A Turing test for collective motion

A widespread problem in biological research is assessing whether a model adequately describes some real-world data. But even if a model captures the large-scale statistical properties of the data, should we be satisfied with it? We developed a method, inspired by Alan Turing, to assess the effectiveness of model fitting. We first built a self-propelled particle model whose properties (order and cohesion) statistically matched those of real fish schools. We then asked members of the public to play an online game (a modified Turing test) in which they attempted to distinguish between the movements of real fish schools or those generated by the model. Even though the statistical properties of the real data and the model were consistent with each other, the public could still distinguish between the two, highlighting the need for model refinement. Our results demonstrate that we can use ‘citizen science’ to cross-validate and improve model fitting not only in the field of collective behaviour, but also across a broad range of biological systems.     

Deciphering CAPTCHAs: what a Turing test reveals about human cognition

Turning Turing's logic on its head, we used widespread letter-based Turing Tests found on the internet (CAPTCHAs) to shed light on human cognition. We examined the basis of the human ability to solve CAPTCHAs, where machines fail. We asked whether this is due to our use of slow-acting inferential processes that would not be available to machines, or whether fast-acting automatic orthographic processing in humans has superior robustness to shape variations. A masked priming lexical decision experiment revealed efficient processing of CAPTCHA words in conditions that rule out the use of slow inferential processing. This shows that the human superiority in solving CAPTCHAs builds on a high degree of invariance to location and continuous transforms, which is achieved during the very early stages of visual word recognition in skilled readers.     

Packet theory of conditioning and timing

Packet theory is based on the assumption that the momentary probability of producing a bout or packet of responding is controlled by the conditional expected time function. Bouts of head entry responses of rats into a food cup appear to have the same characteristics across a range of conditions. The conditional expected time function is the mean expected time remaining until the next food delivery as a function of time since an event such as food or stimulus onset. The conditional expected time function encodes mean interval duration as well as the distribution form so that both the mean response rate and form of responding in time can be predicted. Simulations of Packet theory produced accurate quantitative predictions of: (1) the effect of reinforcement density (mean food-food interval) and distribution form on responding; (2) scalar variance in fixed interval responding; (3) CS-US and intertrial interval effects on the strength of conditioning; and (4) the effect of the ratio of cycle:trial time on the strength of conditioning.     

A comparative test of a theory for the evolution of anisogamy

Why are sperm small and eggs large? The dominant explanation for the evolution of gamete size dimorphism envisages two opposing selection pressures acting on gamete size: small gametes are favoured because many can be produced, whereas large gametes contribute to a large zygote with consequently increased survival chances. This model predicts disruptive selection on gamete size (i.e. selection for anisogamy) if increases in zygote size confer disproportional increases in fitness (at least over part of its size range). It therefore predicts that increases in adult size should be accompanied by stronger selection for anisogamy. Using data from the green algal order Volvocales, we provide the first phylogenetically controlled test of the model''s predictions using a published phylogeny and a new phylogeny derived by a different method. The predictions that larger organisms should (i) have a greater degree of gamete dimorphism and (ii) have larger eggs are broadly upheld. However, the results are highly sensitive to the phylogeny and the mode of analysis used.     

Population differences in the timing of diapause: a test of hypotheses

Summary The reproductive phenology of the freshwater copepod Diaptomus sanguineus differs markedly between populations residing in two Rhode Island ponds. In a permanent pond the population switches abruptly from making subitaneous (immediately hatching) eggs to diapausing eggs at the end of March each year. In contrast, a temporary pond population switches egg types in May, returns to production of subitaneous eggs in June, and concludes the reproductive season by making diapausing eggs in July. An ESS model suggests that the pattern of diapause expected of a copepod population is a function of annual variation in the onset of harsh conditions (catastrophe date). When variation is relatively low, the superior strategy is for diapause to begin a constant period before the mean catastrophe date. When variation is high, females should make first subitaneous eggs and then diapausing eggs irrespective of the expected catastrophe date. With discrete generations, such a population would alternate between egg types. In the permanent pond, variation of catastrophe date the spring onset of planktivory by sunfish is low, whereas in the temporary pond variation of the catastrophe (pond drying) is high. The model predicts well the phenology of the two copepod populations.In the research reported here, we tested the hypothesis that copepods from the permanent pond, which switch to diapause at the same time every year, are cued by the environment to begin diapause (i.e. by photoperiod, temperature, or both), whereas those from the temporary pond make both egg types regardless of environmental conditions. In opposition to our hypothesis, experimental results indicate that diapause in both populations is cued by the environment. The distinct reproductive phenologies documented in the two populations apparently result from the copepods responding to different environmental cues, rather than one being responsive to the environment while the other is not.     

Canny's compensating pressure theory fails a test

Canny's compensating pressure theory for water transport (American Journal of Botany 85: 897–909) has evolved from the premise that cavitation pressures are only a few tenths of a megapascal negative (approximately −0.3 MPa). In contradiction, “vulnerability curves” indicate that xylem pressures can drop below −3 MPa in some species without causing a loss of hydraulic conductivity. Canny claims these curves do not measure the limits to negative pressure by cavitation, but rather the limits to the compensating tissue pressure that otherwise quickly refills cavitated conduits. Compensating pressure is derived from the turgor pressure of the living cells in the tissue. To test this claim, we compared vulnerability curves of Betula nigra stems given three treatments: (1) living control, (2) killed in a microwave oven, and (3) perfused with a −1.5 MPa (10% w/w) mannitol solution. According to Canny's theory, the microwaved and mannitol curves should show cavitation and loss of conductance beginning at approximately −0.3 MPa because in both cases, the turgor pressure would be eliminated or substantially reduced compared to controls. We also tested the refilling capability of nonstressed stems where compensating pressure would be in full operation and compared this with dead stems with no compensating pressure. According to Canny's interpretation of vulnerability curves, the living stems should refill within 5 min. Results failed to support the compensating tissue theory because (a) all vulnerability curves were identical, reaching a −1.5 MPa threshold before substantial loss of conductance occurred, and (b) killed or living stems had equally slow refilling rates showing no significant increase in conductivity after 30 min. In consequence, the cohesion theory remains the most parsimonious explanation of xylem sap ascent in plants.     

A test of the maximum-power stimulus theory for strength

The main purpose was to test the hypothesis that the true force and power in weightlifting were related significantly to the strengthening stimulus. Secondary hypotheses were (a) slower, heavier weight training for strength would increase strength, not maximum power, (b) faster, lighter weight training for maximum power would increase maximum power, not strength and (c) there would be no significant difference between force = mass (F = m) and true force = mass multiplied by acceleration (F = ma) for arm weightlifting. Using an optical encoder, digital recorder and a data-logging computer on an arm weightlifting machine, F = m and F = ma were significantly different between 25% and 94%, contrary to published reports, but not at 100% of strength. A second-order polynomial equation predicted force, F = ma, as a multiple of the weight lifted, from the velocity of the lift with R2 = 0.997. A group was trained for strength and a matched group was trained for maximum power. The strength group gained significantly in maximum power and the power group gained significantly in strength and maximum power. Both groups gained significantly in velocity, but not force, at maximum power. The correlations between strength and maximum power were high (r = 0.95-0.98, P < 0.02), consistent (before and after training) and valid (gain in standard error of estimate of 6 N or 2% of strength). The evidence suggested that maximum power was the strength stimulus. The maximum-power stimulus theory may unify and simplify theories of response and adaptation of structure and function induced by muscle.     

Honeyeater foraging: A test of optimal foraging theory

Honeyeaters (Meliphagidae) were observed foraging for nectar from Lambertia formosa inflorescences, each of which has seven flowers. The frequency distribution of numbers of flowers probed per visit to an inflorescence was found to be bimodal, with one peak at two and the other at seven. It is hypothesized that this frequency distribution results from a rule of departure from inflorescences that maximizes the net rate of energy gain. Patterns of nectar distribution were determined for a large sample of inflorescences. In addition the extent to which the honeyeaters re-probe flowers during a visit to an inflorescence was estimated. From these data and from field measurements of the times required by the honeyeaters to perform the various foraging behaviours, computer simulations of honeyeater foraging were constructed. These simulations led in turn to optimal frequency distributions of numbers of flowers probed per inflorescence that were bimodal but had peaks at 1 and 7 instead of 2 and 7. Although the observed and predicted behaviour were consequently similar, the difference between them was nevertheless significant. This difference could have been due to the birds' transient occupancy of the study area.     

A new necessary condition for Turing instabilities

Reactivity (a.k.a initial growth) is necessary for diffusion driven instability (Turing instability). Using a notion of common Lyapunov function we show that this necessary condition is a special case of a more powerful (i.e. tighter) necessary condition. Specifically, we show that if the linearised reaction matrix and the diffusion matrix share a common Lyapunov function, then Turing instability is not possible. The existence of common Lyapunov functions is readily checked using semi-definite programming. We apply this result to the Gierer-Meinhardt system modelling regenerative properties of Hydra, the Oregonator, to a host-parasite-hyperparasite system with diffusion and to a reaction-diffusion-chemotaxis model for a multi-species host-parasitoid community.     

A Turing model with correlated random walk

 If in the classical Turing model the diffusion process (Brownian motion) is replaced by a more general correlated random walk, then the parameters describing spatial spread are the particle speeds and the rates of change in direction. As in the Turing model, a spatially constant equilibrium can become unstable if the different species have different turning rates and different speeds. Furthermore, a Hopf bifurcation can be found if the reproduction rate of the activator is greater than its rate of change of direction, and oscillating patterns are possible. Received 24 February 1995; received in revised form 6 September 1995     

Propagation of Turing patterns in a plankton model

The paper is devoted to a reaction-diffusion system of equations describing phytoplankton and zooplankton distributions. Linear stability analysis of the model is carried out. Turing and Hopf stability boundaries are found. Emergence of two-dimensional spatial structures is illustrated by numerical simulations. Travelling waves between various stationary solutions are investigated. Transitions between homogeneous in space stationary solutions and Turing structures are studied.     

Propagation of Turing patterns in a plankton model

The paper is devoted to a reaction–diffusion system of equations describing phytoplankton and zooplankton distributions. Linear stability analysis of the model is carried out. Turing and Hopf stability boundaries are found. Emergence of two-dimensional spatial structures is illustrated by numerical simulations. Travelling waves between various stationary solutions are investigated. Transitions between homogeneous in space stationary solutions and Turing structures are studied.     

A test of the karyotypic fissioning theory of primate evolution

Karyotypic fissioning theory has been put forward by a number of researchers as a possible driving force of mammalian evolution. Most recently, Giusto and Margulis (BioSystems, 13 (1981) 267–302) hypothesized that karyotypic fissioning best explains the evolution of Old World monkeys, apes, and humans. According to their hypothesis, hominoid karyotypes were derived from the monkey chromosome complement by just such such a fissioning event. That hypothesis is tested here by comparing the G-banded chromosomes of humans and great apes with eight species of Old World monkeys. Five submetacentric chromosomes between apes and monkeys have identical banding patterns and nine chromosomes share the same pericentric inversion. Such extensive karyological similarities are not in accodance with, or predicted by karyotypic fissioning. Apparently, karyotypic fissioning is an extremely uneconomical model of chromosomal evolution. The strong conservation of banding patterns sometimes involving the retention of identical chromosomes indicates that ancient linkages of genes have probably been maintained through many speciation events.     

A test of the stochastic theory of stem cell differentiation.

Stochastic theories of stem cell renewal are shown to predict turnover of intestinal crypts. While I found ample evidence of production of new crypts from direct in vivo studies in adult mice, I failed to find evidence of crypt loss. Thus, it would appear that the simple stochastic models may not provide an adequate theory of control of intestinal stem cell function.     

Turing bifurcations with a temporally varying diffusion coefficient

This paper is concerned with the possibility of Turing bifurcations in a reaction-diffusion system in which the diffusion coefficient of one species varies periodically in time. This problem was introduced and investigated numerically by Timm and Okubo (J. Math. Biol. 30, 307, 1992) in the context of predator-prey interactions in plankton populations. Here, I consider the simple case in which the temporal variation in diffusivity has a square-tooth form, alternating between two constant values, with a period that is long compared with the time scale of the kinetics. The analysis is valid for any set of reaction kinetics. I derive explicit expressions for the Floquet multipliers that determine the stability of the steady state, and thereby obtain the conditions for diffusion driven instability to occur. These conditions imply that, depending on the kinetics, the homogeneous equilibrium may be either more or less stable than when the diffusion coefficient is a constant equal to the mean of the variable diffusivity. I go on to consider the form of the solution when diffusion driven instability does occur, and I use perturbation theory to determine the effect of a small temporal variation in the diffusion coefficient on the spatial wavelength of the pattern that results from diffusion driven instability.     

Spatial pattern in catch rates: A test of economic theory

Gordon (1953,J. Fish. Res. Bd Can.10, 442–457) used economic theory to predict how catch rates, price and fishing costs should balance in a multi-area, open-access fishery. We use the data from the Tasmanian rock lobster fishery to test this theory. We find that, as prediced by theory, areas with higher monetary and non-monetary costs have consistently higher catch rates than areas with lower costs. We show that this theory also predicts that an increase in price would result in an overall increase in catch rate, and suggest that in fisheries with spatial variation in costs, catch rates may be determined as much by economic factors as biological ones.