Hamilton's Theory Research Articles

Inclusive fitness and differential productivity across the life course determine intergenerational transfers in a small-scale human society.

Transfers of resources between generations are an essential element in current models of human life-history evolution accounting for prolonged development, extended lifespan and menopause. Integrating these models with Hamilton's theory of inclusive fitness, we predict that the interaction of biological kinship with the age-schedule of resource production should be a key driver of intergenerational transfers. In the empirical case of Tsimane’ forager–horticulturalists in Bolivian Amazonia, we provide a detailed characterization of net transfers of food according to age, sex, kinship and the net need of donors and recipients. We show that parents, grandparents and siblings provide significant net downward transfers of food across generations. We demonstrate that the extent of provisioning responds facultatively to variation in the productivity and demographic composition of families, as predicted by the theory. We hypothesize that the motivation to provide these critical transfers is a fundamental force that binds together human nuclear and extended families. The ubiquity of three-generational families in human societies may thus be a direct reflection of fundamental evolutionary constraints on an organism's life-history and social organization.

‘From Man to Bacteria’: W.D. Hamilton, the theory of inclusive fitness, and the post-war social order

W.D. Hamilton's theory of inclusive fitness aimed to define the evolved limits of altruism with mathematical precision. Although it was meant to apply universally, it has been almost irretrievably entwined with the particular case of social insects that featured in his famous 1964 papers. The assumption that social insects were central to Hamilton's early work contradicts material in his rich personal archive. In fact, careful study of Hamilton's notes, letters, diaries, and early essays indicates the extent to which he had humans in mind when he decided altruism was a topic worthy of biological inquiry. For this reason, this article reconsiders the role of extra-scientific factors in Hamilton's early theorizing. In doing so, it offers an alternative perspective as to why Hamilton saw self-sacrifice to be an important subject. Although the traditional narrative prioritizes his distaste for benefit-of-the-species explanations as a motivating factor behind his foundational work, I argue that greater attention ought to be given to Hamilton's hope that science could be used to address social ills. By reconsidering the meaning Hamilton intended inclusive fitness to have, we see that while he was no political ideologue, the socio-political relevance of his theory was nevertheless integral to its development.

Distributed containment control and state observer design for multi-agent robotic system

Aiming at the distributed containment control problem for multi-agent robotic system with stationary leaders, a position-sensorless control strategy is proposed based on binocular visual servo and feedback dissipative Hamilton theory. Firstly, the topological relationship among the robots is built by using directed graph, which makes each follower determine its neighbour robots. Secondly, a binocular visual servo model is established, so as to describe the dynamic information of the tracking target point for each follower through the neighbour robots' image information. Thirdly, the distributed containment controllers are designed based on the pre-feedback control strategy and feedback dissipative Hamilton theory; furthermore, in the case that each follower is not equipped with internal position sensor, the full-order state observers are developed by using the 'expansion + feedback' method, and then realise the position-sensorless control. Finally, a simulation is carried out on multiple two degrees-of-freedom (DOF) robots, and results show the validity of the proposed control strategy.

Kin Selection and Its Critics

Hamilton's theory of kin selection is the best-known framework for understanding the evolution of social behavior but has long been a source of controversy in evolutionary biology. A recent critique of the theory by Nowak, Tarnita, and Wilson sparked a new round of debate, which shows no signs of abating. In this overview, we highlight a number of conceptual issues that lie at the heart of the current debate. We begin by emphasizing that there are various alternative formulations of Hamilton's rule, including a general version, which is always true; an approximate version, which assumes weak selection; and a special version, which demands other restrictive assumptions. We then examine the relationship between the neighbor-modulated fitness and inclusive fitness approaches to kin selection. Finally, we consider the often-strained relationship between the theories of kin and multilevel selection.

Analysis of Dynamic Behavior for Ballastless Track-Bridge with a Hybrid Method

A hybrid method combining finite element method (FEM) and statistical energy analysis (SEA) was recently presented for predicting the steady-state response of vibro-acoustic systems. Based on the structural characteristics of vehicle-CRTS II ballastless track-bridge system, the hybrid method of vehicle-track-bridge elements was presented. Using finite element method and Hamilton Theory, the coupled equation of vehicle-track-bridge can be established. Computational software is coded with Matlab. As an application, the vibration characteristics of the track-bridge system vertical profile assumed as random irregularity were calculated and the effect of random irregularity wavelength was analyzed. The computational results show that (1) The changes of the rail random irregularity wavelength have little influences on vertical displacement of track structure. (2) While it has very significant influences on vertical wheel/rail contact forces, and vertical acceleration amplitude of rail and slab, and the influenc...

Quantitative genetic versions of Hamilton's rule with empirical applications

Hamilton's theory of inclusive fitness revolutionized our understanding of the evolution of social interactions. Surprisingly, an incorporation of Hamilton's perspective into the quantitative genetic theory of phenotypic evolution has been slow, despite the popularity of quantitative genetics in evolutionary studies. Here, we discuss several versions of Hamilton's rule for social evolution from a quantitative genetic perspective, emphasizing its utility in empirical applications. Although evolutionary quantitative genetics offers methods to measure each of the critical parameters of Hamilton's rule, empirical work has lagged behind theory. In particular, we lack studies of selection on altruistic traits in the wild. Fitness costs and benefits of altruism can be estimated using a simple extension of phenotypic selection analysis that incorporates the traits of social interactants. We also discuss the importance of considering the genetic influence of the social environment, or indirect genetic effects (IGEs), in the context of Hamilton's rule. Research in social evolution has generated an extensive body of empirical work focusing—with good reason—almost solely on relatedness. We argue that quantifying the roles of social and non-social components of selection and IGEs, in addition to relatedness, is now timely and should provide unique additional insights into social evolution.

Towards greater realism in inclusive fitness models: the case of worker reproduction in insect societies

The conflicts over sex allocation and male production in insect societies have long served as an important test bed for Hamilton's theory of inclusive fitness, but have for the most part been considered separately. Here, we develop new coevolutionary models to examine the interaction between these two conflicts and demonstrate that sex ratio and colony productivity costs of worker reproduction can lead to vastly different outcomes even in species that show no variation in their relatedness structure. Empirical data on worker-produced males in eight species of Melipona bees support the predictions from a model that takes into account the demographic details of colony growth and reproduction. Overall, these models contribute significantly to explaining behavioural variation that previous theories could not account for.

The Analysis of Vibration for Ballastless Track-Bridge Base on a Hybrid FE-SEA Method

In this study, the methods for combining statistical energy analysis (SEA) and the finite element method (FEM) for the vibration analysis of structures are studied. Using the two methods simultaneously isnt entirely extend a primarily low frequency method, the finite element method, and high frequency method, SEA, to the mid frequency region are addressed. This approach is intended to extend the frequency range for a FEM based vibration analysis . A new finite element elementl for elevated slab ballastless track is proposed in which the new model can be used for modeling the track structural constituents of elevated slab ballastless track. Using finite element method and Hamilton theory, the coupled equation of vehicle-track-bridge can be established. In calculating example, both the rail displacement induced by single four-layer beam model. Specifically, it showed that the method yields very good result and high performance in the numerical example of previous research.

Flutter Analysis of Composite Wing Using Differential Quadrature Method

Considering the geometric and material coupling of a composite wing, the equations of motion are derived based on Hamilton theory. Frequencies computing and validation of a composite wing with bending-torsion coupling using differential quadrature method (DQM). And the DQM is applied to the flutter speed solution of a composite wing. The results thus obtained are then compared with some available results and a good agreement is observed. The computing time of DQM is highly improved compared with Galerkin method. Moreover, the effect of material coupling rigidity on flutter speed is analyzed and this is important to the design of composite wings.

Study on Kinetic Energy for Saving Materials with Analysis of Lumped Mass Matrix of Variable Cross-Section Beam Element

Based on positional finite element method (FEM), a new, simple and accurate lumped mass matrix to solve dynamic geometrical nonlinear problems of materials applied to variable cross-section beam element has been proposed. According to Hamilton theory and the concept of Kinetic energy, concentrate the beam element mass to the two nodes in certain proportion, the lumped mass matrix is deduced. The lumped mass matrix is diagonal matrix and its calculated quantity is less than using consistent mass matrix about properties of materials under the same calculation precision.

The Lagrange Mechanization and Application of Multi-Machine Power System

The fast development of Hamilton system theory provides a powerful tool for the nonlinear control and stability analysis of power system. The construction of Hamilton function plays an important role in Hamilton realization. Based on Hamilton canonical equations, the energy integration of system is given. This paper expands the odd-order power system to even-order system and gives the responding conditions of Hamilton realization by using the self-adjoint methods of analytical mechanics. Besides, the standard Hamilton form of power system is derived by the combinations of Lagrange mechanization and Hamilton theory, and the form of Hamilton function is also given. Based on non-conservative analytical mechanical principles, the controllers are designed in allusion to the characteristics of power system and Matlab program is realized in IEEE3-9 standard system. The simulation effects are discussed in the transient conditions of three-phase fault by comparison of different approaches, which proves the effectiveness of the control strategy. This approach to construct Hamilton function and design the controllers has an extensive prospect of application

Robust Coordinated Control of Excitation and SVCs in Multi-Machine Power System

Nonlinear controller of excitation and FACTS in power system has drawn considerable attention for years in the literature. It has substantial potential and advantage in enhancing the power system stability compared with traditional linear methods. In this paper, the coordinated and robust design of the excitation and SVC controllers in multi-machine power system is studied. The generalized Hamilton theory is used in the controller design process, which has a more general form and a wider range of application. A Lyapunov function with uncertain parameters is constructed and proven to be a real one under some assumptions. The strictly dissipative generalized Hamiltonian realization of the multi-machine power system with SVCs is explicitly illustrated. Then the coordinated and robust control strategy of excitation and SVCs is designed via an energy-based conception. Experimental results demonstrate the effectiveness and the practicability of the presented methodology

Analyses of rigid-flexible coupling dynamic properties of a rotating internal cantilever beam

The rigid-flexible coupling dynamic properties of an internal cantilever beam attached to a rotating hub are studied in this paper. Based on the accurate description of non-linear deformation of the flexible beam, the first-order approximation coupling model is derived from Hamilton theory and assumed mode method, taking into account the second-order coupling quantity of axial displacement caused by transverse displacement of the beam. The simplified first-order approximation coupling model which neglects the effect of axial deformation of a beam is presented. The simplified model is transformed into dimensionless form in which dimensionless parameters are identified. Firstly, the dynamic response of an internal cantilever beam is compared with that of an external cantilever beam, which are both in non-inertia system. Then, the stability of an internal cantilever beam is analyzed. Finally, the convergence of critical rotating speed of an internal cantilever beam is analyzed. Generally, it is pointed that an internal cantilever beam has a dynamic softening phenomenon, which is different from the dynamic stiffening phenomenon of an external cantilever beam. The critical ratio of the internal radius to the length of the beam for unconditional stability and the critical rotating speed of conditional stability of an internal cantilever beam are derived. When the first natural frequency decreases as the rotating speed increases, the dynamic system of the internal cantilever beam is conditionally stable. As the number of modes increases, the critical rotating speed of an internal cantilever beam decreases, and it has a convergent value.

Lumped Mass Matrix of Three-Node Beam Element

According to Hamilton theory and the concept of Kinetic energy, lumped mass matrix of three-node beam element based on positional finite element method (FEM) is deduced. By concentrating the mass at the three nodes of beam element, the lumped mass matrix is characterized. When dynamic analysing, lumped mass matrix is simpler and more common than consistent mass matrix because lumped mass matrix is diagonal matrix, and calculation work is less under the same calculation precision.

In-Plane and Transverse Eigenmodes of High-Speed Rotating Composite Disks

We apply Hamilton's principle and model the coupled in-plane and transverse vibrations of high-speed spinning disks, which are fiber-reinforced circumferentially. We search for eigenmodes in the linear regime using a collocation scheme, and compare the mode shapes of composite and isotropic disks. As the azimuthal wavenumber varies, the radial nodes of in-plane waves are remarkably displaced in isotropic disks while they resist such displacements in composite disks. The reverse of this phenomenon happens for transversal waves and the radial nodes move toward the outer disk edge as the azimuthal wavenumber is increased in composite disks. This result is in accordance with the predictions of Nowinski's theory, and therefore, it is independent of the magnitude of the spinning velocity and the mode frequency. Although there are notable differences between the form of governing equations derived from Hamilton's principle and Nowinski's theory, transverse eigenmodes differ a little in the two approaches. We argue that the application of orthotropic composites as the core material of the next generation of hard disk drives, together with an angular velocity controller, can enhance the data access rate.

旋转内接微梁的动力学建模及稳定性分析

The dynamic properties of the micro beam are obviously different from those of the traditional macro beam due to the size effect of material on a micro scale. The rigid-flexible coupling dynamic properties analysis of an internal micro beam attached to a rotating hub is studied in this paper. Based on the accurate description of non-linear deformation of the flexible beam, the first-order approximation coupling model are derived from couple stress theory and Hamilton theory, taking the second-order coupling quantity of axial displacement caused by transverse displacement of the beam into account. The simplified first-order approximation coupling model which neglects the effect of axial deformation of a beam is presented. The simplified model is transformed into dimensionless form in which dimensionless parameters are identified. Firstly, the dynamic response of an internal micro beam is compared with that of an external micro beam, which are both in non-inertia system. Then, the influence of size effect on the dynamic properties of an internal micro beam is studied. Generally, it is pointed out that an internal micro beam has dynamic softening phenomena, which is different from the dynamic stiffening phenomena of an external micro beam. The critical ratio of the internal radius to the length of the beam for unconditional stability and the critical angular speed of conditional stability of an internal micro beam are derived. The size effect results in the descending of vibration amplitude and the increasing of vibration frequency and critical angular speed of conditional stability of the micro beam. As the number of modes increases, the critical rotating speed of an internal cantilever beam decreases, and it has a convergent value.

Social Evolution: Evolving Sex Ratios

A recent study comparing sex ratios produced by experimental evolution in spider mites with those predicted by Hamilton's Local Mate Competition Theory clearly demonstrates Evolutionary Theory's success as a quantitatively predictive science.

A quantitative test of Hamilton's rule for the evolution of altruism.

Author SummaryOne of the enduring puzzles in biology and the social sciences is the origin and persistence of altruism, whereby a behavior benefiting another individual incurs a direct cost for the individual performing the altruistic action. This apparent paradox was resolved by Hamilton's theory, known as kin selection, which states that individuals can transmit copies of their own genes not only directly through their own reproduction but also indirectly by favoring the reproduction of kin, such as siblings or cousins. While many studies have provided qualitative support for kin selection theory, quantitative tests have not yet been possible due to the difficulty of quantifying the costs and benefits of helping acts. In this study, we conduct simulations with the help of a simulated system of foraging robots to manipulate the costs and benefits of altruism and determine the conditions under which altruism evolves. By conducting experimental evolution over hundreds of generations of selection in populations with different costs and benefits of altruistic behavior, we show that kin selection theory always accurately predicts the minimum relatedness necessary for altruism to evolve. This high accuracy is remarkable given the presence of pleiotropic and epistatic effects, as well as mutations with strong effects on behavior and fitness. In addition to providing a quantitative test of kin selection theory in a system with a complex mapping between genotype and phenotype, this study reveals that a fundamental principle of natural selection also applies to synthetic organisms when these have heritable properties.

Flexible and Vibration Characteristics Simulation for the Large Megawatt Size Wind Turbine Blades

In the development of new large megawatt size wind turbines, aerodynamic and structural reserch is interesting and important for study wind turbine performace and boost the development of wind power. In this paper, the aerodynamic and aeroelastic characteristic of blades is investigated and presented based on Blade Element Momentum and Hamilton theory. Then the flexible characteristics of balde is researched with the aerodynamic and aeroelastic model of the rotor. The flapwise and edgewise displacements, velocities and accelerations of blade tip are simulated and plotted to validate the model which is presented in this paper. The results have very important significance to investigate the vibration and fatigue lifetime of the wind turbine blades.

On the minimal representation of non-linear eddy-viscosity models

This study attempts to provide a minimal explicit non-linear relationship between the Reynolds stresses and the mean strain rate and vorticity. Such relationship is also referred to as the nonlinear eddy-viscosity model (EVM) of the Reynolds stresses. Based on the observation of the independent terms in the Reynolds stress anisotropy tensor, it is proposed here that the explicit Reynolds stress closure can be formulated in a compact vorticity tensor to form a minimal representation. With the application of the generalized Cayley–Hamilton theory, it is shown that the explicit algebraic stress model with 10 integrity bases can be transformed into a five-term model expression. Thus, the present work provides a framework for the development of the explicit Reynolds stress closure in the compact form. Indeed, a cubic EVM is developed here that is capable of revealing the quadratic behaviour of the tangential velocity with respect to the radial distance in the fully developed turbulent rotating pipe flow. This model, hence, removed some major defects in the lower-order EVMs, while the model complexity is kept at minimum.