Constrained growth flips the direction of optimal phenological responses among annual plants.

Phenological changes among plants due to climate change are well documented, but often hard to interpret. In order to assess the adaptive value of observed changes, we study how annual plants with and without growth constraints should optimize their flowering time when productivity and season length changes. We consider growth constraints that depend on the plant's vegetative mass: self-shading, costs for nonphotosynthetic structural tissue and sibling competition. We derive the optimal flowering time from a dynamic energy allocation model using optimal control theory. We prove that an immediate switch (bang-bang control) from vegetative to reproductive growth is optimal with constrained growth and constant mortality. Increasing mean productivity, while keeping season length constant and growth unconstrained, delayed the optimal flowering time. When growth was constrained and productivity was relatively high, the optimal flowering time advanced instead. When the growth season was extended equally at both ends, the optimal flowering time was advanced under constrained growth and delayed under unconstrained growth. Our results suggests that growth constraints are key factors to consider when interpreting phenological flowering responses. It can help to explain phenological patterns along productivity gradients, and links empirical observations made on calendar scales with life-history theory.

Phenology of two interdependent traits in migratory birds in response to climate change.

In migratory birds, arrival date and hatching date are two key phenological markers that have responded to global warming. A body of knowledge exists relating these traits to evolutionary pressures. In this study, we formalize this knowledge into general mathematical assumptions, and use them in an ecoevolutionary model. In contrast to previous models, this study novelty accounts for both traits-arrival date and hatching date-and the interdependence between them, revealing when one, the other or both will respond to climate. For all models sharing the assumptions, the following phenological responses will occur. First, if the nestling-prey peak is late enough, hatching is synchronous with, and arrival date evolves independently of, prey phenology. Second, when resource availability constrains the length of the pre-laying period, hatching is adaptively asynchronous with prey phenology. Predictions for both traits compare well with empirical observations. In response to advancing prey phenology, arrival date may advance, remain unchanged, or even become delayed; the latter occurring when egg-laying resources are only available relatively late in the season. The model shows that asynchronous hatching and unresponsive arrival date are not sufficient evidence that phenological adaptation is constrained. The work provides a framework for exploring microevolution of interdependent phenological traits.

Testing for effects of climate change on competitive relationships and coexistence between two bird species.

Climate change is expected to have profound ecological effects, yet shifts in competitive abilities among species are rarely studied in this context. Blue tits (Cyanistes caeruleus) and great tits (Parus major) compete for food and roosting sites, yet coexist across much of their range. Climate change might thus change the competitive relationships and coexistence between these two species. Analysing four of the highest-quality, long-term datasets available on these species across Europe, we extend the textbook example of coexistence between competing species to include the dynamic effects of long-term climate variation. Using threshold time-series statistical modelling, we demonstrate that long-term climate variation affects species demography through different influences on density-dependent and density-independent processes. The competitive interaction between blue tits and great tits has shifted in one of the studied sites, creating conditions that alter the relative equilibrium densities between the two species, potentially disrupting long-term coexistence. Our analyses show that long-term climate change can, but does not always, generate local differences in the equilibrium conditions of spatially structured species assemblages. We demonstrate how long-term data can be used to better understand whether (and how), for instance, climate change might change the relationships between coexisting species. However, the studied populations are rather robust against competitive exclusion.

Adaptation of reproductive phenology to climate change with ecological feedback via dominance hierarchies.

Phenological shifts belong to the most commonly observed biological responses to recent climate change. It is, however, often unclear how these shifts are linked to demography and competitive interactions. We develop an eco-evolutionary model to study adaptation of timing of reproduction in organisms with social dominance hierarchies. We focus on residential birds with winter flocks, where success in competition for territories among offspring depends on ranking given by prior residence. We study the effects of environmental change on breeding population densities, ensuing selection pressures and long-term evolutionary equilibria. We consider changes in food peak date, in winter survival, in total reproductive output and in the width of the food distribution. We show that the evolutionarily stable hatching date will advance with increasing winter survival and reproductive output since these parameters increase habitat saturation and post-fledging competition. Increasing the length of the breeding season also selects for earlier hatching date due to the reduced costs for producing offspring with high ranking. Our analysis shows that there is little correlation between short-term and long-term population responses across different scenarios of environmental change. However, short-term population growth consistently predicts selection for earlier reproduction. Hence, the model identifies changed breeding population density as a key factor to understanding phenological adaptation in systems with prior residence advantages. While selection for change in reproductive phenology is often explained by changed seasonal variation in environmental variables, such as food abundance, we show that environmental change without apparent effects on seasonality can critically affect phenological adaptation. Such factors can mask or even override influences of changed seasonality on phenology. The model thus offers a conceptually new set of explanations for understanding phenological and demographic trends in a changing climate.

Impact of climate change on communities: revealing species' contribution.

1. Although climate is known to play an important role in structuring biological communities, high-resolution analyses of recent climatic impacts on multiple components of diversity are still sparse. Additionally, there is a lack of knowledge about which species drive community response to environmental change. 2. We used a long-term breeding bird data set that encompasses a large latitudinal and altitudinal range to model the effect of temperature on spatial and temporal patterns in alpha and beta diversity. We also established a novel framework for identifying species-specific contributions to these macroecological patterns, hence combining two different approaches for identifying climatic impacts. 3. Alpha diversity increased over time, whilst beta diversity declined; both diversity metrics showed a significant relationship with recent temperature anomalies. By partitioning beta diversity, we showed that the decline was predominately driven by changes in species turnover rather than nestedness suggesting a process of replacement by more common species. 4. Using jackknife analyses we identified how individual species influenced the modelled relationships of diversity with temperature and time. Influential species tended to be habitat generalists with moderate to large distributions. 5. We demonstrate that different facets of avian diversity can respond rapidly to temperature anomalies and as a result have undergone significant changes in the last decade. In general, it appears that warming temperatures are driving compositional homogenization of temperate bird communities via range expansion of common generalist species.

Game theory sheds new light on ecological responses to current climate change when phenology is historically mismatched.

Phenological changes are well documented biological effects of current climate change but their adaptive value and demographic consequences are poorly known. Game theoretical models have shown that deviating from the fitness-maximising phenology can be evolutionary stable under frequency-dependent selection. We study eco-evolutionary responses to climate change when the historical phenology is mismatched in this way. For illustration we model adaptation of arrival dates in migratory birds that compete for territories at their breeding grounds. We simulate climate change by shifting the timing and the length of the favourable season for breeding. We show that initial trends in changes of population densities can be either reinforced or counteracted during the ensuing evolutionary adaptation. We find in total seven qualitatively different population trajectories during the transition to a new evolutionary equilibrium. This surprising diversity of eco-evolutionary responses provides adaptive explanations to the observed variation in phenological responses to recent climate change.

Effects of territory competition and climate change on timing of arrival to breeding grounds: a game-theory approach.

Phenology is an important part of life history that is gaining increased attention because of recent climate change. We use game theory to model phenological adaptation in migratory birds that compete for territories at their breeding grounds. We investigate how the evolutionarily stable strategy (ESS) for the timing of arrival is affected by changes in the onset of spring, the timing of the resource peak, and the season length. We compare the ESS mean arrival date with the environmental optimum, that is, the mean arrival date that maximizes fitness in the absence of competition. When competition is strong, the ESS mean arrival date responds less than the environmental optimum to shifts in the resource peak but more to changes in the onset of spring. Increased season length may not necessarily affect the environmental optimum but can still advance the ESS mean arrival date. Conversely, shifting a narrow resource distribution may change the environmental optimum without affecting the ESS mean arrival date. The ESS mean arrival date and the environmental optimum may even shift in different directions. Hence, treating phenology as an evolutionary game rather than an optimization problem fundamentally changes what we predict to be an adaptive response to environmental changes.

The role of harvesting in age-structured populations: disentangling dynamic and age truncation effects.

Understanding the processes generating fluctuations of natural populations lies at the very heart of academic ecology. It is also very important for applications such as fisheries management and pest control. We are interested in the effect of harvesting on population fluctuations and for that purpose we develop and analyze an age-structured model where recruitment is a stochastic process and the adult segment of the population is harvested. When a constant annual harvest is taken the coefficient of variation of the adult population increases for most parameter values due to the age truncation effect, i.e. an increased variability in a juvenescent population due to the removal of older individuals. However, if a constant proportion of the adults is harvested the age truncation effect is sometimes counteracted by a stabilizing dynamic effect of harvesting. Depending on parameter values mirroring different life histories, proportional harvest can either increase or decrease the relative fluctuations of an exploited population. When there is a demographic Allee effect the ratio of juveniles to adults may actually decrease with harvesting. We conclude that, depending on life history and harvest strategy, harvesting can either reinforce or dampen population fluctuations due to the relative importance of stabilizing dynamic effects and the age truncation effect. The strength of the latter is highly dependent on the fished population's endogenous, age-structured dynamics. More specifically, we predict that populations with strong and positively autocorrelated dynamics will show stronger age truncation effect, a testable prediction that offers a simple rule-of-thumb assessment of a population's vulnerability to exploitation.

Individual heterogeneity and senescence in silvereyes on Heron Island.

Individual heterogeneity and correlations between life history traits play a fundamental role in life history evolution and population dynamics. Unobserved individual heterogeneity in survival can be a nuisance for estimation of age effects at the individual level by causing bias due to mortality selection. We jointly analyze survival and breeding output from successful breeding attempts in an island population of Silvereyes (Zosterops lateralis chlorocephalus) by fitting models that incorporate age effects and individual heterogeneity via random effects. The number of offspring produced increased with age of parents in their first years of life but then eventually declined with age. A similar pattern was found for the probability of successful breeding. Annual survival declined with age even when individual heterogeneity was not accounted for. The rate of senescence in survival, however, depends on the variance of individual heterogeneity and vice versa; hence, both cannot be simultaneously estimated with precision. Model selection supported individual heterogeneity in breeding performance, but we found no correlation between individual heterogeneity in survival and breeding performance. We argue that individual random effects, unless unambiguously identified, should be treated as statistical nuisance or taken as a starting point in a search for mechanisms rather than given direct biological interpretation.

On observation distributions for state space models of population survey data.

1. State space models are starting to replace more simple time series models in analyses of temporal dynamics of populations that are not perfectly censused. By simultaneously modelling both the dynamics and the observations, consistent estimates of population dynamical parameters may be obtained. For many data sets, the distribution of observation errors is unknown and error models typically chosen in an ad-hoc manner. 2. To investigate the influence of the choice of observation error on inferences, we analyse the dynamics of a replicated time series of red kangaroo surveys using a state space model with linear state dynamics. Surveys were performed through aerial counts and Poisson, overdispersed Poisson, normal and log-normal distributions may all be adequate for modelling observation errors for the data. We fit each of these to the data and compare them using AIC. 3. The state space models were fitted with maximum likelihood methods using a recent importance sampling technique that relies on the Kalman filter. The method relaxes the assumption of Gaussian observation errors required by the basic Kalman filter. Matlab code for fitting linear state space models with Poisson observations is provided. 4. The ability of AIC to identify the correct observation model was investigated in a small simulation study. For the parameter values used in the study, without replicated observations, the correct observation distribution could sometimes be identified but model selection was prone to misclassification. On the other hand, when observations were replicated, the correct distribution could typically be identified. 5. Our results illustrate that inferences may differ markedly depending on the observation distributions used, suggesting that choosing an adequate observation model can be critical. Model selection and simulations show that for the models and parameter values in this study, a suitable observation model can typically be identified if observations are replicated. Model selection and replication of observations, therefore, provide a potential solution when the observation distribution is unknown.

Stochastic demography and population dynamics in the red kangaroo Macropus rufus.

1. Many organisms inhabit strongly fluctuating environments but their demography and population dynamics are often analysed using deterministic models and elasticity analysis, where elasticity is defined as the proportional change in population growth rate caused by a proportional change in a vital rate. Deterministic analyses may not necessarily be informative because large variation in a vital rate with a small deterministic elasticity may affect the population growth rate more than a small change in a less variable vital rate having high deterministic elasticity. 2. We analyse a stochastic environment model of the red kangaroo (Macropus rufus), a species inhabiting an environment characterized by unpredictable and highly variable rainfall, and calculate the elasticity of the stochastic growth rate with respect to the mean and variability in vital rates. 3. Juvenile survival is the most variable vital rate but a proportional change in the mean adult survival rate has a much stronger effect on the stochastic growth rate. 4. Even if changes in average rainfall have a larger impact on population growth rate, increased variability in rainfall may still be important also in long-lived species. The elasticity with respect to the standard deviation of rainfall is comparable to the mean elasticities of all vital rates but the survival in age class 3 because increased variation in rainfall affects both the mean and variability of vital rates. 5. Red kangaroos are harvested and, under the current rainfall pattern, an annual harvest fraction of c. 20% would yield a stochastic growth rate about unity. However, if average rainfall drops by more than c. 10%, any level of harvesting may be unsustainable, emphasizing the need for integrating climate change predictions in population management and increase our understanding of how environmental stochasticity translates into population growth rate.

Bet-hedging as an evolutionary game: the trade-off between egg size and number.

Bet-hedging theory addresses how individuals should optimize fitness in varying and unpredictable environments by sacrificing mean fitness to decrease variation in fitness. So far, three main bet-hedging strategies have been described: conservative bet-hedging (play it safe), diversified bet-hedging (don't put all eggs in one basket) and adaptive coin flipping (choose a strategy at random from a fixed distribution). Within this context, we analyse the trade-off between many small eggs (or seeds) and few large, given an unpredictable environment. Our model is an extension of previous models and allows for any combination of the bet-hedging strategies mentioned above. In our individual-based model (accounting for both ecological and evolutionary forces), the optimal bet-hedging strategy is a combination of conservative and diversified bet-hedging and adaptive coin flipping, which means a variation in egg size both within clutches and between years. Hence, we show how phenotypic variation within a population, often assumed to be due to non-adaptive variation, instead can be the result of females having this mixed strategy. Our results provide a new perspective on bet-hedging and stress the importance of extreme events in life history evolution.

Climate change and the optimal arrival of migratory birds.

Recent climate change has sparked an interest in the timing of biological events, which is a general problem in life-history evolution. Reproduction in many organisms breeding in seasonal environments, e.g. migratory birds, is dependent on the exploitation of a short but rich food supply. If the seasonal timing of the food peak advances owing to climate change, then one would expect the bird to track those changes, hence, initiate migration and breeding earlier. However, when there is competition for territories and a risk of pre-breeding mortality, the optimal response to a shifting food distribution is no longer obvious. We develop a theoretical model to study how the optimal arrival time depends on the mean and variance of the food distribution, the degree of competition for territories and the risk of mortality. In general, the optimal shift in arrival date should never be as extreme as the shift in food peak date. Our results also show that we should expect the high variation of trends in arrival date observed among migratory birds, even if migration and information about climate change were unconstrained.

Reduction in an almond moth Ephestia cautella (Lepidoptera: Pyralidae) population by means of mating disruption.

Pheromone-based mating disruption of the almond moth (Ephestia cautella) (Walk.) (Lepidoptera: Pyralidae) was carried out in a chocolate factory in Sweden. Population monitoring was conducted with pheromone-baited traps and water traps. Pheromone traps showed a 94% catch reduction, and monitoring with water traps showed a significant decrease in total catch (5.0 and 1.6 individuals per trap per week before and during treatment respectively). The significance of the results was tested by fitting the observed data to a first-order autoregressive model. This made it possible to test the data with a 95% confidence interval, comparing trap catches before mating disruption treatment with trapping data during the experiment. It is suggested that this statistical approach may be used more frequently in mating disruption experiments where it is extremely difficult to control external factors and therefore equally difficult to use a comparable control plot to evaluate the treatment.

Change in spring arrival of migratory birds under an era of climate change, Swedish data from the last 140 years.

Many migratory bird species have advanced their spring arrival during the latest decades, most probably due to climate change. However, studies on migratory phenology in the period before recent global warming are scarce. We have analyzed a historical dataset (1873-1917) of spring arrival to southern and central Sweden of 14 migratory bird species. In addition, we have used relative differences between historical and present-day observations (1984-2013) to evaluate the effect of latitude and migratory strategy on day of arrival over time. There was a larger change in spring phenology in short-distance migrants than in long-distance migrants. Interestingly, the results further suggest that climate change has affected the phenology of short-distance migrants more in southern than in central Sweden. The results suggest that the much earlier calculated arrival to southern Sweden among short-distance migrants mirrors a change in location of wintering areas, hence, connecting migration phenology and wintering range shifts.

A theory of stochastic harvesting in stochastic environments.

We investigate how model populations respond to stochastic harvesting in a stochastic environment. In particular, we show that the effects of variable harvesting on the variance in population density and yield depend critically on the autocorrelation of environmental noise and on whether the endogenous dynamics of the population display over- or undercompensation to density. These factors interact in complicated ways; harvesting shifts the slope of the renewal function, and the net effect of this shift will depend on the sign and magnitude of the other influences. For example, when environmental noise exhibits a positive autocorrelation, the relative importance of a variable harvest to the variance in density increases with overcompensation but decreases with undercompensation. For a fixed harvesting level, an increasing level of autocorrelation in environmental noise will decrease the relative variation in population density when overcompensation would otherwise occur. These and other intricate interactions have important ramifications for the interpretation of time series data when no prior knowledge of demographic or environmental details exists. These effects are important whenever the harvesting rate is sufficiently high or variable, conditions likely to occur in many systems, whether the harvesting is caused by commercial exploitation or by any other strong agent of density-independent mortality.

Habitat selection and population regulation in temporally fluctuating environments.

Understanding and predicting the distribution of organisms in heterogeneous environments lies at the heart of ecology, and the theory of density-dependent habitat selection (DDHS) provides ecologists with an inferential framework linking evolution and population dynamics. Current theory does not allow for temporal variation in habitat quality, a serious limitation when confronted with real ecological systems. We develop both a stochastic equivalent of the ideal free distribution to study how spatial patterns of habitat use depend on the magnitude and spatial correlation of environmental stochasticity and also a stochastic habitat selection rule. The emerging patterns are confronted with deterministic predictions based on isodar analysis, an established empirical approach to the analysis of habitat selection patterns. Our simulations highlight some consistent patterns of habitat use, indicating that it is possible to make inferences about the habitat selection process based on observed patterns of habitat use. However, isodar analysis gives results that are contingent on the magnitude and spatial correlation of environmental stochasticity. Hence, DDHS is better revealed by a measure of habitat selectivity than by empirical isodars. The detection of DDHS is but a small component of isodar theory, which remains an important conceptual framework for linking evolutionary strategies in behavior and population dynamics.

The irreducible uncertainty of the demography-environment interaction in ecology.

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.

Climate change and the optimal flowering time of annual plants in seasonal environments.

Long-term phenology monitoring has documented numerous examples of changing flowering dates during the last century. A pivotal question is whether these phenological responses are adaptive or not under directionally changing climatic conditions. We use a classic dynamic growth model for annual plants, based on optimal control theory, to find the fitness-maximizing flowering time, defined as the switching time from vegetative to reproductive growth. In a typical scenario of global warming, with advanced growing season and increased productivity, optimal flowering time advances less than the start of the growing season. Interestingly, increased temporal spread in production over the season may either advance or delay the optimal flowering time depending on overall productivity or season length. We identify situations where large phenological changes are necessary for flowering time to remain optimal. Such changes also indicate changed selection pressures. In other situations, the model predicts advanced phenology on a calendar scale, but no selection for early flowering in relation to the start of the season. We also show that the optimum is more sensitive to increased productivity when productivity is low than when productivity is high. All our results are derived using a general, graphical method to calculate the optimal flowering time applicable for a large range of shapes of the seasonal production curve. The model can thus explain apparent maladaptation in phenological responses in a multitude of scenarios of climate change. We conclude that taking energy allocation trade-offs and appropriate time scales into account is critical when interpreting phenological patterns.