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Isolation-by-distance (IBD) is a widely used model explaining population structure and how gene flow decreases with increasing distance. It is biologically intuitive that populations which rarely exchange individuals should drift apart genetically. However, the model is based on the assumptions that populations are large, equal in size and stable over time — conditions that are unlikely to occur in natural conditions. The model has been challenged in the past, for example, in the light of metapopulations or variance in reproductive success. However, an appraisal of the assumption of a large and stable population size per se is lacking. We investigate the robustness of the results concerning IBD patterns when smaller and fluctuating population sizes, or differences in population size are allowed. Through computer simulations we show that allowing for different population sizes and random fluctuations lead to unpredictable patterns regarding the results concerning gene flow and IBD. A pattern of IBD could be the result of high gene flow or no gene flow at all, depending on how populations differ in size and how they fluctuate. Adding environmental noise (white, red and blue noise corresponding to random, positive and negative autocorrelation respectively) gives even more unpredictable results concerning patterns of IBD. Our results have important implications for genetic and conservation research. Interpreting an IBD pattern, or lack thereof, is not as easy as earlier thought and needs to be more thoroughly explored.

Linkage between environmental variability and population renewal processes is assumed invariable in standard population models. We explored adaptive, density-dependent population dynamics in a setting where population consists of individuals differing in location of their optimum performance relative to a stochastic and autocorrelated environmental variable, such as temperature, humidity or salinity. Relative growth rates of phenotypes are determined by a Gaussian unimodal function of the environmental variable, which also has a unimodal distribution. Adaptive dynamics causes a significant increase in mean population growth performance and decreases its variance. Population growth fluctuates more rapidly, i.e. has a blue-shifted spectrum. This also causes a blue-shift in density-dependent population dynamics in a wide range of population growth rates and autocorrelation of the environment. The blue-shift is most pronounced when the breadth of environmental response is moderately smaller that the breadth of environmental fluctuations. The causes of the blue-shift are discussed. The blue-shift caused by adaptive dynamics is in contrast with views that evolutionary processes redden population time series, i.e. cause slow fluctuations, due to slow changes in population properties. Mean genetic variance is maximised in rapidly fluctuating blue and white noise environments, and when genotype performance breadth is small. In contrast, genotype diversity is maximised in slowly fluctuating red environments and in populations with large performance breadth. Genetic variance and genetic diversity also have marked temporal fluctuations. Temporal variability of genetic variance increases with noise redness and small response breadth. However, genetic diversity is maximised in slightly reddened environments and narrow performance breadth populations. That genetic variance and diversity are affected by the spectrum of environmental noise and also fluctuate temporally, suggest that models assuming constant amount of genetic variability (equilibrium variance) may not be successful in predicting the consequences of environmental changes.

We assessed how non-linear biological responses to environmental noise, or “noise filtering”, impact the spectra of density-dependent population dynamics, and the correlation between noise and population dynamics. The noise was assumed to affect population growth rate in a discrete-time population model by Hassell [J. Anim. Ecol. 44 (1975) 283–295] where the population growth rate was linked to the environment with an optimum type filter. When compared to unfiltered noise, the filtered noise can distort the stationary distribution of population values. The optimum type filter can make cyclic population dynamics more regular and low population values can become more frequent or rare depending on the strength of density dependence. Filtering can cause blue shifted and red shifted population dynamics and determine the strength of correlation between environmental noise and population size. In most cases, optimum type filtering makes linear correlation between population dynamics and noise weaker. The filter effect on population spectra and noise versus population correlation is sensitive to changes in population model parameters, the location where noise hits the filter, and noise colour.

Seed bank is a plant life history strategy against the unpredictability of the biotic and the abiotic environment. We simulated competition between a seed banking and a non-banking morph of an annual plant. A constant fraction of the banker morph seeds was allocated to the seed bank, where they had a constant mortality and germination rate. All surviving seeds of the non-banker morph germinated in the next generation. The seedlings of both morphs experienced similar density-dependent mortality. Whether one of the morphs wins or the morphs coexist was evaluated from parameter space plots and statistically with logistic regression analysis. All parameters of the model had a significant, nonlinear effect on the persistence of the morphs, supporting our approach of numerically covering a wide range of parameter values. The seed production of a focal morph increased its survival and decreased the survival of the other morph. Otherwise, the morphs showed opposite response to changes in the model parameters. The banker morph was usually the winning strategy when it had a higher seed production than the non-banker morph. The banker morph benefitted from high germination probability, while the non-banker benefitted from high allocation to seed bank and high seed mortality. The coexistence of the morphs was inhibited by high banker morph seed production and seed mortality and promoted by high values of all other parameters. The system showed complex dynamics when banking was the winning strategy or the morphs coexisted. In addition, a part of the parameter space where the non-banker morph wins showed complex dynamics. Our results suggest that seed banking is a beneficial strategy if seed number is increased consequently, e.g. due to a decreased seed size. If banking decreases seed number, the non-banker morph wins or the two morphs coexist.

Research on the evolution of life histories addresses the topic of fitness trade-offs between semelparity (reproducing once in a lifetime) and iteroparity (repeated reproductive bouts per lifetime). Bulmer (1994) derived the relationship v+P(A)

Evidence from wildlife and human populations indicates that conditions during early development can have marked effects on the subsequent performance of individuals and cohorts. Likewise, the effects of maternal and, more generally, parental environments can be transferred among individuals between generations. These delayed life-history effects are found consistently and suggestions have been made that they can be one source of both variability and of delayed density dependence in population dynamics. Assessments of several different time series indicate that population variability and delayed density dependence are common and that understanding the mechanisms giving rise to them is crucial for the interpretation and application of such models to basic and applied research. Therefore, it is necessary to assess the different ways in which history in the life history might give rise to variability and delayed density dependence in population dynamics. Here, we build on recent appraisals of the pervasive influence of past environmental conditions on current and future fitness and link the details of these life-history studies to classic features of population dynamics.

In social foraging, scroungers take a disproportionately large share of the food found relative to their own food-searching efforts, while producers find more food than they manage to monopolize. We present a model of social foraging acknowledging the finder's advantage and foraging role asymmetries among individuals but incorporating the possibility that producers and scroungers differ in vigilance level and in vulnerability to predators. This allows simultaneous examination of both foraging benefits and anti-predatory aspects of grouping behaviour. Instead of seeking for equal payoff conditions, we first look for groups in which foraging character combinations and anti-predatory properties of producers and scroungers minimize the phenotype-specific predation hazard over food-intake rate, Ri/Ii, that is, fixed phenotype Ri/Ii minima. In the second approach, we allow individuals to change their foraging status to achieve lower Ri/Ii and look for combinations where it no longer pays for either producers or scroungers to change their roles, that is, evolutionarily stable group compositions, ESS. Various character combinations allow the phenotype-specific minima. In most cases, however, producers' and scroungers' minima are achievable only in different group compositions. The ESS combinations of producers and scroungers deviate widely from those combinations yielding phenotype-specific minima of Ri/Ii. If individuals are allowed to be flexible in adopting either a producer or a scrounger role, ESS group compositions will emerge, even though they are more expensive for both producers and scroungers in terms of Ri/Ii than group compositions yielding the phenotype-specific Ri/Ii minima. Copyright 1998 The Association for the Study of Animal Behaviour Copyright 1998 The Association for the Study of Animal Behaviour.

The producer–scrounger model of Barnard & Sibly (1981,Anim. Behav.,29,543–550) predicts that at a certain ratio of producers and scroungers in a foraging group the payoff curves for individuals of the two phenotypes intercept. At this point all the group members obtain equal payoffs. In this paper, the original model is elaborated further by allowing individuals to differ not only in their food-finding abilities but also in their abilities to compete for the food once it is found. As in Barnard & Sibly's original model foraging individuals are assumed to share information about the whereabouts of food patches and to benefit from patches found by others. Here it is determined under which combinations of searching and sharing characters food intake rate in mixed-phenotype groups would be equal for producing and scrounging individuals. In the present model the payoffs are much affected by both the finder's advantage (the fraction of prey available only to the finder of the food-patch) and the combination of the foraging characters of the two phenotypes. Generally the intake rate of producers increases with their presence in the group and with increases in the finder's advantage. Our model suggests that the equal payoffs arise only when the relative food-searching and competitive abilities of producers and scroungers fall within a narrow range of options acknowledging also the finder's advantage. Moreover, such combinations are predicted to be unstable if only foraging benefits are called for in group formation, this being a common feature of social foraging models incorporating foraging role asymmetries.

The relationship between fish yield, water quality and fishing effort was explored in 70 Finnish lakes. The total yield (kg ha−1 yr−1) was also split to species level (11 species). Fishing effort was estimated by the number of fishermen (fishermen km−2). The principal components of water quality variables were extracted. The first component comprised total nitrogen and phosphorus, water colour and oxygen saturation; the second was an association of pH, alkalinity and conductivity. Together they retained about 77% of the variation in the original data. The best single predictor for the total fish yield was the number of fishermen (R2 = 0.47), but also the second principal component entered as a variable in a stepwise regression model (R2 = 0.53). No regional differences were found, so the model is potentially valid for the whole country. However, the spread of the data around the model was considerable; close to 50% of the variation in yield remained unexplained. At the species level, fishing effort was needed as a variable in six models (in four of them as the first variable entering the model) and water quality in five models (four times as the first variable). The variation of yield explained by these models ranged from 21% to 49%. Generally, water quality was less important in determining the yield than fishing effort. This was confirmed by partitioning out the effect of effort variables from the correlation between yield and water quality. No obvious improvements in the coefficients were observed.

We examined the relationship between water quality and fish catch in 80 small Finnish lakes. Generally, fishing effort and gear may vary considerably among lakes; therefore, the detection of any relationship between water quality and fish catch may be hampered. To avoid this bias, fish in the present study were trapped with a standardised gill net (catch refers to the pooled biomass of trapped fish, catch per unit effort (CPUE). Water quality was assessed by measuring lake-specific values of pH, calcium, dissolved and total aluminium, conductivity, alkalinity and water colour. From these data, we extracted two principal components, together they retained 78% of the variation in the original data. Despite our efforts to minimise noise in the catch data, we could not find any predictive relationship between water quality and total biomass of fish. We conclude that in Finnish lakes it is difficult, if not impossible, to predict the lake-specific fish catch based on water quality. However, even with the present data there were differences in the total catch of fish originating from lakes with diverse values along the first principal component (a gradient composed of pH, calcium, conductivity and alkalinity). Lakes in the low end averaged a catch of 6.4 kg, while those at the high end averaged 9.2 kg. This was due to roach having increasing catches along the gradual transition from acid to neutral lakes.

One of the paradigms in the management of freshwater fish resources is that the annual yield is a function of water quality. We attempted to predict the yield of seven fish species (vendace, whitefish, perch, pike, burbot, roach and id) in 83 Northern Finnish lakes based on 16 variables of water quality. In the first step of our analysis, we demonstrate that the species have somewhat differing water quality requirements. This justifies the search for empirical models which could potentially be used to predict the yield of the species based on water quality of the lakes. In the pursuit of the predictive models, we used stepwise regression analysis in two differing ways. First, with a forward stepping method we attempted to find the best predictor combination out of the 16 water quality variables. The success was poor; only with perch did water conductivity fulfil the minimum criteria of a variable to be included in a regression model. However, even in this case the predictive power of the model remained poor ( R 2 = 0.06). Second, we began with a full regression model including the 16 water quality variables and also six variables characterising fishing effort (traps ha −1 ) in the study lakes. From the total of 22 variables, we removed the variables which were not needed in the regression model with a stepwise elimination method. The results were clear cut. In no case were water quality variables powerful enough to remain in the model. For six species, variables of fishing effort were accepted into the model (vendace gill nets for vendace, gill nets for whitefish and burbot, weirs for perch and id, and number of fishermen for pike). The coefficients of determination in these models were ∼ 50%. In roach, none of the 22 variables was powerful enough to be used in a predictive model.

A dynamic multi-period game theory model is developed to study evolutionary stable scanning strategies of birds foraging in flocks. Scanning, while foraging, is carried out to detect attacking predators. In our model there is a chance that birds are killed by predators during foraging days. After each loss of a flock mate the remaining birds face the following foraging day in a smaller flock. The model has non-unique solutions. The evolutionary stable scanning rates may be constant over the foraging season, or they may show a monotonic decreasing trend with time. The former ESS solution does not depend on the future survival probabilities, and is independent of the future flock dynamics. Hence, the scanning rates depend on the current flock size only. The latter ESS solution is interpreted as follows. A loss of a flock mate decreases the future survival of each remaining bird. Hence, the birds increase their scanning rates to take care of their flock mates and to face the future predator attacks in a bigger flock. The choice between the ESS solutions depends on the behavior of the birds at the end of the foraging season. The scanning rates depend on the behavior of the predators.

The relationship between annual fish catch, fishing effort and water quality in 155 small (area 46–6500 ha) lakes originating from three different drainage areas in North-eastern Finland is studied. The three first principal components explain 70% of the variation in the original 12 water quality variables. Attempts are made to predict lake-specific yield with the help of the principal components. No common statistical model can be found for the three drainage areas. In all three drainage areas annual yield correlates positively with the fishing effort. Because one has to know beforehand the lake-specific effort this model has no practical applications in fisheries management. A common predictive model for the fish catch in these lakes was the positive relationship between the logarithm of lake area and the logarithm of catch per trap, and this holds even when lakes with the most effective traps are excluded. The most efficient way to predict the lake, specific value in fisheries terms is to regress (log) fish catch on (log) lake area. This model gives a good fit on all three drainage areas. Values of the predictor variable, lake area, are reliably estimated and there is also not much annual variation. This makes the empirical relationship between lake area and fish catch a rather simple but effective tool in lake management applications.