An Experimental Test of the Accumulated Copying Error Model of Cultural Mutation for Acheulean Handaxe Size

Archaeologists interested in explaining changes in artifact morphology over long time periods have found it useful to create models in which the only source of change is random and unintentional copying error, or ‘cultural mutation’. These models can be used as null hypotheses against which to detect non-random processes such as cultural selection or biased transmission. One proposed cultural mutation model is the accumulated copying error model, where individuals attempt to copy the size of another individual''s artifact exactly but make small random errors due to physiological limits on the accuracy of their perception. Here, we first derive the model within an explicit mathematical framework, generating the predictions that multiple independently-evolving artifact chains should diverge over time such that their between-chain variance increases while the mean artifact size remains constant. We then present the first experimental test of this model in which 200 participants, split into 20 transmission chains, were asked to faithfully copy the size of the previous participant''s handaxe image on an iPad. The experimental findings supported the model''s prediction that between-chain variance should increase over time and did so in a manner quantitatively in line with the model. However, when the initial size of the image that the participants resized was larger than the size of the image they were copying, subjects tended to increase the size of the image, resulting in the mean size increasing rather than staying constant. This suggests that items of material culture formed by reductive vs. additive processes may mutate differently when individuals attempt to replicate faithfully the size of previously-produced artifacts. Finally, we show that a dataset of 2601 Acheulean handaxes shows less variation than predicted given our empirically measured copying error variance, suggesting that other processes counteracted the variation in handaxe size generated by perceptual cultural mutation.     

A dynamic model of photosynthesis in varying light taking account of stomatal conductance, C3-cycle intermediates, photorespiration and Rubisco activation

Abstract. A dynamic model of whole leaf C₃ photosynthesis is constructed using a modified version of the Farquliar-von Caemmerer approach. The model is designed to provide a physiological basis to understand observations of assimilation in environments with varying photon flux densities, including induction phenomena. The model couples the effect of light activation and dark deactivation of enzymes, stomatal conductance responses, and variations in the pools of carbon cycle intermediates. The dynamic components are viewed on three time scales, the slowest of which (min to h) involves changes in stomatal conductance and the activation stale of Rubisco. On a time scale of seconds to a few minutes, adjustments in pools of biochemical components of the photosynthetic pathway occurs. The most rapid time scale corresponds to the equilibration time of intercelluar CO₂ concentration through gaseous diffusion and is here assumed to occur instantaneously. The model form includes a single pool for reduced intermediates including RuBP, a single pool for components of the glycolate pathway, and a third component corresponding to the activation state of Rubisco. This is coupled to a previously described model for the dynamics of stomatal conductance, giving a final model form consisting of six non-linear ordinary differential equations, of which three control conductance dynamics and three control assimilation. The coupling between these occurs through the variable p_i, the intercellular partial pressure of CO_2. Only three of the parameters for the assimilation portion of the model require dynamic data to estimate. The remaining parameters are estimated from steady-state data. The model is calibrated using previously collected data on the tropical understory plant Alocasia macrorrhiza and is shown to have qualitatively similar behaviour to that of experimental measurements using simple changes in PFD, as well as a complex sequence of such changes.     

Effects of transient receptor potential-like current on the firing pattern of action potentials in the Hodgkin-Huxley neuron during exposure to sinusoidal external voltage

Transient receptor potential vanilloid-1 (TRPV1) channels play a role in several inflammatory and nociceptive processes. Previous work showed that magnetic electrical field-induced antinociceptive [corrected] action is mediated by activation of capsaicin-sensitive sensory afferents. In this study, a modified Hodgkin-Huxley model, in which TRP-like current (ITRP) was incorporated, was implemented to predict the firing behavior of action potentials (APs), as the model neuron was exposed to sinusoidal changes in externally-applied voltage. When model neuron is exposed to low-frequency sinusoidal voltage, increased maximal conductance of ITRP can enhance repetitive bursts of APs accompanied by a shortening of inter-spike interval (ISI) in AP firing. The change in ISIs with number of interval is periodic with the phase-locking. In addition, increased maximal conductance of ITRP can abolish chaotic pattern of AP firing in model neuron during exposure to high-frequency voltage. The ISI pattern is converted from irregular to constant, as maximal conductance of ITRP is increased under such high-frequency voltage. Our simulation results suggest that modulation of TRP-like channels functionally expressed in small-diameter peripheral sensory neurons should be an important mechanism through which it can contribute to the firing pattern of APs.     

Coalescent approximation for structured populations in a stationary random environment

We establish convergence to the Kingman coalescent for the genealogy of a geographically-or otherwise-structured version of the Wright-Fisher population model with fast migration. The new feature is that migration probabilities may change in a random fashion. This brings a novel formula for the coalescent effective population size (EPS). We call it a quenched EPS to emphasize the key feature of our model — random environment. The quenched EPS is compared with an annealed (mean-field) EPS which describes the case of constant migration probabilities obtained by averaging the random migration probabilities over possible environments.     

Desensitization and recovery at the frog neuromuscular junction

The time course of carbachol-induced desensitization onset and recovery of sensitivity after desenitization have been compared at the frog neuromuscular junction. The activation-desensitization sequence was determined from input conductance measurements using potassium-depolarized muscle preparations. Both desensitization onset and recovery from desensitization could be adequately described by single time constant expressions, with tauonset being considerably shorter than taurecovery. In nine experiments, tauonset was 13+/-1.3 s and taurecovery was 424+/-51 s with 1 mM carbachol. Elevating the external calcium or carbachol concentration accelerated desensitization onset without changing the recovery of sensitivity after equilibrium desensitization. Desensitization onset was accelerated by a prior activation-desensitization sequence to an extent determined by the recovery interval that followed the initial carbachol application. The time course of return of tauonset was closely parallel to, but slower than the time course of recovery of sensitivity. These results are consistent with a cyclic model in which intracellular calcium is a factor controlling the rate of development of desensitization.     

A simple completion of Fisher’s fundamental theorem of natural selection

Fisher''s fundamental theorem of natural selection shows that the part of the rate of change of mean fitness that is due to natural selection equals the additive genetic variance in fitness. Fisher embedded this result in a model of total fitness, adding terms for deterioration of the environment and density dependence. Here, a quantitative genetic version of this neglected model is derived that relaxes its assumptions that the additive genetic variance in fitness and the rate of deterioration of the environment do not change over time, allows population size to vary, and includes an input of mutational variance. The resulting formula for total rate of change in mean fitness contains two terms more than Fisher''s original, representing the effects of stabilizing selection, on the one hand, and of mutational variance, on the other, making clear for the first time that the fundamental theorem deals only with natural selection that is directional (as opposed to stabilizing) on the underlying traits. In this model, the total (rather than just the additive) genetic variance increases mean fitness. The unstructured population allows an explanation of Fisher''s concept of fitness as simply birth rate minus mortality rate, and building up to the definition in structured populations.     

Photopigment quenching is Ca2+ dependent and controls response duration in salamander L-cone photoreceptors

The time scale of the photoresponse in photoreceptor cells is set by the slowest of the steps that quench the light-induced activity of the phototransduction cascade. In vertebrate photoreceptor cells, this rate-limiting reaction is thought to be either shutoff of catalytic activity in the photopigment or shutoff of the pigment''s effector, the transducin-GTP–phosphodiesterase complex. In suction pipette recordings from isolated salamander L-cones, we found that preventing changes in internal [Ca²⁺] delayed the recovery of the light response and prolonged the dominant time constant for recovery. Evidence that the Ca²⁺-sensitive step involved the pigment itself was provided by the observation that removal of Cl⁻ from the pigment''s anion-binding site accelerated the dominant time constant for response recovery. Collectively, these observations indicate that in L-cones, unlike amphibian rods where the dominant time constant is insensitive to [Ca²⁺], pigment quenching rate limits recovery and provides an additional mechanism for modulating the cone response during light adaptation.     

Dyar's Rule and the Investment Principle: optimal moulting strategies if feeding rate is size-dependent and growth is discontinuous

We consider animals whose feeding rate depends on the size of structures that grow only by moulting (e.g. spiders'' legs). Our Investment Principle predicts optimum size increases at each moult; under simplifying assumptions these are a function of the scaling of feeding rate with size, the efficiency of moulting and the optimum size increase at the preceding moult. We show how to test this quantitatively, and make the qualitative prediction that size increases and instar durations change monotonically through development. Thus, this version of the model does not predict that proportional size increases necessarily remain constant, which is the pattern described by Dyar''s Rule. A literature survey shows that in nature size increases tend to decline and instar durations to increase, but exceptions to monotonicity occur frequently: we consider how relaxing certain assumptions of the model could explain this. Having specified various functions relating fitness to adult size and time of emergence, we calculate (using dynamic programming) the effect of manipulating food availability, time of hatching and size of the initial (or some intermediate) instar. The associated norms of reaction depend on the fitness function and differ from those when growth follows Dyar''s Rule or is continuous. We go on to consider optimization of the number of instars. The Investment Principle then predicts upper and lower limits to observed size increases and explains why increases usually change little or decline through development. This is thus a new adaptive explanation for Dyar''s Rule and for the most common deviation from the Rule.     

Transient response in a somatic shunt cable model for synaptic input activated at the terminal

Rall's neuron model is extended by including a non-uniform time constant together with synaptic input modeled as a square step of conductance. An analytic solution (in series form) for the electrotonic potential is obtained. The major conclusion reached is that a lower somatic time constant attenuates the amplitude of the potential at the soma, brought about by the activation of a synapse located at the distal end of the dendritic cable in an initially polarized neuron.     

The kinetics of monazomycin-induced voltage-dependent conductance. I. Proof of the validity of an empirical rate equation

Monazomycin (a positively-charged, polyene-like antibiotic) induces a strongly voltage-dependent conductance in thin lipid membranes when added to one of the bathing solutions. We show here that the kinetics of conductance changes after a step of membrane potential are only superficially similar to the kinetics of the potassium gating system of squid giant axons, in that the beginning of conductance increases are growth functions of the time, as opposed to power functions of the time. We find that the rate constant (reciprocal of the time constant) of the growth varies with the approximately 2.6 power of the monazomycin concentration. The rate constant also varies exponentially with membrane potential such that an e-fold change is associated with a 10-11 mV change of membrane potential. We show that solutions of a simple differential equation are able to reproduce the actual conductance changes almost exactly. In the accompanying paper (Muller and Peskin. 1981. J. Gen. Physiol. 78:201-229), we derive the differential equation from a molecular model and use the theoretical equation so obtained to investigate the gating current of this system and to predict an interesting form of memory.     

Activation of Ca(2+)-dependent K(+) channels contributes to rhythmic firing of action potentials in mouse pancreatic beta cells

We have applied the perforated patch whole-cell technique to beta cells within intact pancreatic islets to identify the current underlying the glucose-induced rhythmic firing of action potentials. Trains of depolarizations (to simulate glucose-induced electrical activity) resulted in the gradual (time constant: 2.3 s) development of a small (<0.8 nS) K(+) conductance. The current was dependent on Ca(2+) influx but unaffected by apamin and charybdotoxin, two blockers of Ca(2+)-activated K(+) channels, and was insensitive to tolbutamide (a blocker of ATP-regulated K(+) channels) but partially (>60%) blocked by high (10-20 mM) concentrations of tetraethylammonium. Upon cessation of electrical stimulation, the current deactivated exponentially with a time constant of 6.5 s. This is similar to the interval between two successive bursts of action potentials. We propose that this Ca(2+)-activated K(+) current plays an important role in the generation of oscillatory electrical activity in the beta cell.     

Density dependence and microevolution interactively determine effects of phenology mismatch on population dynamics

Life cycle events in plants and animals are typically adaptively tuned to anticipate predictable seasonal changes in environmental conditions or resources. Climate change is expected to affect the temporal component of species’ interactions, e.g. by creating a mismatch between a predator's breeding time (when ample food supply is critical) and the time when prey abundance is high. The demographic implications of such a mismatch remain unclear, however. Here we focussed on changes in the phenology of consumers relative to that of their food. We developed a model where reproductive output of the consumer up to offspring independence depended on mismatch and recruitment of the offspring to breeders depended on offspring density according to a Beverton–Holt function. Using a deterministic version of the model, we clarified how the effects of (constant) mismatch on equilibrium population size depended on the emergent strength of negative density dependence (DD). Using a stochastic, individual‐based version, we showed that when the environment changed abruptly, the rate of population recovery was faster when heritability of seasonal timing was higher and DD was stronger. When the environment shifted continuously, the rate of decline in population size was inversely proportional to the rate of microevolution, but stronger DD slowed the rate of decline for a given heritability and thus effectively ‘bought time’ for evolutionary rescue. These results highlight the importance of negative DD, which interacts with the effects of trait heritability and stabilizing selection strength, in influencing the fate of populations experiencing environmental change. We emphasize, however, that outcomes in nature will depend crucially on the exact nature of DD, in particular whether population growth rate differences are greatest at low or high densities, highlighting the need for empirical comparisons of compensatory processes in different populations or species.     

Estimating the carrying capacity of French Frigate Shoals for the endangered Hawaiian monk seal using Ecopath with Ecosim

The carrying capacity of the French Frigate Shoals (FFS) region for the endangered Hawaiian monk seal was appraised using an updated version of the original FFS Ecopath model ( Polovina 1984 ). Model parameters were updated using recent literature, and data from surveys of the seal population and its bottom‐associated prey. Together they produced a static mass balance model for 1998 when the prey surveys began. The Ecopath‐estimated monk seal biomass was 0.0045 t/km², which was in close agreement with the biomass calculated from monk seal field beach counts (0.0046 t/km²). Model simulations through time were done in Ecosim using the Ecopath balanced model and included fisheries data time series from 1998 to 2008. Monk seal biomass declined concurrently with decreases in benthic bottomfish biomass, which were influenced by large‐scale changes in the environment of the North Pacific. This model scenario was extended from 2010, when the last permitted fishery in the Northwestern Hawaiian Islands was closed, through to 2040, assuming a constant environmental signal. Model results for this time period did not show a recovery of monk seals that exceeded the initial 1998 model biomass levels, highlighting the importance of including environmental variability in estimates of monk seals recovery at FFS.     

Voltage-induced nonconductive pre-pores and metastable single pores in unmodified planar lipid bilayer

Electric fields promote pore formation in both biological and model membranes. We clamped unmodified planar bilayers at 150-550 mV to monitor transient single pores for a long period of time. We observed fast transitions between different conductance levels reflecting opening and closing of metastable lipid pores. Although mean lifetime of the pores was 3 +/- 0.8 ms (250 mV), some pores remained open for up to approximately 1 s. The mean amplitude of conductance fluctuations (approximately 500 pS) was independent of voltage and close for bilayers of different area (40,000 and 10 microm(2)), indicating the local nature of the conductive defects. The distribution of pore conductance was rather broad (dispersion of approximately 250 pS). Based on the conductance value and its dependence of the ion size, the radius of the average pore was estimated as approximately 1 nm. Short bursts of conductance spikes (opening and closing of pores) were often separated by periods of background conductance. Within the same burst the conductance between spikes was indistinguishable from the background. The mean time interval between spikes in the burst was much smaller than that between adjacent bursts. These data indicate that opening and closing of lipidic pores proceed through some electrically invisible (silent) pre-pores. Similar pre-pore defects and metastable conductive pores might be involved in remodeling of cell membranes in different biologically relevant processes.     

Kinetic properties of a voltage-dependent junctional conductance

We have proposed that the gap junctions between amphibian blastomeres are comprised of voltage-sensitive channels. The kinetic properties of the junctional conductance are here studied under voltage clamp. When the transjunctional voltage is stepped to a new voltage of the same polarity, the junctional conductance changes as a single exponential to a steady-state level. The time constant of the conductance change is determined by the existing transjunctional voltage and is independent of the previous voltage. For each voltage polarity, the relations between voltage, time constant, and steady-state conductance are well modeled by a reversible two-state reaction scheme in which the calculated rate constants for the transitions between the states are exponential functions of voltage. The calculated rate constant for the transition to the low-conductance state is approximately twice as voltage dependent as that for the transition to the high-conductance state. When the transjunctional voltage polarity is reversed, the junctional conductance undergoes a transient recovery. The polarity reversal data are well modeled by a reaction scheme in which the junctional channel has two gates, each with opposite voltage sensitivity, and in which an open gate may close only if the gate in series with it is open. A simple explanation for this contingent gating is a mechanism in which each gate senses only the local voltage drop within the channel.     

Stomatal regulation and water economy in crassulacean acid metabolism plants: an optimization model

It has been found that the stomatal behaviour of C₃ and C₄ plants can be predicted from the assumption that they increase transpiration whenever the increase δW in daily water loss is offset by a gain of at least λδW in carbon assimilation, where the minimum acceptable marginal conversion efficiency λ is determined by long term ecological factors, and is essentially constant within the course of a day. This paradigm is here extended to plants with Crassulacean acid metabolism (CAM). During daytime assimilation the results are the same as for C₃ and C₄ metabolisms. However night-time assimilation can be inhibited by the accumulation of malate in the cell vacuoles. In this event our model predicts that in a constant environment the stomatal conductance remains proportional to the square root of the mesophyll conductance as the latter declines. This is intermediate between keeping a constant stomatal conductance and keeping a constant intercellular CO₂ concentration (as tends to occur in the C₃/C₄ model when illumination varies), and results in an increasing intercellular CO₂ concentration towards the end of the night. This prediction accords with the Agave data of Nobel & Hartsock 1979. The model also predicts the allocation of time between C₃ and CAM for different degrees of water stress. The results agree qualitatively with observation, even though physiological changes (other than stomatal conductance) are not included in the model.     

Episodic Evolution of Protein Hormones in Mammals

Pituitary growth hormone (GH) and prolactin have been shown previously to display a pattern of evolution in which episodes of rapid change are imposed on a low underlying basal rate (near-stasis). This study was designed to explore whether a similar pattern is seen in the evolution of other protein hormones in mammals. Seven protein hormones were examined (with the common α-subunit of the glycoprotein hormones providing an additional polypeptide for analysis)—those for which sequences from at least four eutherian orders are available with a suitable non-eutherian outgroup. Six of these (GH, prolactin, insulin, parathyroid hormone, glycoprotein hormone α-subunit, and luteinizing hormone β-subunit) showed markedly variable evolutionary rates in each case with a pattern of a slow basal rate and bursts of rapid change, the precise positions of the bursts varying from protein to protein. Two protein hormones (follicle-stimulating hormone β-subunit and thyroid-stimulating hormone β-subunit) showed no significant rate variation. Based on the sequences currently available, and pooling data from all eight proteins, the phase of slow basal change occupied about 85% of the sampled evolutionary time, but most evolutionary change (about 62% of the substitutions accepted) occurred during the episodes of rapid change. It is concluded that, in mammals at least, a pattern of prolonged periods of near-stasis with occasional episodes of rapid change provides a better model of evolutionary change for protein hormones than the one of constant evolutionary rates that is commonly favored. The mechanisms underlying this episodic evolution are not yet clear, and it may be that they vary from one group to another; in some cases, positive selection appears to underlie bursts of rapid change. Where gene duplication is associated with a period of accelerated evolution this often occurs at the end rather than the beginning of the episode. To what extent the type of pattern seen for protein hormones can be extended to other proteins remains to be established. Received: 10 October 2000 / Accepted: 18 December 2000     

Building a home from foam—túngara frog foam nest architecture and three-phase construction process

Frogs that build foam nests floating on water face the problems of over-dispersion of the secretions used and eggs being dangerously exposed at the foam : air interface. Nest construction behaviour of túngara frogs, Engystomops pustulosus, has features that may circumvent these problems. Pairs build nests in periodic bursts of foam production and egg deposition, three discrete phases being discernible. The first is characterized by a bubble raft without egg deposition and an approximately linear increase in duration of mixing events with time. This phase may reduce initial over-dispersion of foam precursor materials until a critical concentration is achieved. The main building phase is marked by mixing events and start-to-start intervals being nearly constant in duration. During the final phase, mixing events do not change in duration but intervals between them increase in an exponential-like fashion. Pairs joining a colonial nesting abbreviate their initial phase, presumably by exploiting a pioneer pair''s bubble raft, thereby reducing energy and material expenditure, and time exposed to predators. Finally, eggs are deposited only in the centre of nests with a continuously produced, approximately 1 cm deep egg-free cortex that protectively encloses hatched larvae in stranded nests.     

Generating oscillatory bursts from a network of regular spiking neurons without inhibition

Avian nucleus isthmi pars parvocellularis (Ipc) neurons are reciprocally connected with the layer 10 (L10) neurons in the optic tectum and respond with oscillatory bursts to visual stimulation. Our in vitro experiments show that both neuron types respond with regular spiking to somatic current injection and that the feedforward and feedback synaptic connections are excitatory, but of different strength and time course. To elucidate mechanisms of oscillatory bursting in this network of regularly spiking neurons, we investigated an experimentally constrained model of coupled leaky integrate-and-fire neurons with spike-rate adaptation. The model reproduces the observed Ipc oscillatory bursting in response to simulated visual stimulation. A scan through the model parameter volume reveals that Ipc oscillatory burst generation can be caused by strong and brief feedforward synaptic conductance changes. The mechanism is sensitive to the parameter values of spike-rate adaptation. In conclusion, we show that a network of regular-spiking neurons with feedforward excitation and spike-rate adaptation can generate oscillatory bursting in response to a constant input.