The evolution of cooperation by negotiation in a noisy world.

Cooperative interactions among individuals are ubiquitous despite the possibility of exploitation by selfish free riders. One mechanism that may promote cooperation is 'negotiation': individuals altering their behaviour in response to the behaviour of others. Negotiating individuals decide their actions through a recursive process of reciprocal observation, thereby reducing the possibility of free riding. Evolutionary games with response rules have shown that infinitely many forms of the rule can be evolutionarily stable simultaneously, unless there is variation in individual quality. This potentially restricts the conditions under which negotiation could maintain cooperation. Organisms interact with one another in a noisy world in which cooperative effort and the assessment of effort may be subject to error. Here, we show that such noise can make the number of evolutionarily stable rules finite, even without quality variation, and so noise could help maintain cooperative behaviour. We show that the curvature of the benefit function is the key factor determining whether individuals invest more or less as their partner's investment increases, investing less when the benefit to investment has diminishing returns. If the benefits of low investment are very small then behavioural flexibility tends to promote cooperation, because negotiation enables cooperators to reach large benefits. Under some conditions, this leads to a repeating cycle in which cooperative behaviour rises and falls over time, which may explain between-population differences in cooperative behaviour. In other conditions, negotiation leads to extremely high levels of cooperative behaviour, suggesting that behavioural flexibility could facilitate the evolution of eusociality in the absence of high relatedness.

An adaptive response to uncertainty can lead to weight gain during dieting attempts.

BACKGROUND AND OBJECTIVES: Peoples' attempts to lose weight by low calorie diets often result in weight gain because of over-compensatory overeating during lapses. Animals usually respond to a change in food availability by adjusting their foraging effort and altering how much energy reserves they store. But in many situations the long-term availability of food is uncertain, so animals may attempt to estimate it to decide the appropriate level of fat storage. METHODOLOGY: We report the results of a conceptual model of feeding in which the animal knows whether food is currently abundant or limited, but does not know the proportion of time, there will be an abundance in the long-term and has to learn it. RESULTS: If the food supply is limited much of the time, such as during cycles of dieting attempts, the optimal response is to gain a lot of weight when food is abundant. CONCLUSIONS AND IMPLICATIONS: This implies that recurring attempts to diet, by signalling to the body that the food supply is often insufficient, will lead to a greater fat storage than if food was always abundant. Our results shed light on the widespread phenomenon of weight gain during weight cycling and indicate possible interventions that may reduce the incidence of obesity.

A dynamic framework for the study of optimal birth intervals reveals the importance of sibling competition and mortality risks.

Human reproductive patterns have been well studied, but the mechanisms by which physiology, ecology and existing kin interact to affect the life history need quantification. Here, we create a model to investigate how age-specific interbirth intervals adapt to environmental and intrinsic mortality, and how birth patterns can be shaped by competition and help between siblings. The model provides a flexible framework for studying the processes underlying human reproductive scheduling. We developed a state-based optimality model to determine age-dependent and family-dependent sets of reproductive strategies, including the state of the mother and her offspring. We parameterized the model with realistic mortality curves derived from five human populations. Overall, optimal birth intervals increase until the age of 30 after which they remain relatively constant until the end of the reproductive lifespan. Offspring helping each other does not have much effect on birth intervals. Increasing infant and senescent mortality in different populations decreases interbirth intervals. We show that sibling competition and infant mortality interact to lengthen interbirth intervals. In lower-mortality populations, intense sibling competition pushes births further apart. Varying the adult risk of mortality alone has no effect on birth intervals between populations; competition between offspring drives the differences in birth intervals only when infant mortality is low. These results are relevant to understanding the demographic transition, because our model predicts that sibling competition becomes an important determinant of optimal interbirth intervals only when mortality is low, as in post-transition societies. We do not predict that these effects alone can select for menopause.

Natural selection can favour 'irrational' behaviour.

Understanding decisions is the fundamental aim of the behavioural sciences. The theory of rational choice is based on axiomatic principles such as transitivity and independence of irrelevant alternatives (IIA). Empirical studies have demonstrated that the behaviour of humans and other animals often seems irrational; there can be a lack of transitivity in choice and seemingly irrelevant alternatives can alter decisions. These violations of transitivity and IIA undermine rational choice theory. However, we show that an individual that is maximizing its rate of food gain can exhibit failure of transitivity and IIA. We show that such violations can be caused because a current option may disappear in the near future or a better option may reappear soon. Current food options can be indicative of food availability in the near future, and this key feature can result in apparently irrational behaviour.

The ecological rationality of state-dependent valuation.

Laboratory studies on a range of animals have identified a bias that seems to violate basic principles of rational behavior: a preference is shown for feeding options that previously provided food when reserves were low, even though another option had been found to give the same reward with less delay. The bias presents a challenge to normative models of decision making (which only take account of expected rewards and the state of the animal at the decision time). To understand the behavior, we take a broad ecological perspective and consider how valuation mechanisms evolve when the best action depends upon the environment being faced. We show that in a changing and uncertain environment, state-dependent valuation can be favored by natural selection: Individuals should allow their hunger to affect learning for future decisions. The valuation mechanism that typically evolves produces the kind of behavior seen in standard laboratory tests. By providing an insight into why learning should be affected by the state of an individual, we provide a basis for understanding psychological principles in terms of an animal's ecology.

Seasonal dispersal of pests: one surge or two?

Many agricultural pest species occur in seasonal metapopulations with a period of asexual reproduction. We use evolutionary theory to predict timing of dispersal for such species, and identify four sequential phases: no dispersal, dispersal from initially occupied patches, dispersal from later colonized patches, and no dispersal. The third type of phase occurs only when reproductive rates are relatively high; we speculate that this could explain why among aphids there can be either one or two waves of dispersal during a season, depending on the species. Our model also explains other features of aphid biology, including a summer crash in colony size, and a decline in the number of colonies towards the end of each reproductive season. The presence of an additional surge of dispersal becomes more likely as season length increases, and does not require further evolution. This could have profound implications for pest management during future climatic warming.

Time-resolved XANES speciation studies of chromium on soils during simulated contamination.

Time-resolved synchrotron X-ray absorption near edge structure (XANES) spectroscopy was used to study changes of chromium speciation in soils upon soil-water interaction. The time resolution was 30-45 min. In a flow-column apparatus operated near the synchrotron beamline, two different types of soil were treated with potassium-dichromate solution, and soil samples were taken and directly analysed by XANES. The results provide insight into different equilibrium times of a few hours, depending on the type of soil. The XANES speciation analyses, based on a model comprising insoluble Cr(III) and Cr(VI) compounds, show how the fate of Cr species on soils can be followed close to real-time. Since the method allowed the soils to be investigated close to real-time, sampling in the field and preservation before analysis were made redundant. This study benefits the development of corresponding in situ remediation techniques.

Comparison of the Hanbury Brown-Twiss effect for bosons and fermions.

Fifty years ago, Hanbury Brown and Twiss (HBT) discovered photon bunching in light emitted by a chaotic source, highlighting the importance of two-photon correlations and stimulating the development of modern quantum optics. The quantum interpretation of bunching relies on the constructive interference between amplitudes involving two indistinguishable photons, and its additive character is intimately linked to the Bose nature of photons. Advances in atom cooling and detection have led to the observation and full characterization of the atomic analogue of the HBT effect with bosonic atoms. By contrast, fermions should reveal an antibunching effect (a tendency to avoid each other). Antibunching of fermions is associated with destructive two-particle interference, and is related to the Pauli principle forbidding more than one identical fermion to occupy the same quantum state. Here we report an experimental comparison of the fermionic and bosonic HBT effects in the same apparatus, using two different isotopes of helium: (3)He (a fermion) and 4He (a boson). Ordinary attractive or repulsive interactions between atoms are negligible; therefore, the contrasting bunching and antibunching behaviour that we observe can be fully attributed to the different quantum statistics of each atomic species. Our results show how atom-atom correlation measurements can be used to reveal details in the spatial density or momentum correlations in an atomic ensemble. They also enable the direct observation of phase effects linked to the quantum statistics of a many-body system, which may facilitate the study of more exotic situations.

Degenerate Bose-Fermi mixture of metastable atoms.

We report the observation of simultaneous quantum degeneracy in a dilute gaseous Bose-Fermi mixture of metastable atoms. Sympathetic cooling of helium-3 (fermion) by helium-4 (boson), both in the lowest triplet state, allows us to produce ensembles containing more than 10(6) atoms of each isotope at temperatures below 1 microK, and achieve a fermionic degeneracy parameter of T/TF = 0.45. Because of their high internal energy, the detection of individual metastable atoms with subnanosecond time resolution is possible, permitting the study of bosonic and fermionic quantum gases with unprecedented precision. This may lead to metastable helium becoming the mainstay of quantum atom optics.

Simultaneous magneto-optical trapping of a boson-fermion mixture of metastable helium atoms.

We simultaneously confine fermionic metastable 3He atoms and bosonic metastable 4He atoms in a magneto-optical trap. The trapped clouds, containing up to 1.5 x 10(8) atoms of each isotope, are characterized by measuring ions and metastable helium atoms escaping from the trap. Optical pumping of 3He atoms to a nontrapped hyperfine state is investigated and it is shown that large atom numbers can be confined without additional repumping lasers. Unique possibilities for quantum degeneracy experiments with mixtures of spin-polarized metastable 3He and 4He atoms are indicated.

A dynamic model of hypothermia as an adaptive response by small birds to winter conditions.

We present a dynamic programming model which is used to investigate hypothermia as an adaptive response by small passerine birds in winter. The model predicts that there is a threshold function of reserves during the night, below which it is optimal to enter hypothermia, and above which it is optimal to rest. This threshold function decreases during the night, with a particularly sharp drop at the end of the night, representing the time and energy costs associated with returning to normal body temperature. The results of the model emphasise the trade-off between energy and predation, not just between foraging options, but also between foraging during the day and entering hypothermia at night. The value of being able to use hypothermia represents not just energy savings, but also reduced predation risk due to changes in the optimal foraging strategy. Conditions which give a high value of hypothermia are short photoperiod, variable food supply, low temperatures, poor and scarce food supplies.

A dynamic game-theoretic model of parental care.

We present a model in which members of a mated pair decide whether to care for their offspring or desert them. There is a breeding season of finite length during which it is possible to produce and raise several batches of offspring. On deserting its offspring, an individual can search for a new mate. The probability of finding a mate depends on the number of individuals of each sex that are searching, which in turn depends upon the previous care and desertion decisions of all population members. We find the evolutionarily stable pattern of care over the breeding season. The feedback between behaviour and mating opportunity can result in a pattern of stable oscillations between different forms of care over the breeding season. Oscillations can also arise because the best thing for an individual to do at a particular time in the season depends on future behaviour of all population members. In the baseline model, a pair splits up after a breeding attempt, even if they both care for the offspring. In a version of the model in which a pair stays together if they both care, the feedback between behaviour and mating opportunity can lead to more than one evolutionarily stable form of care.

Incorporating rules for responding into evolutionary games.

Evolutionary game theory is concerned with the evolutionarily stable outcomes of the process of natural selection. The theory is especially relevant when the fitness of an organism depends on the behaviour of other members of its population. Here we focus on the interaction between two organisms that have a conflict of interest. The standard approach to such two-player games is to assume that each player chooses a single action and that the evolutionarily stable action of each player is the best given the action of its opponent. We argue that, instead, most two-player games should be modelled as involving a series of interactions in which opponents negotiate the final outcome. Thus we should be concerned with evolutionarily stable negotiation rules rather than evolutionarily stable actions. The evolutionarily stable negotiation rule of each player is the best rule given the rule of its opponent. As we show, the action chosen as a result of the negotiation is not the best action given the action of the opponent. This conclusion necessitates a fundamental change in the way that evolutionary games are modelled.

A general technique for computing evolutionarily stable strategies based on errors in decision-making.

Realistic models of contests between animals will often involve a series of state-dependent decisions by the contestants. Computation of evolutionarily stable strategies for such state-dependent dynamic games are usually based on damped iterations of the best response map. Typically this map is discontinuous so that iterations may not converge and even if they do converge it may not be clear if the limiting strategy is a Nash equilibrium. We present a general computational technique based on errors in decision making that removes these computational difficulties. We show that the computational technique works for a simple example (the Hawk-Dove game) where an analytic solution is known, and prove general results about the technique for more complex games. It is also argued that there is biological justification for inclusion of the types of errors we have introduced.

Currencies for foraging based on energetic gain.

We carry out a theoretical investigation of the behavior of a foraging animal that maximizes either the net amount of energy obtained (self-feeding) or the amount of energy delivered to another animal such as its young or to a store (provisioning). Using an novel graphical approach, we derive general results concerning the effects of constraints on the amount of energy the animal can spend or acquire. In the context of an animal that is provisioning, that is, both feeding itself and delivering energy to a given location, we establish a general relationship between the best foraging option when feeding itself and the best option to use when delivering energy. Our results extend and unify previous results in this area.

State-dependent life histories.

Life-history theory is concerned with strategic decisions over an organism's lifetime. Evidence is accumulating about the way in which these decisions depend on the organism's physiological state and other components such as external circumstances. Phenotypic plasticity may be interpreted as an organism's response to its state. The quality of offspring may depend on the state and behaviour of the mother. Recent theoretical advances allow these and other state-dependent effects to be modelled within the same framework.

State-dependent life history evolution in Soay sheep: dynamic modelling of reproductive scheduling.

Adaptive decisions concerning the scheduling of reproduction in an animal's lifetime, including age at maturity and clutch or litter size, should depend on an animal's body condition or state. In this state-dependent case, we are concerned with the optimization of sequences of actions and so dynamic optimization techniques are appropriate. Here we show how stochastic dynamic programming can be used to study the reproductive strategies and population dynamics of natural populations, assuming optimal decisions. As examples we describe models based upon field data from an island population of Soay sheep on St. Kilda. This population shows persistent instability, with cycles culminating in high mortality every three or four years. We explore different assumptions about the extent to which Soay ewes use information about the population cycle in making adaptive decisions. We compare the observed distributions of strategies and population dynamics with model predictions; the results indicate that Soay ewes make optimal reproductive decisions given that they have no information about the population cycle. This study represents the first use of a dynamic optimization life history model of realistic complexity in the study of a field population. The techniques we use are potentially applicable to many other populations, and we discuss their extension to other species and other life history questions.

Evolutionary paths in strategy space: an improvement algorithm for life-history strategies.

Life-history strategies are analysed using a matrix population model. Within this framework an organism can be characterized at a particular time by a suitable state variable such as age or size, or both. A life-history strategy specifies the action an organism takes in each state. Given a life-history strategy one can find the reproductive value of the various states under this strategy. One can then ask whether an organism following the strategy chooses actions to maximize the reproductive value of itself and its offspring in one year's time. It is shown that if it does not, then a simple procedure identifies a life-history strategy with higher fitness. This strategy-improvement result leads to a necessary and sufficient condition by which (globally) optimal life-history strategies in natural populations can be recognized. We can define two life-history strategies to be one step away from each other if they specify the same actions at all states but one. Using this concept one can then define a topology on the phenotypic space of all life-history strategies. The topology taken together with a fitness measure defines the landscape of "strategy space". Results on strategy improvement are used to show that, in contrast to the landscapes usually envisaged for genotype space, strategy space is unimodal: there are no local optima other than global optima, and from every strategy one can reach a global optimum by a non-descending path.

Genetic algorithms and evolution.

The genetic algorithm (GA) as developed by Holland (1975, Adaptation in Natural and Artificial Systems. Ann Arbor: University of Michigan Press) is an optimization technique based on natural selection. We use a modified version of this technique to investigate which aspects of natural selection make it an efficient search procedure. Our main modification to Holland's GA is the subdividing of the population into semi-isolated demes. We consider two examples. One is a fitness landscape with many local optima. The other is a model of singing in birds that has been previously analysed using dynamic programming. Both examples have epistatic interactions. In the first example we show that the GA can find the global optimum and that its success is improved by subdividing the population. In the second example we show that GAs can evolve to the optimal policy found by dynamic programming.

Markers of serious illness in infants under 6 months old presenting to a children's hospital.

Six hundred and eighty two assessments were performed on 641 babies under 6 months of age who presented to the emergency department of the Royal Children's Hospital, Melbourne, to try and determine the best markers of serious illness in young infants. Detailed, specific questions that quantified a baby's functional response to illness gave the most useful information. As a group, the six most common predictive symptoms of serious illness were: taking less than half the normal amount of feed over the preceding 24 hours, breathing difficulty, having less than four wet nappies in the preceding 24 hours, decreased activity, drowsiness, and a history of being both pale and hot. The presence of the corresponding sign on examination increased the predictive value of the symptom by 10-20%. Specific, highly predictive (though less common) signs included moderate to severe chest wall recession, respiratory grunt, cold calves, and a tender abdomen. A list of low, medium, and high risk symptoms has been constructed and the five measurements that were most useful in predicting serious illness in young infants have been detailed.