Evolutionary dynamics of biological auctions

Many scenarios in the living world, where individual organisms compete for winning positions (or resources), have properties of auctions. Here we study the evolution of bids in biological auctions. For each auction, n individuals are drawn at random from a population of size N. Each individual makes a bid which entails a cost. The winner obtains a benefit of a certain value. Costs and benefits are translated into reproductive success (fitness). Therefore, successful bidding strategies spread in the population. We compare two types of auctions. In “biological all-pay auctions”, the costs are the bid for every participating individual. In “biological second price all-pay auctions”, the cost for everyone other than the winner is the bid, but the cost for the winner is the second highest bid. Second price all-pay auctions are generalizations of the “war of attrition” introduced by Maynard Smith. We study evolutionary dynamics in both types of auctions. We calculate pairwise invasion plots and evolutionarily stable distributions over the continuous strategy space. We find that the average bid in second price all-pay auctions is higher than in all-pay auctions, but the average cost for the winner is similar in both auctions. In both cases, the average bid is a declining function of the number of participants, n. The more individuals participate in an auction the smaller is the chance of winning, and thus expensive bids must be avoided.     

Optimization under frequency-dependent selection

We consider a model of frequency-dependent selection, which we refer to as the Wildcard Model. A variety of more specific models, representing quite diverse biological situations, are covered by the Wildcard Model as particular cases. Two very different particular models that are subsumed by the Wildcard Model are the game theoretically motivated two-phenotype model of Lessard [Lessard, S.,1984. Evolutionary dynamics in frequency-dependent two-phenotype models, Theor. Popul. Biol. 25, 210-234], and the model of selection on a continuous trait due to intraspecific competition of Bürger [Bürger, R., 2005. A multilocus analysis of intraspecific competition and stabilizing selection on a quantitative trait. J. Math. Biol. 50 (4), 355-396] and Schneider [Schneider, K.A., 2006. A multilocus-multiallele analysis of frequency-dependent selection induced by intraspecific competition. J. Math. Biol. 52 (4), 483-523]. Both these models have been shown in the past to have a global Lyapunov function (LF) under appropriate genetic assumptions. We show that (i) the Wildcard Model in continuous time for a single multiallelic locus, or for multiple multiallelic loci in linkage equilibrium, has a global LF, of which the Lessard and Bürger-Scheneider LF are special cases in spite of their widely different biological interpretations; (ii) the LF of the Wildcard Model can be derived from an LF previously identified for a model of density- and frequency-dependent selection due to Lotka-Volterra competition, with one locus, multiple alleles, multiple species and continuous-time dynamics [Matessi, C., Jayakar, S.D., 1981. Coevolution of species in competition: A theoretical study. Proc. Natl. Acad. Sci. USA, 78 (2, part2), 1081-1084]. We extend the LF with density and frequency dependence to the multilocus case with linkage-equilibrium dynamics. As a possible application of our results, the optimization principle we established can be used as a tool in the study of long-term evolution of various models subsumed by the Wildcard Model based on explicit short-term dynamics.     

Variable valuations and voluntarism under group selection: An evolutionary public goods game

In biological systems, as in human society, competing social groups may depend heavily on a small number of volunteers to advance the group’s prospects. This phenomenon can be understood as the solution to an evolutionary public goods game, in which a beneficent individual or a small number of individuals may place the highest value on group success and contribute the most to achieving it while profiting very little. Here we demonstrate that this type of solution, recently recognized in the social sciences, is evolutionarily stable and evolves in evolutionary simulations sensitive to alternative ways of gaining fitness beyond the present social group. The public goods mechanism may help explain biological voluntarism in cases like predator inspection and foraging on behalf of non-relatives and may determine the extent of commitment to group welfare at different intensities of group selection.     

Combined effects of host quality and local mate competition on sex allocation inLariophagus distinguendus

Summary Many parasitoid wasps are known to adjust sex ratio in response to either local mate competition (LMC) or host quality. Nevertheless, few studies have investigated the combined effects of these two factors on sex allocation. The sex allocation pattern inLariophagus distinguendus, a parasitoid of granary weevil larvae, is contrasted to the expectations of Werren's (1984) model combining LMC and host quality. Several predictions of the model are confirmed, but others are not. Sex ratio on both large and small hosts declines with proportion of small hosts attacked in a manner consistent with the model. However, when only one host size is parasitized, sex ratio is not independent of that host size, as predicted by the model. Various possibilities for the deviation between expected and observed are discussed. A partial LMC/host quality model is developed which allows for some matings outside the natal patch, and predictions of this model conform more closely to the pattern observed inL. distinguendus. Finally, the application of parasitoid studies to basic questions in evolutionary ecology is briefly discussed.     

ALLOCATION TO ATTRACTIVE STRUCTURES IN ANIMAL-POLLINATED FLOWERS

An optimal allocation model was developed for the evolutionarily stable size of attractive structures of flowers (ESA) in animal-pollinated plants. It was assumed that a plant can change the sizes of attractive and sexual structures of a flower and the size and the number of flowers. In the absence of constraints on flower size, the ESA should not depend on the frequency of self-fertilization or the sexuality of plants. However, with constraints on flower size, the ESA decreases with increasing self-fertilization, except in special cases, and it is possible that males have a larger or a smaller ESA than females. Thus, differences in self-fertilization and sexuality alone cannot explain the differences in allocation among nondomesticated plants. In addition, attractive structures can contribute more to male or female function depending on the cost of gamete production, pollination efficiency for pollen and ovules, and pollinator availability.     

On sex allocation and selfing in higher plants

Summary Sex allocation (male allocation/female allocation) as a function of selfing rate is studied in the wild riceOryza perennis. Using dry weight measures, the male/female ratio is linearly related to the selfing rate. This linear relationship may have a fairly radical interpretation in terms of current sex allocation theory. It suggests that the intermediate selfing rates are themselves maintained by a form of frequency dependence. In particular, the linearity suggests: (i) the relative fitness of a selfed versus outcrossed offspring decreases with increased selfing; (ii) in equilibrium, a selfed offspring is approximately half as fit as an outcrossed offspring; (iii) the frequency dependence, being the opposite of that proposed in most selfing models, may result from the same forces thought to be involved in the maintenance of sex itself, and (iv) the position of the fitted line contains information about the plant's use of wind pollination for male reproduction. It suggests that wind shows much less mixing of pollen than previously assumed, and/or that there are severe morphological constraints on pollen presentation. The above interpretations are clearly speculative and tentative. Possible problems in the analysis, and some alternatives for data interpretation are discussed.     

Euthyroid Sick Syndrome as a Prognostic Indicator of COVID-19 Pulmonary Involvement,Associated With Poorer Disease Prognosis and Increased Mortality

ObjectiveThe prevalence of euthyroid sick syndrome (ESS) and its association with the prognosis of COVID-19 and mortality in patients with lung involvement in COVID-19 have not yet been elucidated.MethodsClinical and laboratory data of patients with COVID-19 with or without ESS were collected retrospectively and analyzed on admission. All subjects were admitted to the Department of Internal Diseases and Clinical Pharmacology at Bieganski Hospital between December 2020 and April 2021.ResultsIn total, 310 medical records of patients with COVID-19 were analyzed retrospectively. Among 215 enrolled patients, 82 cases of ESS were diagnosed. The patients with ESS had higher pro-inflammatory factor levels, longer hospitalizations, and a higher risk of requiring high-flow nasal oxygen therapy or intubation than the patients without ESS. The Kaplan-Meier curve indicated that the patients with ESS had a lower probability of survival when computed tomography showed ≤50% parenchymal involvement compared with that in patients without ESS. However, no differences in mortality were noted in those with more than 50% parenchymal involvement. The survival curve showed that ESS was associated with a higher risk of mortality during hospitalization.ConclusionESS is closely associated with a poor prognosis, including longer hospitalizations, more frequent intubation, transfer to the intensive care unit, and a higher mortality rate in patients with COVID-19. ESS is a potential prognostic predictor of survival, regardless of lung involvement in COVID-19.     

Nonlinear frequency-dependent selection at a single locus with two alleles and two phenotypes

 The paper investigates the discrete frequency dynamics of two phenotype diploid models where genotypic fitness is an exponential function of the expected payoff in the matrix game. Phenotypic and genotypic equilibria are defined and their stability compared to frequency-dependent selection models based on linear fitness when there are two possible phenotypes in the population. In particular, it is shown that stable equilibria of both types can exist in the same nonlinear model. It is also shown that period-doubling bifurcations emerge when there is sufficient selection in favor of interactions between different phenotypes. Received: 22 October 1998     

Red Queens and ESS: the coevolution of evolutionary rates

Summary The Red Queen principle states that a set of interacting species reaches an evolutionary equilibrium at which all their rates of coevolution exactly balance each other. The lag-load model, which is one way of searching for Red Queens, has, by itself, previously predicted that they do not exist. But this model has assumed that infinite maladaptedness is possible. The lag-load model is improved by assuming that once the lag load of all but one species is determined, so is that of the final species. This assumption eliminates the possibility of infinite maladaptedness. Its result is to allow the lag-load model to yield Red Queen coevolution. It does this whether or not speciation and extinction rates are included. Thus the lag-load model is harmonized with the earlier Red Queen model derived from studies of predation.Because of the intercorrelation of phenotypic traits, the predatory model concluded that the eventual stable rate of coevolution must be zero (except for intermittent bursts after some correlation or compromise is successfully broken). Another model that predicts stable coevolutionary rates of zero is that of evolutionarily stable strategies (ESS).Red Queen assumes that the more extreme a phenotypic trait is, the better it is, and that there are no constraints on the growth of such a phenotypic trait value. Such traits are the key to the Red Queen prediction of progressive coevolution. ESS models make no such assumptions. Eliminating unbounded traits from the model of predator-victim evolution changed its prediction from progressive coevolution to stasis. Before this paper, no model had dealt simultaneously with both unbounded and constrained traits.To handle both sorts of phenotypic traits at the same time in the same model, we abandoned lag load as a measure of evolutionary rate (lag loads do not uniquely determine phenotype). Instead, we used the traditional assumption that rate is proportional to the slope of the adaptive landscape. A model, relying on continuous evolutionary game theory, was developed and simulated under various conditions in two or three species sets, with up to five independent traits coevolving simultaneously. The results were: (1) there was always a set of equilibrium densities eventually achieved by coevolution; if the population interaction represented by this stable coevolutionary state is also stable, then the system should persist whether it evolves further or not; (2) whenever traits were present which were unbounded and best at their most extreme values, then a Red Queen emerged; (3) whenever traits were present which were correlated with each other or constrained below infinity, then an ESS emerged; (4) if both types were present, both results occurred: Red Queen in the unbounded traits and ESS in the constrained ones.Because unbounded traits may not exist, the Red Queen may have no domain. But the domain of ESS is real. ESS should lead to the evolutionary pattern called punctuated equilibrium. The changes in design rules which punctuate stasis should lead to an ever-expanding independence of traits from each other, i.e. to more and more refined differentiation. A single set of design rules which governs a set of species is called a fitness-generating function. Such functions may help to define the concepts of adaptive zone and ecological guild.     

On the changing concept of evolutionary population stability as a reflection of a changing point of view in the quantitative theory of evolution

 Eighteen different terms, currently employed to define various concepts of evolutionary stability in population dynamics are mentioned in this paper. Most of these terms are used in different connotations and even different meanings by different authors. On the other hand, different terms are often employed by different authors to define quite the same concept. Twenty-five years ago there was only one, well-defined, concept of stability, universally recognized in the field. In this paper I will try to relate the recent confusion, concerning concepts of population stability, with a more serious, though not that well-recognized, confusion in the modern analytic approach to population dynamics and quantitative evolution. Concepts of population stability will be examined in relation to each other on the one hand and, on the other hand, in relation to two dichotomies regarding the dynamic processes to which they correspond: Short-term versus long-term processes and processes concerning phenotypic changes versus process concerning genotypic changes. A hopefully more consistent use of the current terminology is suggested. Received 15 August 1993; received in revised form 15 September 1994