Hawks, doves, and mixed-symmetry games.

The hawk-dove game has proved to be an important tool for understanding the role of aggression in social interactions. Here, the game is presented in a more general form (GHD) to facilitate analyses of interactions between individuals that may differ in "size", where size is interpreted as a surrogate for resource holding power. Three different situations are considered, based on the availability and use of information that interacting individuals have about their sizes: the classical symmetric case, in which no information about sizes is used, the asymmetric case, in which the individuals know their relative sizes and thus their chances of prevailing in combat, and a mixed-symmetry case, in which each individual only knows its own size (or only knows its opponent's size). I describe and use some recently developed methods for multitype games-evolutionary games involving two or more categories of players. With these methods and others, the evolutionarily stable strategies (ESSs) that emerge for the three different cases are identified and compared. A proof of the form and uniqueness of the ESS for the mixed-symmetry case is presented. In this situation, one size category at most can play a mixed strategy; larger individuals are aggressive and smaller individuals are not. As the number of size categories approaches infinity and the size distribution becomes continuous, there is a threshold size, above which all individuals are aggressive, and below which they are not.

Solving the complementarity dilemma: evolving strategies for simultaneous hermaphroditism.

We introduce a complementarity dilemma, a two-player, binary response game in which the playoffs are highest when the two players respond differently. Using the classifier EvA, we determine the evolutionary dynamics and structure of strategies that evolve to play an iterated version of this game, and we relate the results to the evolution of major types of sexual reproduction, particularly simultaneous hermaphroditism. We find that complementarity strategies consistently evolve under a broad range of conditions, but that those most consistent with the simultaneous hermaphroditism can predominate only when a substantial cost of repeatedly adopting the female role is imposed. The cost is analogous to the fecundity reduction to be expected when a single partner must repeatedly produce the eggs in sexual reproduction.

Evolving cooperation: the role of individual recognition.

To evaluate the role of individual recognition in the evolution of cooperation, we formulated and analyzed genetic algorithm model (EvCo) for playing the Iterated Prisoner's Dilemma (IPD) game. Strategies compete against each other during each generation, and successful strategies contribute more of their attributes to the next generation. Each strategy is encoded on a 'chromosome' that plays the IPD, responding to the sequences of most recent responses by the interacting individuals (chromosomes). The analysis reported in this paper considered different memory capabilities (one to five previous interactions), pairing continuities (pairs of individuals remain together for about one, two, five, or 1000 consecutive interactions), and types of individual recognition (recognition capability was maximal, nil, or allowed to evolve between these limits). Analysis of the results focused on the frequency of mutual cooperation in pairwise interactions (a good indicator of overall success in the IPD) and on the extent to which previous responses by the focal individual and its partner were associated with the partner's identity (individual recognition). Results indicated that a fixed, substantial amount of individual recognition could maintain high levels of mutual cooperation even at low pairing continuities, and a significant but limited capability for individual recognition evolved under selection. Recognition generally increased mutual cooperation more when the recent responses of individuals other than the current partner were ignored. Titrating recognition memory under selection using a fitness cost suggested that memory of the partner's previous responses was more valuable than memory of the focal's previous responses. The dynamics produced to date by EvCo are a step toward understanding the evolution of social networks, for which additional benefits associated with group interactions must be incorporated.

Evolving cooperation: strategies as hierarchies of rules.

To better understand the evolutionary dynamics of cooperative strategies and their behavioral components in populations subjected to individual selection, a new classifier-system model (EvA) was developed. In EvA, strategies are encoded as algorithms composed of a fixed number of rules relating behavior remembered from the recent past to the present action to be taken. Each algorithm is the genotype of an individual within the population, and these individuals play the Iterated Prisoner's Dilemma game against each other to determine their relative contributions to the next generation. The rules are hierarchical, with more specific rules, when they apply, overriding more general rules. Maximal mutual cooperation was obtained when interaction sequences for each pair of individuals playing the game were long, when only the immediately preceeding plays in the game were remembered, and when the algorithms consisted of an intermediate number of rules (20-40). Under other conditions, mutual cooperation was reduced--even becoming less frequent than would be expected if behavior were completely random, with very few rules per algorithm. The algorithms that evolved could sometimes be recognized as Tit-For-Tat, Simpleton, or other well-known strategies; but when memory of several previous events was invoked by algorithms based on a substantial number of rules, the resulting strategies were considerably more complex. This approach shows considerable promise for providing a much deeper understanding of how cooperation may evolve in nature. Moreover, classifier-system models could prove to be broadly useful for addressing many optimization questions in biology.

Avoiding erroneously high levels of detection in combinations of semi-independent tests : An application to testing for density dependence.

A randomization procedure is proposed which allows statistical tests to be combined into a single test to maintain specified and acceptable levels of false detection. This method was applied to the problem of detecting density dependence in 135 unpublished time-series (of ≥10 generations) from insect populations, and to simulated density-dependent and density-independent data, so that the correctness of observed levels of detection from the published data could be verified. To allow the application of the randomization procedure to Bulmer's (1975) tests and Varley and Gradwell's (1960) test, these were recast as randomization tests. The randomization procedure was tested with 39 combinations of tests for density dependence (and limitation/attraction); it generally producedcombined tests with levels of detection that were intermediate between detection levels of the constituent tests (and hence was limite by these). The specified rate of false detection (5%) was never exceeded (by more than 1%) when combined tests were applied to time-series from a random-walk model. Two different combinations of tests produced levels of detection from the published time-series which were slightly greater than their constituent tests when they were combined into single tests. These were the randomized form of Bulmer's (1975) first test with the tests of Pollard et al. (1987) and Reddingius and den Boer (1989) with the randomized form of Bulmer's second test. The combination of Bulmer's first and Pollard et al.'s test produced a greater level of detection (21.5%) than any other single test or combination of tests. These results were confirmed by the analysis of modelled density dependent data. Although the increase in power of combinations of tests over single tests is small with the data we used, the combined tests (listed above) had rates of detection that were less influenced by the form of data (of two forms of density-dependent data) than were their constituent tests. Hence, it appears that the combined tests are of greater generality than single test statistics. The method presented here for combining several statistical tests into a single randomization test is applicable in many other areas of ecology where we wish to apply several tests and take the most probable result of these; and if the tests being conducted are, or can be expressed as, randomization tests.

Density dependence, boundedness, and attraction: detecting stability in stochastic systems.

By analogy with deterministic stability, the stability of stochastic ecological systems can be viewed as a tendency for population densities to avoid dynamic boundaries (i.e. boundedness) or to approach a dynamic attractor (i.e. attraction). At the population level, these two views generate predictions consistent with density dependence. I therefore devised two new statistical tests of attraction, the "random-walk attraction test" and the "randomized attraction test"; I then used them successfully, along with randomization techniques that detect boundedness and two autocorrelation methods, to test for density dependence in published sequences of population densities. The attraction tests identify the apparent attractor, the band of densities toward which density tends to shift between generations. Locating the apparent attractor can generate a prediction of the next direction of density change; for data from a dragonfly assemblage, about 80% of these predictions were correct. From the single-population tests, I also developed two multispecies tests of attraction (the multispecies random-walk and randomized attraction tests) and two multispecies tests of boundedness (the multispecies permutation and randomization tests). These detected attraction and boundedness in the dragonfly assemblage and attraction in a collection of laboratory fruitfly populations. An evaluation of the statistical power of the new density attraction tests indicates a strong dependence on the sequence length n and on the number of populations m: power increases with n and particularly with m. Nevertheless, detecting attraction becomes likely even in populations with strong linear density-dependence only with n>30 or for shorter sequences in multispecies assemblages.

Variability and stability of a dragonfly assemblage.

Using 12 years of monthly sweep-net data from 9-12 permanent sampling stations, we evaluated the variability and stability of the dragonfly assemblage in Bays Mountain Lake (northeastern Tennessee, USA). To do this, we adopted the view that a stable assemblage (i.e. one capable of recovering quickly from disturbances) should have low variability (i.e. high persistence of taxa, relatively constant densities, and high rank concordance), except with disturbances more intense and frequent than those in this system. Moreover, a stable assemblage should contain populations that exhibit density dependence and should tend to remain within a restricted range of densities (boundedness), shifting toward a narrow density interval between generations (attraction). To test some specific predictions derived from these views, we analyzed 12-year sequences of larval population sizes just before the onset of emergence for the 13 dominant dragonfly taxa in the lake. Most but not all of the 13 dominant taxa persisted during the 12-year period. Variabilities of taxon densities, measured as standard deviations across generations of log-transformed population sizes, were representative of the broad range for other invertebrates but somewhat higher than those of terrestrial vertebrates. There were fewer than three significant abundance trends over the 12-year period, and rank concordance between generations was high (W=0.716). Density dependence was detected among some of the dragonfly density sequences by five different methods. Using techniques presented in the companion paper, we found strong indications of both boundedness and attraction in the whole assemblage. We conclude tentatively that an assemblage consisting of at least 11 of the 13 dominant dragonfly taxa at Bays Mountain Lake has low-to-moderate variability and is stable, but that the complete 29-species assemblage is probably not stable at the scale of this single lake. We emphasize the need for coupling such long-term descriptive analyses with studies of responses to experimental disturbances.

Intraspecific interference among larvae in a semivoltine dragonfly population.

This study focuses on ways that the size distribution of individuals influences the types and intensities of competitive interactions within a population of aquatic arthropod predators. Three field experiments and one laboratory experiment were designed to test for feeding interference, interference mortality, and dispersal effects within and between larval size classes of the primarily semivoltine dragonfly Tetragoneuria cynosura in Bays Mountain Lake. One field experiment documented the temporal pattern of colonization of large-mesh cylinders by the small, first-year-class larvae during a 30-day period; the results are consistent with passive (density-independent) colonization. A second field experiment examined the effect of large, second-year-class larvae at densities of 1 or 3 per cylinder (14 or 42 m-2) on colonization by small larvae; this colonization was inhibited at the high density of large larvae. In the laboratory experiment, when larvae of the two size-classes were together in the same aquarium, small larvae moved around less than when by themselves (dispersal inhibition). Thus the inhibition of colonization observed in the field may result from interference mortality, rather than from a flight response to the presence of larger conspecifics.To evaluate this interpretation, the third field experiment measured the in-situ functional response of large larvae to each other and to their small conspecific prey. Results suggest a type 1 (linear) functional response, with feeding inteference among large larvae. Moreover, the interference mortality inflicted by larger larvae on smaller conspecifics was apparently more intense on larger individuals within the small size-class. Taken together, the three field experiments and a statistical power analysis show how colonization and interference interact to determine the local density of small larvae, and why such interference effects are difficult to detect experimentally in the field.