the MD simulations were too short to sample fully the equilibrium distribution of structures in each case, standard Poisson-Boltzmann titration state analysis of the resulting configurations shows general agreement between the overall titration behavior of the protein and the charge state assumed during MD simulation: at pH 7, the total net charge of the protein resulting from the titration analysis is consistently lower for the protein with the N terminus assumed to be neutral than for the protein with the N terminus assumed to be charged. For most of the ionizable residues, the differences in the calculated pKaS among the four trajectories are statistically negligible and remain in good agreement with the data obtained by crystal structure titration and by experiment. The exceptions include the N terminus, which responds directly to the change of its imposed charge; the C terminus, which in the NMR structure interacts strongly with the former; and a few other residues (Arg 1, Glu 7, Tyr 35, and Arg 42) whose pKaS reflect the initial structure and the limited trajectory lengths. This study illustrates the importance of the careful assignment of protonation states at the start of MD simulations and points to the need for simulation methods that allow for the variation of the protonation state in the calculation of equilibrium properties.     

Analysis of kinematic invariances of multijoint reaching movement

 There is a no unique relationship between the trajectory of the hand, represented in cartesian or extrinsic space, and its trajectory in joint angle or intrinsic space in the general condition of joint redundancy. The goal of this work is to analyze the relation between planning the trajectory of a multijoint movement in these two coordinate systems. We show that the cartesian trajectory can be planned based on the task parameters (target coordinates, etc.) prior to and independently of angular trajectories. Angular time profiles are calculated from the cartesian trajectory to serve as a basis for muscle control commands. A unified differential equation that allows planning trajectories in cartesian and angular spaces simultaneously is proposed. Due to joint redundancy, each cartesian trajectory corresponds to a family of angular trajectories which can account for the substantial variability of the latter. A set of strategies for multijoint motor control following from this model is considered; one of them coincides with the frog wiping reflex model and resolves the kinematic inverse problem without inversion. The model trajectories exhibit certain properties observed in human multijoint reaching movements such as movement equifinality, straight end-point paths, bell-shaped tangential velocity profiles, speed-sensitive and speed-insensitive movement strategies, peculiarities of the response to double-step targets, and variations of angular trajectory without variations of the limb end-point trajectory in cartesian space. In humans, those properties are almost independent of limb configuration, target location, movement duration, and load. In the model, these properties are invariant to an affine transform of cartesian space. This implies that these properties are not a special goal of the motor control system but emerge from movement kinematics that reflect limb geometry, dynamics, and elementary principles of motor control used in planning. All the results are given analytically and, in order to compare the model with experimental results, by computer simulations. Received: 6 April 1994/Accepted in revised form: 25 April 1995     

Multilocus selection in subdivided populations I. Convergence properties for weak or strong migration

The dynamics and equilibrium structure of a deterministic population-genetic model of migration and selection acting on multiple multiallelic loci is studied. A large population of diploid individuals is distributed over finitely many demes connected by migration. Generations are discrete and nonoverlapping, migration is irreducible and aperiodic, all pairwise recombination rates are positive, and selection may vary across demes. It is proved that, in the absence of selection, all trajectories converge at a geometric rate to a manifold on which global linkage equilibrium holds and allele frequencies are identical across demes. Various limiting cases are derived in which one or more of the three evolutionary forces, selection, migration, and recombination, are weak relative to the others. Two are particularly interesting. If migration and recombination are strong relative to selection, the dynamics can be conceived as a perturbation of the so-called weak-selection limit, a simple dynamical system for suitably averaged allele frequencies. Under nondegeneracy assumptions on this weak-selection limit which are generic, every equilibrium of the full dynamics is a perturbation of an equilibrium of the weak-selection limit and has the same stability properties. The number of equilibria is the same in both systems, equilibria in the full (perturbed) system are in quasi-linkage equilibrium, and differences among allele frequencies across demes are small. If migration is weak relative to recombination and epistasis is also weak, then every equilibrium is a perturbation of an equilibrium of the corresponding system without migration, has the same stability properties, and is in quasi-linkage equilibrium. In both cases, every trajectory converges to an equilibrium, thus no cycling or complicated dynamics can occur.      

Oligomerization of a symmetric β‐trefoil protein in response to folding nucleus perturbation

Gene duplication and fusion events in protein evolution are postulated to be responsible for the common protein folds exhibiting internal rotational symmetry. Such evolutionary processes can also potentially yield regions of repetitive primary structure. Repetitive primary structure offers the potential for alternative definitions of critical regions, such as the folding nucleus (FN). In principle, more than one instance of the FN potentially enables an alternative folding pathway in the face of a subsequent deleterious mutation. We describe the targeted mutation of the carboxyl‐terminal region of the (internally located) FN of the de novo designed purely‐symmetric β‐trefoil protein Symfoil‐4P. This mutation involves wholesale replacement of a repeating trefoil‐fold motif with a “blade” motif from a β‐propeller protein, and postulated to trap that region of the Symfoil‐4P FN in a nonproductive folding intermediate. The resulting protein (termed “Bladefoil”) is shown to be cooperatively folding, but as a trimeric oligomer. The results illustrate how symmetric protein architectures have potentially diverse folding alternatives available to them, including oligomerization, when preferred pathways are perturbed.     

On the possibility of linear modelling the human arm neuromuscular apparatus

It has been widely claimed that linear models of the neuromuscular apparatus give very inaccurate approximations of human arm reaching movements. The present paper examines this claim by quantifying the contributions of the various non-linear effects of muscle force generation on the accuracy of linear approximation. We performed computer simulations of a model of a two-joint arm with six monarticular and biarticular muscles. The global actions of individual muscles resulted in a linear dependence of the joint torques on the joint angles and angular velocities, despite the great non-linearity of the muscle properties. The effect of time delay in force generation is much more important for model accuracy than all the non-linear effects, while ignoring this time delay in linear approximation results in large errors. Thus, the viscosity coefficients are rather underestimated and some of them can even be paradoxically estimated to be negative. Similarly, our computation showed that ignoring the time delay resulted in large errors in the estimation of the hand equilibrium trajectory. This could explain why experimentally estimated hand equilibrium trajectories may be complex, even during a simple reaching movement. The hand equilibrium trajectory estimated by a linear model becomes simple when the time delay is taken into account, and it is close to that actually used in the non-linear model. The results therefore provide a theoretical basis for estimating the hand equilibrium trajectory during arm reaching movements and hence for estimating the time course of the motor control signals associated with this trajectory, as set out in the equilibrium point hypothesis. Received: 17 February 1999 / Accepted in revised form: 22 October 1999     

Sliding Mode Control of Outbreaks of Emerging Infectious Diseases

This paper proposes and analyzes a mathematical model of an infectious disease system with a piecewise control function concerning threshold policy for disease management strategy. The proposed models extend the classic models by including a piecewise incidence rate to represent control or precautionary measures being triggered once the number of infected individuals exceeds a threshold level. The long-term behaviour of the proposed non-smooth system under this strategy consists of the so-called sliding motion-a very rapid switching between application and interruption of the control action. Model solutions ultimately approach either one of two endemic states for two structures or the sliding equilibrium on the switching surface, depending on the threshold level. Our findings suggest that proper combinations of threshold densities and control intensities based on threshold policy can either preclude outbreaks or lead the number of infecteds to a previously chosen level.     

Alternative life-history styles of some African cichlid fishes

Synopsis About 50% of African cichlid species have been described. Little is known about cichlid ecology, behaviour or about the evolution and interactions of communities. Nevertheless, trends which provide an insight into cichlid life histories, into evolutionary alternatives and into behavioural alternatives which may be followed during the life time of these fishes are emerging. Cichlids which spend their entire life history in a single habitat belong to species flocks that have spectated greatly. In contrast, those groups which live in a variety of habitats during their life history have spectated little. Despite the trophic specializations that have occurred among cichlids, many and perhaps all species, have the ability to feed upon alternative food resources. They do so by switching or by markedly modifying their behaviour and all are particularly opportunistic. The extensive adaptive radiation of cichlids with regard to those attributes of morphology and behaviour that are associated with survival and growth, is apparently not matched by similar radiations in reproductive behaviour. The perceived evolutionary conservatism with regard to reproductive behaviour is attributed to the effects of stabilizing selection, but this still needs to be tested. The constraints of stabilizing selection appear to be lifted with regard to coloration. If colour is an important component of the specific-mate recognition system then it should also be subjected to stabilizing selection so the readiness with which colour variation occurs within and between populations needs explanation. Parental care in cichlids has followed a variety of evolutionary alternatives, all of which are geared to improve the chances of survival of offspring in their specific micro-habitats.     

Detection of Diffusion Heterogeneity in Single Particle Tracking Trajectories Using a Hidden Markov Model with Measurement Noise Propagation

We develop a Bayesian analysis framework to detect heterogeneity in the diffusive behaviour of single particle trajectories on cells, implementing model selection to classify trajectories as either consistent with Brownian motion or with a two-state (diffusion coefficient) switching model. The incorporation of localisation accuracy is essential, as otherwise false detection of switching within a trajectory was observed and diffusion coefficient estimates were inflated. Since our analysis is on a single trajectory basis, we are able to examine heterogeneity between trajectories in a quantitative manner. Applying our method to the lymphocyte function-associated antigen 1 (LFA-1) receptor tagged with latex beads (4 s trajectories at 1000 frames s⁻¹), both intra- and inter-trajectory heterogeneity were detected; 12–26% of trajectories display clear switching between diffusive states dependent on condition, whilst the inter-trajectory variability is highly structured with the diffusion coefficients being related by D ₁ = 0.68D ₀ − 1.5 × 10⁴ nm² s⁻¹, suggestive that on these time scales we are detecting switching due to a single process. Further, the inter-trajectory variability of the diffusion coefficient estimates (1.6 × 10² − 2.6 × 10⁵ nm² s⁻¹) is very much larger than the measurement uncertainty within trajectories, suggesting that LFA-1 aggregation and cytoskeletal interactions are significantly affecting mobility, whilst the timescales of these processes are distinctly different giving rise to inter- and intra-trajectory variability. There is also an ‘immobile’ state (defined as D < 3.0 × 10³ nm² s⁻¹) that is rarely involved in switching, immobility occurring with the highest frequency (47%) under T cell activation (phorbol-12-myristate-13-acetate (PMA) treatment) with enhanced cytoskeletal attachment (calpain inhibition). Such ‘immobile’ states frequently display slow linear drift, potentially reflecting binding to a dynamic actin cortex. Our methods allow significantly more information to be extracted from individual trajectories (ultimately limited by time resolution and time-series length), and allow statistical comparisons between trajectories thereby quantifying inter-trajectory heterogeneity. Such methods will be highly informative for the construction and fitting of molecule mobility models within membranes incorporating aggregation, binding to the cytoskeleton, or traversing membrane microdomains.