Factors influencing route choice by avian migrants: a dynamic programming model of Pacific brant migration

We used stochastic dynamic programming to investigate a spectacular migration strategy in the black brant Branta bernicla nigricans, a species of goose. Black brant migration is well suited for theoretical analysis since there are a number of existing strategies that easily can be compared. In early autumn, almost the entire population of the black brant gathers at Izembek Lagoon on the Alaska Peninsula to stage and refuel before the southward migration. There are at least three distinct strategies, with most geese making a spectacular direct migration more than 5000km across the Gulf of Alaska to their wintering grounds in southern Baja California or mainland Mexico. This is a potentially dangerous strategy since foraging is not possible during the overseas passage. Some individuals instead use shorter flights to make a detour along the coast, a longer route that all individuals use for northwards migration in spring. Since flight costs accelerate with increasing body mass, migration by short flights is energetically cheaper than long-distance flights. A small but increasing part of the population has recently begun to winter at Izembek. We investigated this migration under two different suppositions using a dynamic state variable model. First, if the geese are free to make a strategic choice, under what assumptions should they prefer direct migration and under what assumptions should they prefer detour migration/winter residency? Second, provided that the dominating direct migration strategy is optimal, what conditions will force the geese to go for detour migration/winter residency? In the second case the geese may try to follow an optimal direct migration strategy, but stochastic events may force them to choose a suboptimal policy. We also simulated possible effects of global warming. The model suggests that the fuel level at arrival in Izembek and fuel gain rates are key factors and that tail winds must have been reliable in the past, otherwise direct migration could not have evolved. It also suggests that a change to milder winters may promote an unexpectedly abrupt change from long-distance to short-distance migration or winter residency. Finally, it produced a number of predictions that might be testable in the field.     

Balancing sampling and specialization: an adaptationist model of incremental development

Development is typically a constructive process, in which phenotypes incrementally adapt to local ecologies. Here, we present a novel model in which natural selection shapes developmental systems based on the evolutionary ecology, and these systems adaptively guide phenotypic development. We assume that phenotypic construction is incremental and trades off with sampling cues to the environmental state. We computed the optimal developmental programmes across a range of evolutionary ecological conditions. Using these programmes, we simulated distributions of mature phenotypes. Our results show that organisms sample the environment most extensively when cues are moderately, not highly, informative. When the developmental programme relies heavily on sampling, individuals transition from sampling to specialization at different times in ontogeny, depending on the consistency of their sampled cue set; this finding suggests that stochastic sampling may result in individual differences in plasticity itself. In addition, we find that different selection pressures may favour similar developmental mechanisms, and that organisms may incorrectly calibrate development despite stable ontogenetic environments. We hope our model will stimulate adaptationist research on the constructive processes guiding development.     

Parental provisioning in a variable environment: Evaluation of three foraging currencies and a state variable model

We estimated the reproductive success of black terns (Chlidonias niger) based on three optimal foraging currencies (maximizing the net rate of energy intake, daily delivery rate, and efficiency, respectively) and a state variable model. There was a broad range of capture intervals (the time required for the parent to capture a single prey) when the flight speeds predicted by the three currencies were so high that they resulted in daily provisioning costs which parents could not fully recover through self-feeding. Whenever the efficiency currency produced higher estimates of reproductive success, parents lost comparatively less weight than when they foraged as rate-maximizers. If parents did not experience any weight loss, the net rate and efficiency currencies made equivalent fitness projections. However, both of these currencies provided lower fitness returns than daily delivery rate at longer capture intervals. There were a number of capture intervals when estimates of reproductive success from the state variable model and at least one of the foraging currencies were equal. Provisioning behaviour under the state variable model was much more flexible and parents were therefore able to reduce their self-feeding rate on days when food was particularly scarce, thereby increasing the total delivery to the nest. This resulted in higher fitness returns than was possible under the foraging currencies. Our results suggest that efficiency-maximizing is more likely to provide fitness returns that are equivalent to the state variable model in comparison with the rate-maximizing alternatives. Furthermore, only the efficiency currency and the state variable model made predictions of flight speed that were similar to speeds measured in black tern parents provisioning young at natural nests.     

A reevaluation of the logic of pilferage effects, predation risk, and environmental variability on avian energy regulation: the critical role of time budgets

We studied the effect of pilferage rates, variation in foodencounter rate, and predation risk on cache and fat-storageregulation using dynamic programming. Previous predictionsthat small birds facing increased pilferage rates should cacheless and store more body fat are not generally supported. Instead,cache investment (caching rate or percent of food cached) is predicted to be unimodal, peaking at intermediate pilferagerates. This pattern is determined, in part, by pilferage-inducedchanges in time budgets: at low pilferage rates, a marginalincrease in pilferage rates can be offset by an increase incache investment. However, increased caching increases time allocated to both caching and foraging. The increased foragingis caused by the energetic costs of caching and by the lossof energy from the cache. Increased time spent caching andforaging in turn decreases time spent resting under low predationrisk. Above some threshold pilferage rate, the marginal valueof resting exceeds the marginal value of caching, and cacheinvestment declines with further increasing pilferage rates.These patterns hold for three levels of variation in food encounterrate: time-invariant, between-day, and within-day variation;they also hold across different mean rates of food encounter.We show that previous predictions concerning decreased energy-storagelevels with increased food abundance are not supported when there is between-day variation in mean food encounter ratesand food abundance increases only on "good" days. Finally,predation risk affects the predictions described above in twoways. First, these trends assume that the birds can rest ina predator-free refuge. If the refuge is not available, birdsare predicted to cache less at higher pilferage rates irrespectiveof the absolute level of pilferage. With the refuge in place,levels of predation risk affect the skew in the pilferage-rate/cachingfunction. As a result, the relative effect of predation riskon caching intensity varies with pilfer rate. At very low pilferrates, lowered predation risk causes more caching, but loweredpredation risk under high pilferage rates can lower caching intensity, contrary to previous predictions. Surprisingly, predationrisk has an appreciable effect on body mass only when the birdis predicted to cease caching (i.e., at the highest pilferrates); otherwise a change of two orders of magnitude in theprobability of encountering predators has little effect on body mass. Our results suggest that the tradeoffs associatedwith the joint regulation of internal energy stores and externallycached stores are more complicated than previous literaturewould indicate. Our results also show that we have underestimatedthe role that time budgets play in patterns of energy regulation.     

Modelling O2 and O2 unidirectional fluxes in plants. III: Fitting of experimental data by a simple model

Photosynthetic assimilation of CO₂ in plants results in the balance between the photochemical energy developed by light in chloroplasts, and the consumption of that energy by the oxygenation processes, mainly the photorespiration in C₃ plants. The analysis of classical biological models shows the difficulties to bring to fore the oxygenation rate due to the photorespiration pathway. As for other parameters, the most important key point is the estimation of the electron transport rate (ETR or J), i.e. the flux of biochemical energy, which is shared between the reductive and oxidative cycles of carbon. The only reliable method to quantify the linear electron flux responsible for the production of reductive energy is to directly measure the O₂ evolution by ¹⁸O₂ labelling and mass spectrometry. The hypothesis that the respective rates of reductive and oxidative cycles of carbon are only determined by the kinetic parameters of Rubisco, the respective concentrations of CO₂ and O₂ at the Rubisco site and the available electron transport rate, ultimately leads to propose new expressions of biochemical model equations. The modelling of ¹⁸O₂ and ¹⁶O₂ unidirectional fluxes in plants shows that a simple model can fit the photosynthetic and photorespiration exchanges for a wide range of environmental conditions. Its originality is to express the carboxylation and the oxygenation as a function of external gas concentrations, by the definition of a plant specificity factor Sp that mimics the internal reactions of Rubisco in plants. The difference between the specificity factors of plant (Sp) and of Rubisco (Sr) is directly related to the conductance values to CO₂ transfer between the atmosphere and the Rubisco site. This clearly illustrates that the values and the variation of conductance are much more important, in higher C₃ plants, than the small variations of the Rubisco specificity factor. The simple model systematically expresses the reciprocal variations of carboxylation and oxygenation exchanges illustrated by a “mirror effect”. It explains the protective sink effect of photorespiration, e.g. during water stress. The importance of the CO₂ compensation point, in classical models, is reduced at the benefit of the crossing points Cx and Ox, concentration values where carboxylation and oxygenation are equal or where the gross O₂ uptake is half of the gross O₂ evolution. This concept is useful to illustrate the feedback effects of photorespiration in the atmosphere regulation. The constancy of Sp and of Cx for a great variation of P under several irradiance levels shows that the regulation of the conductance maintains constant the internal CO₂ and the ratio of photorespiration to photosynthesis (PR/P). The maintenance of the ratio PR/P, in conditions of which PR could be reduced and the carboxylation increased, reinforces the hypothesis of a positive role of photorespiration and its involvement in the plant-atmosphere co-evolution.