Search

While the strength of sexual signals is important in mate attraction, the ability to accurately compare signals may also have a major effect on mate choice. Large distances between competitors may reduce competition, as accurate comparison of signals becomes harder. This may be advantageous to weak signallers and detrimental to stronger signallers. We create a mathematical model examining optimal distance from stronger competitors for sexual signallers and test its predictions using the common glow-worm Lampyris noctiluca. Female glow-worms are flightless and attract males by glowing. Males prefer the brightest female if two females are close to each other. Our model gave different predictions depending on whether searchers fly or not. The model and experiment showed that weak signallers should move away from competitors and strong signallers should move closer to weaker competitors when searchers fly. In contrast, the model predicted that the distance between competing signallers has no effect when searchers do not fly. This reveals an unexpected spatial competition between strong and weak signallers. We conclude that, while signal strength is important in sexual selection, location in relation to others is similarly important as ornamentation in determining the result of mate attraction.

The timing and intensity of plant reproduction vary due to internal and external factors. Although this variation has been widely studied in species exhibiting masting (intermittent synchronous reproduction), it has attracted less attention in nonmasting species. Here, we studied intra-individual variation in the flowering intensity and plant size of a nonmasting, rare terrestrial orchid, Cypripedium calceolus, using long-term monitoring data from three populations in Finland and two populations in Estonia. Flowering intensity and plant size showed 2-year cycles, indicating that reproduction and growth were regulated by past costs of reproduction and extensive clonal growth. In addition, flowering intensity and plant size were positively correlated with size from the previous year and were also affected by the weather conditions of spring and of the previous growing season. However, there was little synchrony among plants, suggesting that the climatic control of reproduction and growth is sufficiently low as to be masked by high annual variation in these two vital rates. Together, these results indicate that the reproduction and growth of C. calceolus depend on individual demographic history and past weather conditions and that intrinsic factors can also lead to cyclic fluctuation in reproduction in nonmasting species.

Theoretical ecologists have long sought to understand how the persistence of populations depends on the interactions between exogenous (biotic and abiotic) and endogenous (e.g., demographic and genetic) drivers of population dynamics. Recent work focuses on the autocorrelation structure of environmental perturbations and its effects on the persistence of populations. Accurate estimation of extinction times and especially determination of the mechanisms affecting extinction times is important for biodiversity conservation. Here we examine the interaction between environmental fluctuations and the scaling effect of the mean population size with its variance. We investigate how interactions between environmental and demographic stochasticity can affect the mean time to extinction, change optimal patch size dynamics, and how it can alter the often-assumed linear relationship between the census size and the effective population size. The importance of the correlation between environmental and demographic variation depends on the relative importance of the two types of variation. We found the correlation to be important when the two types of variation were approximately equal; however, the importance of the correlation diminishes as one source of variation dominates. The implications of these findings are discussed from a conservation and eco-evolutionary point of view.

The probability of, and time to, fixation of a mutation in a population has traditionally been studied by the classic Wright-Fisher model where population size is constant. Recent theoretical expansions have covered fluctuating populations in various ways but have not incorporated models of how the environment fluctuates in combination with different levels of density-compensation affecting fecundity. We tested the hypothesis that the probability of, and time to, fixation of neutral, advantageous and deleterious mutations is dependent on how the environment fluctuates over time, and on the level of density-compensation. We found that fixation probabilities and times were dependent on the pattern of autocorrelation of carrying capacity over time and interacted with density-compensation. The pattern found was most pronounced at small population sizes. The patterns differed greatly depending on whether the mutation was neutral, advantageous, or disadvantageous. The results indicate that the degree of mismatch between carrying capacity and population size is a key factor, rather than population size per se, and that effective population sizes can be very low also when the census population size is far above the carrying capacity. This study highlights the need for explicit population dynamic models and models for environmental fluctuations for the understanding of the dynamics of genes in populations.

Both the length of the season that is favourable for insect growth and reproduction and the number of generations emerging per season (voltinism) increase with decreasing latitude. Thus, time constraints on reproduction and juvenile development decrease with decreasing latitude, except where voltinism changes and time constraints suddenly increase as the season must be shared with one more generation. I studied the evolution of insect life histories in relation to time constraints from two perspectives: polymorphism and clinal variation. Life history polymorphism in seasonal environments was studied with the butterfly Pieris napi that has discrete life history strategies, and polymorphic natural populations. Experimental studies showed that asymmetric intraspecific larval competition and divergent timing of reproduction between the strategies may promote the maintenance of polymorphism. A simulation model showed that the divergent timing of reproduction between the strategies is sufficient to maintain polymorphism even in the absence of intraspecific competition. Clinal variation was studied empirically with four geometrid moths (Cabera exanthemata, Cabera pusaria, Chiasmia clathrata and Lomaspilis marginata) and generally in theory. Due to latitudinal saw-tooth variation in time constraints, traditional theory predicts a saw-tooth cline in body size and development time. A common garden experiment with the four geometrid moths did not support the traditional theory even when a saw-tooth cline in body size was found, suggesting that the theory is based on unrealistic assumptions. A theoretical analysis showed that reproductive effort should be high in populations under intense time constraints and low in populations experiencing no time constraints, resulting in a saw-tooth cline. In the four geometrid moths, support for these predictions was found, although the observed clinal variation deviated from the predicted pattern. The results imply that clinal var, Tiivistelmä Hyönteisten kasvu ja kehitys ovat pääsääntöisesti mahdollisia vain kesän aikana. Etelään päin mentäessä kesä pitenee, ja saman kesän aikana kehittyvien hyönteissukupolvien määrä kasvaa. Kesän pituus aiheuttaa lisääntymiseen ja toukkien kasvuun kohdistuvan aikarajoitteen, joka heikkenee etelään päin siirryttäessä. Aikarajoite kuitenkin tiukkenee siellä, missä yksi uusi sukupolvi ehtii juuri kehittymään saman kesän aikana, sillä kesä on nyt jaettava useamman sukupolven kesken. Väitöstyössä tarkastelin hyönteisten elinkierto-ominaisuuksien evoluutiota suhteessa aikarajoitteisiin sekä diskreetin että jatkuvan muuntelun näkökulmista. Diskreettiä muuntelua tutkin lanttuperhosella (Pieris napi), jolla esiintyy diskreettejä elinkiertostrategioita. Kokeellisesti osoitin, että toukkien välinen kilpailu on epäsymmetristä, mikä yhdessä eri elinkiertostrategioiden erilaisen lisääntymisen ajoittumisen kanssa voi ylläpitää diskreettiä muuntelua. Simulaatiomalli osoitti, että erilaiset elinkiertostrategiat voivat säilyä populaatiossa pelkästään niiden erilaisen lisääntymisen ajoittumisen ansiosta. Elinkierto-ominaisuuksien jatkuvaa muuntelua tutkin neljän mittariperhosen (Cabera exanthemata, Cabera pusaria, Chiasmia clathrata ja Lomaspilis marginata) avulla ja teoreettisesti yleisellä tasolla. Aikaisempi teoria ennustaa ruumiinkoon ja kehitysajan muuntelevan sahalaitakuvion mukaisesti siirryttäessä pohjoisesta etelään, koska aikarajoitteet muuntelevat samalla tavalla. Tämä teoria perustunee epärealistisiin oletuksiin, koska kokeelliset tulokset eivät tukeneet teoriaa silloinkaan, kun mittariperhosten ruumiinkoko muunteli ennustetulla tavalla. Teoreettinen tutkimus osoitti, että myös lisääntymispanostuksen tulisi muunnella sahalaitakuvion mukaisesti suhteessa kesän pituuteen siten, että se on korkeimmillaan siellä, missä aikarajoitteet ovat tiukat. Mittariperhosten tutkiminen antoi jossain määrin tukea tälle ennusteelle. Tulosten perusteella jatkuvaa maantieteellistä muu

The classical theory of the ideal free distribution (IFD) predicts that the spatial distribution of consumers should follow the distribution of the resources they depend on. Here, we study consumer-resource matching in a community context. Our model for the community is a food chain with three levels. We study whether the primary consumers are able to match resources both under predation risk and in its absence. Both prey and predators have varying degrees of knowledge of the global and local resource distribution. We present two versions of the model. In the "resource maximising" model, the consumers consider the availability of their resource only. In the "balancing" model, individual consumers minimise predation risk per unit of resource that they can gain access to. We show that both models can lead to perfect matching of consumers on resources and predators on consumers, assuming that individuals have full knowledge of the whole environment. However, when the consumers' information and freedom of movement are greater than those of the predators, then the predators generally undermatch the consumers. In the opposite case, we observe overmatching and high consumer movement rates. Furthermore, undermatching of predators on consumers tends to induce overmatching of consumers on resources.

Availability of resources is a limiting factor for many populations. Diminished resource availability due to intraspecific competition is expected to decrease the annual growth increments of individuals. We study an age-structured population model for individuals with indeterminate growth and annual reproduction; parameters of the model are chosen to characterize a population with life history similar to the Eurasian perch. Different variants of this model are analyzed, all of which have a potential for exhibiting non-equilibrium population fluctuations. We demonstrate that incorporating density-dependent individual growth into these models changes the dynamics of these populations by damping or even eradicating fluctuations in abundance and biomass. This finding offers an explanation for the observed stable dynamics of unperturbed perch populations. Further, density-dependent individual growth may also be a significant factor contributing to the conspicuous empirical rarity of non-equilibrium population dynamics in general.

Availability of resources is a limiting factor for many populations. Diminished resource availability due to intraspecific competition is expected to decrease the annual growth increments of individuals. We study an age-structured population model for individuals with indeterminate growth and annual reproduction; parameters of the model are chosen to characterize a population with life history similar to the Eurasian perch. Different variants of this model are analyzed, all of which have a potential for exhibiting non-equilibrium population fluctuations. We demonstrate that incorporating density-dependent individual growth into these models changes the dynamics of these populations by damping or even eradicating fluctuations in abundance and biomass. This finding offers an explanation for the observed stable dynamics of unperturbed perch populations. Further, density-dependent individual growth may also be a significant factor contributing to the conspicuous empirical rarity of non-equilibrium population dynamics in general.

The interpretation of ecological data has been greatly improved by bridging the gap between ecological and statistical models. The major challenge is to separate competing hypotheses concerning demography, or other ecological relationships, and environmental variability (noise). In this paper we demonstrate that this may be an arduous, if not impossible, task. It is the lack of adequate ecological theory, rather than statistical sophistication, which leads to this problem. A reconstruction of underlying ecological processes can only be done if we are certain of either the demographic or the noise model, which is something that can only be achieved by an improved theory of stochastic ecological processes. Ignoring the fact that this is a real problem may mislead ecologists and result in erroneous conclusions about the relative importance of endogenous and exogenous factors in natural ecosystems. The lack of correct model identification may also have far-reaching consequences for population management and conservation.

Availability of resources is a limiting factor for many populations. Diminished resource availability due to intraspecific competition is expected to decrease the annual growth increments of individuals. We study an age- structured population model for individuals with indeterminate growth and annual reproduction; parameters of the model are chosen to characterize a population with life history similar to the Eurasian perch. Different variants of this model are analyzed, all of which have a potential for exhibiting non-equilibrium population fluctuations. We demonstrate that by incorporating density-dependent individual growth into these models changes the dynamics of these populations by damping or even eradicating fluctuations in abundance and biomass. This finding offers an explanation for the observed stable dynamics of unperturbed perch populations. Further, density-dependent individual growth may also be a significant factor for contributing to the conspicuous empirical rarity of non-equilibrium population dynamics in general.

Availability of resources is a limiting factor for many populations. Diminished resource availability due to intraspecific competition is expected to decrease the annual growth increments of individuals. We study an age- structured population model for individuals with indeterminate growth and annual reproduction; parameters of the model are chosen to characterize a population with life history similar to the Eurasian perch. Different variants of this model are analyzed, all of which have a potential for exhibiting non-equilibrium population fluctuations. We demonstrate that by incorporating density-dependent individual growth into these models changes the dynamics of these populations by damping or even eradicating fluctuations in abundance and biomass. This finding offers an explanation for the observed stable dynamics of unperturbed perch populations. Further, density-dependent individual growth may also be a significant factor for contributing to the conspicuous empirical rarity of non-equilibrium population dynamics in general.

Availability of resources is a limiting factor for many populations. Diminished resource availability due to intraspecific competition is expected to decrease the annual growth increments of individuals. We study an age- structured population model for individuals with indeterminate growth and annual reproduction; parameters of the model are chosen to characterize a population with life history similar to the Eurasian perch. Different variants of this model are analyzed, all of which have a potential for exhibiting non-equilibrium population fluctuations. We demonstrate that by incorporating density-dependent individual growth into these models changes the dynamics of these populations by damping or even eradicating fluctuations in abundance and biomass. This finding offers an explanation for the observed stable dynamics of unperturbed perch populations. Further, density-dependent individual growth may also be a significant factor for contributing to the conspicuous empirical rarity of non-equilibrium population dynamics in general.

According to Fisherian seu allocation theory, parents that can adjust their offspring sex ratio in response to skews in population sex ratio will maximize their fitness over parents lacking this ability. There is good evidence that adaptive sex ratio adju, Addresses: Ranta E, Univ Helsinki, Dept Systemat & Ecol, Div Populat Biol, Integrat Ecol Unit, POB 17, FIN-00014 Helsinki, Finland. Univ Helsinki, Dept Systemat & Ecol, Div Populat Biol, Integrat Ecol Unit, FIN-00014 Helsinki, Finland. Univ Turku, Dept Bi

Positively autocorrelated red environmental noise is characterized by a strong dependence of expected sample variance on sample length. This dependence has to be taken into account when assessing extinction risk under red and white uncorrelated environmental noise. To facilitate a comparison between red and white noise, their expected variances can be scaled to be equal, but only at a chosen time scale. We show with a simple one-dimensional population dynamics model that the different but equally reasonable choices of the time scale yield qualitatively different results on the dependence of extinction risk on the colour of environmental noise: extinction risk might increase as well as decrease when the temporal correlation of noise increases.

We review the basic patterns of complex non-uniqueness in simple discrete-time population dynamics models. We begin by studying a population dynamics model of a single species with a two-stage, two-habitat life cycle. We then explore in greater detail two ecological models describing hostmacroparasite and hostparasitoid interspecific interactions. In general, several types of attractors, e.g. point equilibria vs. chaotic, periodic vs. quasiperiodic and quasiperiodic vs. chaotic attractors, may coexist in the same mapping. This non-uniqueness also indicates that the bifurcation diagrams, or the routes to chaos, depend on initial conditions and are therefore non-unique. The basins of attraction, defining the initial conditions leading to a certain attractor, may be fractal sets. The fractal structure may be revealed by fractal basin boundaries or by the patterns of self-similarity. The fractal basin boundaries make it more difficult to predict the final state of the system, because the initial values can be known only up to some precision. We conclude that non-unique dynamics, associated with extremely complex structures of the basin boundaries, can have a profound effect on our understanding of the dynamical processes of nature.

We review the basic patterns of complex non-uniqueness in simple discrete-time population dynamics models. We begin by studying a population dynamics model of a single species with a two-stage, two-habitat life cycle. We then explore in greater detail two ecological models describing hostmacroparasite and hostparasitoid interspecific interactions. In general, several types of attractors, e.g. point equilibria vs. chaotic, periodic vs. quasiperiodic and quasiperiodic vs. chaotic attractors, may coexist in the same mapping. This non-uniqueness also indicates that the bifurcation diagrams, or the routes to chaos, depend on initial conditions and are therefore non-unique. The basins of attraction, defining the initial conditions leading to a certain attractor, may be fractal sets. The fractal structure may be revealed by fractal basin boundaries or by the patterns of self-similarity. The fractal basin boundaries make it more difficult to predict the final state of the system, because the initial values can be known only up to some precision. We conclude that non-unique dynamics, associated with extremely complex structures of the basin boundaries, can have a profound effect on our understanding of the dynamical processes of nature.

Positively autocorrelated red environmental noise is characterized by a strong dependence of expected sample variance on sample length. This dependence has to be taken into account when assessing extinction risk under red and white uncorrelated environmental noise. To facilitate a comparison between red and white noise, their expected variances can be scaled to be equal, but only at a chosen time scale. We show with a simple one-dimensional population dynamics model that the different but equally reasonable choices of the time scale yield qualitatively different results on the dependence of extinction risk on the colour of environmental noise: extinction risk might increase as well as decrease when the temporal correlation of noise increases.

Characterizing population fluctuations and their causes is a major theme in population ecology. The debate is on the relative merits of density-dependent and density-independent effects. One paradigm (revived by the research on global warming and its relation to long-term population data) states that fluctuations in population densities can often be accounted for by external noise. Several empirical models have been suggested to support this view Mt followed this by assuming a given population skeleton dynamics (Ricker dynamics and second-order autoregressive dynamics) topped off with noise composed of low- and high-frequency components. Our aim was to determine to what extent the modulated population dynamics correlate with the noise signal. High correlations (with time-lag -1) were observed with both model categories in the region of stable dynamics, but not in the region of periodic or complex dynamics. This finding is not very sensitive to low-frequency noise. High correlations throughout the entire range of dynamics are only achievable when the impact of the noise is very high. Fitted parameter values of skeleton dynamics modulated with noise are prone to err substantially. This casts doubt as to what degree the underlying dynamics are any more recognizable after being modulated hv the external noise.

Positively autocorrelated red environmental noise is characterized by a strong dependence of expected sample variance on sample length. This dependence has to be taken into account when assessing extinction risk under red and white uncorrelated environmental noise. To facilitate a comparison between red and white noise, their expected variances can be scaled to be equal, but only at a chosen time scale. We show with a simple one-dimensional population dynamics model that the different but equally reasonable choices of the time scale yield qualitatively different results on the dependence of extinction risk on the colour of environmental noise: extinction risk might increase as well as decrease when the temporal correlation of noise increases.

We review the recent theoretical developments explaining the evolution of age-schedules of reproduction in animals with indeterminate growth. Indeterminate growth, i.e. growth that continues past maturation and may continue until the end of life, is characteristic for a large number of invertebrate taxa (e.g. clams, cladocerans and crayfish) and 'lower' vertebrate taxa (e.g. fish, amphibians, lizards and snakes). Many plants also exhibit indeterminate growth, and we liberally include studies focused on plants when they can be interpreted in terms of animal life histories. We focus on different measures used to determine the fittest life histories, on indeterminate growth as a problem of resource allocation and on the effects of environment to the evolution of the resource allocation schemes.

In the 1970s ecological research detected chaos and other forms of complex dynamics in simple population dynamics models, initiating a new research tradition in ecology. However, the investigations of complex population dynamics have mainly concentrated on single populations and not on higher dimensional ecological systems. Here we report a detailed study of the complicated dynamics occurring in a basic discrete-time model of hostparasitoid interaction. The complexities include (a) non-unique dynamics, meaning that several attractors coexist, (b) basins of attraction (defined as the set of the initial conditions leading to a certain type of an attractor) with fractal properties (pattern of self-similarity and fractal basin boundaries), (c) intermittency, (d) supertransients, (e) chaotic attractors, and (f) transient chaos. Because of these complexities minor changes in parameter or initial values may strikingly change the dynamic behavior of the system. All the phenomena presented in this paper should be kept in mind when examining and interpreting the dynamics of ecological systems.

We review the recent theoretical developments explaining the evolution of age-schedules of reproduction in animals with indeterminate growth. Indeterminate growth, i.e. growth that continues past maturation and may continue until the end of life, is characteristic for a large number of invertebrate taxa (e.g. clams, cladocerans and crayfish) and 'lower' vertebrate taxa (e.g. fish, amphibians, lizards and snakes). Many plants also exhibit indeterminate growth, and we liberally include studies focused on plants when they can be interpreted in terms of animal life histories. We focus on different measures used to determine the fittest life histories, on indeterminate growth as a problem of resource allocation and on the effects of environment to the evolution of the resource allocation schemes.

In the 1970s ecological research detected chaos and other forms of complex dynamics in simple population dynamics models, initiating a new research tradition in ecology. However, the investigations of complex population dynamics have mainly concentrated on single populations and not on higher dimensional ecological systems. Here we report a detailed study of the complicated dynamics occurring in a basic discrete-time model of hostparasitoid interaction. The complexities include (a) non-unique dynamics, meaning that several attractors coexist, (b) basins of attraction (defined as the set of the initial conditions leading to a certain type of an attractor) with fractal properties (pattern of self-similarity and fractal basin boundaries), (c) intermittency, (d) supertransients, (e) chaotic attractors, and (f) transient chaos. Because of these complexities minor changes in parameter or initial values may strikingly change the dynamic behavior of the system. All the phenomena presented in this paper should be kept in mind when examining and interpreting the dynamics of ecological systems.

Frequency-dependent selection is so fundamental to modern evolutionary thinking that everyone `knows' the concept. Yet the term is used to refer to different types of selection. The concept is well defined in the original context of population genetics theory, which focuses on short-term evolutionary change. The original concept becomes ambiguous, however, when used in the context of long-term evolution, where density dependence becomes essential. Weak and strong frequency dependence, as distinguished in this article, refer to two very different forms of selection.

Frequency-dependent selection is so fundamental to modern evolutionary thinking that everyone `knows' the concept. Yet the term is used to refer to different types of selection. The concept is well defined in the original context of population genetics theory, which focuses on short-term evolutionary change. The original concept becomes ambiguous, however, when used in the context of long-term evolution, where density dependence becomes essential. Weak and strong frequency dependence, as distinguished in this article, refer to two very different forms of selection.

Frequency-dependent selection is so fundamental to modern evolutionary thinking that everyone interested in evolutionary biology 'knows' the concept. It is even so fundamental that many authors of textbooks do not bother to define it. Yet it turns out that different authors (and sometimes even one and the same author) use the term to refer to different types of selection. In this paper we try to uncover the sources of this confusion. The concept is fairly well defined in the original concept of population genetical theory, which focuses on short-term evolutionary change, and basically ignores density-dependence. The problems start when the original concept is used in the context of long-term evolution, in which density-dependence is essential: without density dependence, lines of descent either die out or explode on the relevant time scales. With density-dependence, the definition of frequency-dependent selection, in the form in which it is usually given, becomes ambiguous. The concept of weak and strong frequency-dependence distinguish between two very different forms of frequency-dependent selection occurring in populations which experience density-dependent population regulation.

We study the evolution of age at maturity in a semelparous life history with two age classes. An individual may either breed in the first year of its life and die, or delay breeding to the second year. In this setting a mixed strategy means that a fraction of the individual's offspring breed in the first possible breeding event, while the remaining fraction delay breeding. Current theory seems to imply that mixed strategies are not evolutionarily stable strategies (ESSs) under a steady-state population dynamical regime. We show that a two-dimensional feedback environment may allow the evolution of mixed age at maturity. Furthermore, different phenotypes need to perceive the environment differently. The biological reasoning behind these conditions is different resource usage or predation pressure between two age classes. Thus, the conventional explanations for the occurrence of mixed strategies in natural populations, environmental stochasticity or complex dynamics, are not needed.

We study the evolution of age at maturity in a semelparous life history with two age classes. An individual may either breed in the first year of its life and die, or delay breeding to the second year. In this setting a mixed strategy means that a fraction of the individual's offspring breed in the first possible breeding event, while the remaining fraction delay breeding. Current theory seems to imply that mixed strategies are not evolutionarily stable strategies (ESSs) under a steady-state population dynamical regime. We show that a two-dimensional feedback environment may allow the evolution of mixed age at maturity. Furthermore, different phenotypes need to perceive the environment differently. The biological reasoning behind these conditions is different resource usage or predation pressure between two age classes. Thus, the conventional explanations for the occurrence of mixed strategies in natural populations, environmental stochasticity or complex dynamics, are not needed.

Frequency-dependent selection is so fundamental to modern evolutionary thinking that everyone interested in evolutionary biology 'knows' the concept. It is even so fundamental that many authors of textbooks do not bother to define it. Yet it turns out that different authors (and sometimes even one and the same author) use the term to refer to different types of selection. In this paper we try to uncover the sources of this confusion. The concept is fairly well defined in the original concept of population genetical theory, which focuses on short-term evolutionary change, and basically ignores density-dependence. The problems start when the original concept is used in the context of long-term evolution, in which density-dependence is essential: without density dependence, lines of descent either die out or explode on the relevant time scales. With density-dependence, the definition of frequency-dependent selection, in the form in which it is usually given, becomes ambiguous. The concept of weak and strong frequency-dependence distinguish between two very different forms of frequency-dependent selection occurring in populations which experience density-dependent population regulation.

Frequency-dependent selection is so fundamental to modern evolutionary thinking that everyone interested in evolutionary biology 'knows' the concept. It is even so fundamental that many authors of textbooks do not bother to define it. Yet it turns out that different authors (and sometimes even one and the same author) use the term to refer to different types of selection. In this paper we try to uncover the sources of this confusion. The concept is fairly well defined in the original concept of population genetical theory, which focuses on short-term evolutionary change, and basically ignores density-dependence. The problems start when the original concept is used in the context of long-term evolution, in which density-dependence is essential: without density dependence, lines of descent either die out or explode on the relevant time scales. With density-dependence, the definition of frequency-dependent selection, in the form in which it is usually given, becomes ambiguous. The concept of weak and strong frequency-dependence distinguish between two very different forms of frequency-dependent selection occurring in populations which experience density-dependent population regulation.

We study the evolution of age-at-maturity in a semelparous life history with two age-classes. An individual may breed in the first year of its life and die, or delay breeding to the second year. In this setting a mixed strategy means that a fraction of the individual's offspring breed in the first possible breeding event, while the remaining fraction delay breeding. Current theory seems to imply that mixed strategies are not evolutionarily stable strategies (ESS) under a steady state population dynamical regime. We show that a two-dimensional feedback environment may allow the evolution of mixed age-at-maturity. Furthermore, different phenotypes need to perceive the environment differently. The biological reasoning behind these conditions is different resource usage or predation pressure between two age-classes. Thus, the conventional explanations for the occurrence of mixed strategies in natural populations, environmental stochasticity or complex dynamics, are not needed.

We study the evolution of age-at-maturity in a semelparous life history with two age-classes. An individual may breed in the first year of its life and die, or delay breeding to the second year. In this setting a mixed strategy means that a fraction of the individual's offspring breed in the first possible breeding event, while the remaining fraction delay breeding. Current theory seems to imply that mixed strategies are not evolutionarily stable strategies (ESS) under a steady state population dynamical regime. We show that a two-dimensional feedback environment may allow the evolution of mixed age-at-maturity. Furthermore, different phenotypes need to perceive the environment differently. The biological reasoning behind these conditions is different resource usage or predation pressure between two age-classes. Thus, the conventional explanations for the occurrence of mixed strategies in natural populations, environmental stochasticity or complex dynamics, are not needed.

We study the evolution of age-at-maturity in a semelparous life history with two age-classes. An individual may breed in the first year of its life and die, or delay breeding to the second year. In this setting a mixed strategy means that a fraction of the individual's offspring breed in the first possible breeding event, while the remaining fraction delay breeding. Current theory seems to imply that mixed strategies are not evolutionarily stable strategies (ESS) under a steady state population dynamical regime. We show that a two-dimensional feedback environment may allow the evolution of mixed age-at-maturity. Furthermore, different phenotypes need to perceive the environment differently. The biological reasoning behind these conditions is different resource usage or predation pressure between two age-classes. Thus, the conventional explanations for the occurrence of mixed strategies in natural populations, environmental stochasticity or complex dynamics, are not needed.

We consider optimal cooperation in transboundary air pollution abatement among several countries under incomplete information, i.e., local information only on marginal emission abatement costs and damage costs. Directions of emission abatement in each country are determined that generate a succession of emissions programs shown to converge to an economic optimum. A cost sharing scheme, that results from appropriately designed international transfers, guarantees that the individual costs of all parties are nonincreasing along the path towards the optimum. A version of Maler's (1989) ''acid rain game'' is used for a numerical application.

In this paper we analyse a fishery resource exploitation model in which a single firm or a cartel has leased the rights to manage the resources independently. Two variables, resource level and the capital level, determine the dynamics of the resource system. The leasing contract includes an incentive for the agent to maintain the resource level high. The main result is that sole-agent resource management and efficiency of the resource use do not necessarily imply that the fishery is stabilized at a unique steady state level. Instead, the optimal resource exploitation may lead to periodic capital investments in fishing vessels and gear which in turn causes cycles in the resource economy. We show analytically that nonzero discount rate and low capital depreciation rate both favor the conditions under which periodic optimal solutions may occur. Simulation results related to a Baltic herring fishery are used to illustrate the results.

In this paper we analyse a fishery resource exploitation model in which a single firm or a cartel has leased the rights to manage the resources independently. Two variables, resource level and the capital level, determine the dynamics of the resource system. The leasing contract includes an incentive for the agent to maintain the resource level high. The main result is that sole-agent resource management and efficiency of the resource use do not necessarily imply that the fishery is stabilized at a unique steady state level. Instead, the optimal resource exploitation may lead to periodic capital investments in fishing vessels and gear which in turn causes cycles in the resource economy. We show analytically that nonzero discount rate and low capital depreciation rate both favor the conditions under which periodic optimal solutions may occur. Simulation results related to a Baltic herring fishery are used to illustrate the results.