Climate warming: a loss of variation in populations can accompany reproductive shifts.

The most documented response of organisms to climate warming is a change in the average timing of seasonal activities (phenology). Although we know that these average changes can differ among species and populations, we do not know whether climate warming impacts within-population variation in phenology. Using data from five study sites collected during a 13-year survey, we found that the increase in spring temperatures is associated with a reproductive advance of 10 days in natural populations of common lizards (Zootoca vivipara). Interestingly, we show a correlated loss of variation in reproductive dates within populations. As illustrated by a model, this shortening of the reproductive period can have significant negative effects on population dynamics. Consequently, we encourage tests in other species to assess the generality of decreased variation in phenological responses to climate change.

The genealogical decomposition of a matrix population model with applications to the aggregation of stages.

Matrix projection models are a central tool in many areas of population biology. In most applications, one starts from the projection matrix to quantify the asymptotic growth rate of the population (the dominant eigenvalue), the stable stage distribution, and the reproductive values (the dominant right and left eigenvectors, respectively). Any primitive projection matrix also has an associated ergodic Markov chain that contains information about the genealogy of the population. In this paper, we show that these facts can be used to specify any matrix population model as a triple consisting of the ergodic Markov matrix, the dominant eigenvalue and one of the corresponding eigenvectors. This decomposition of the projection matrix separates properties associated with lineages from those associated with individuals. It also clarifies the relationships between many quantities commonly used to describe such models, including the relationship between eigenvalue sensitivities and elasticities. We illustrate the utility of such a decomposition by introducing a new method for aggregating classes in a matrix population model to produce a simpler model with a smaller number of classes. Unlike the standard method, our method has the advantage of preserving reproductive values and elasticities. It also has conceptually satisfying properties such as commuting with changes of units.

A new approach to the generation time in matrix population models.

The generation time is commonly defined as the mean age of mothers at birth. In matrix population models, a general formula is available to compute this quantity. However, it is complex and hard to interpret. Here, we present a new approach where the generation time is envisioned as a return time in an appropriate Markov chain. This yields surprisingly simple results, such as the fact that the generation time is the inverse of the sum of the elasticities of the growth rate to changes in the fertilities. This result sheds new light on the interpretation of elasticities (which as we show correspond to the frequency of events in the ancestral lineage of the population), and we use it to generalize a result known as Lebreton's formula. Finally, we also show that the generation time can be seen as a random variable, and we give a general expression for its distribution.

Trophic groups and modules: two levels of group detection in food webs.

Within food webs, species can be partitioned into groups according to various criteria. Two notions have received particular attention: trophic groups (TGs), which have been used for decades in the ecological literature, and more recently, modules. The relationship between these two group concepts remains unknown in empirical food webs. While recent developments in network theory have led to efficient methods for detecting modules in food webs, the determination of TGs (groups of species that are functionally similar) is largely based on subjective expert knowledge. We develop a novel algorithm for TG detection. We apply this method to empirical food webs and show that aggregation into TGs allows for the simplification of food webs while preserving their information content. Furthermore, we reveal a two-level hierarchical structure where modules partition food webs into large bottom-top trophic pathways, whereas TGs further partition these pathways into groups of species with similar trophic connections. This provides new perspectives for the study of dynamical and functional consequences of food-web structure, bridging topological and dynamical analysis. TGs have a clear ecological meaning and are found to provide a trade-off between network complexity and information loss.

Density-dependent life history and the dynamics of small populations.

1. Small population dynamics depend importantly on the strength and shape of density dependence. Unfortunately, the lack of reliable life-history data often prevents to make accurate demographic predictions for populations regulated by density dependence. 2. We created a gradient from low to high densities in small experimental populations of common lizards (Zootoca vivipara) and investigated the shape and strength of the density dependence of life-history traits during a yearly cycle. We then analysed stochastic population dynamics using one-sex and two-sex age-structured matrix models. 3. Body growth and reproductive performances decreased with density, yearling and adult survival and body size at birth were density-independent, and juvenile survival increased with density. The density dependence of reproduction was partly explained by positive effects of body size on age at first reproduction and clutch size. 4. Parturition date decreased with density in sparse populations and then increased, providing one of the first empirical evidence of a component Allee effect in the phenology of reproduction. 5. Population growth rate (λ) was most affected by variations in juvenile and yearling survival. However, density at equilibrium was most affected by juvenile access to reproduction and yearling clutch size. 6. Stochastic simulations revealed that negative density dependence buffers the effects of initial density on extinction probability, has positive effects on the persistence of sparse populations and interacts with sex ratio fluctuations to shape extinction dynamics. 7. This study demonstrates that negative density dependence modifies the dynamics of small populations and should be investigated together with Allee effects to predict extinction risks.

Ecological emergence of thermal clines in body size.

The unprecedented rate of global warming requires a better understanding of how ecosystems will respond. Organisms often have smaller body sizes under warmer climates (Bergmann's rule and the temperature-size rule), and body size is a major determinant of life histories, demography, population size, nutrient turnover rate, and food-web structure. Therefore, by altering body sizes in whole communities, current warming can potentially disrupt ecosystem function and services. However, the underlying drivers of warming-induced body downsizing remain far from clear. Here, we show that thermal clines in body size are predicted from universal laws of ecology and metabolism, so that size-dependent selection from competition (both intra and interspecific) and predation favors smaller individuals under warmer conditions. We validate this prediction using 4.1 × 10(6) individual body size measurements from French river fish spanning 29 years and 52 species. Our results suggest that warming-induced body downsizing is an emergent property of size-structured food webs, and highlight the need to consider trophic interactions when predicting biosphere reorganizations under global warming.

The co-evolution of multiply-informed dispersal: information transfer across landscapes from neighbors and immigrants.

Dispersal plays a key role in natural systems by shaping spatial population and evolutionary dynamics. Dispersal has been largely treated as a population process with little attention to individual decisions and the influence of information use on the fitness benefits of dispersal despite clear empirical evidence that dispersal behavior varies among individuals. While information on local density is common, more controversial is the notion that indirect information use can easily evolve. We used an individual-based model to ask under what conditions indirect information use in dispersal will evolve. We modeled indirect information provided by immigrant arrival into a population which should be linked to overall metapopulation density. We also modeled direct information use of density which directly impacts fitness. We show that immigrant-dependent dispersal evolves and does so even when density dependent information is available. Use of two sources of information also provides benefits at the metapopulation level by reducing extinction risk and prolonging the persistence of populations. Our results suggest that use of indirect information in dispersal can evolve under conservative conditions and thus could be widespread.

Eco-evolutionary feedbacks, adaptive dynamics and evolutionary rescue theory.

Adaptive dynamics theory has been devised to account for feedbacks between ecological and evolutionary processes. Doing so opens new dimensions to and raises new challenges about evolutionary rescue. Adaptive dynamics theory predicts that successive trait substitutions driven by eco-evolutionary feedbacks can gradually erode population size or growth rate, thus potentially raising the extinction risk. Even a single trait substitution can suffice to degrade population viability drastically at once and cause 'evolutionary suicide'. In a changing environment, a population may track a viable evolutionary attractor that leads to evolutionary suicide, a phenomenon called 'evolutionary trapping'. Evolutionary trapping and suicide are commonly observed in adaptive dynamics models in which the smooth variation of traits causes catastrophic changes in ecological state. In the face of trapping and suicide, evolutionary rescue requires that the population overcome evolutionary threats generated by the adaptive process itself. Evolutionary repellors play an important role in determining how variation in environmental conditions correlates with the occurrence of evolutionary trapping and suicide, and what evolutionary pathways rescue may follow. In contrast with standard predictions of evolutionary rescue theory, low genetic variation may attenuate the threat of evolutionary suicide and small population sizes may facilitate escape from evolutionary traps.

Evolutionary entropy predicts the outcome of selection: Competition for resources that vary in abundance and diversity.

Competition between individuals for resources which are limited and diverse in composition is the ultimate driving force of evolution. Classical studies of this event contend that the outcome is a deterministic process predicted by the growth rate of the competing types-a tenet called the Malthusian selection principle. Recent studies of competition indicate that the dynamics of selection is a stochastic process, regulated by the population size, the abundance and diversity of the resource, and predicted by evolutionary entropy-a statistical parameter which characterizes the rate at which the population returns to the steady state condition after a random endogenous or exogenous perturbation. This tenet, which we will call the entropic selection principle entails the following relations: This article delineates the analytic, computational and empirical support for this tenet. We show moreover that the Malthusian selection principle, a cornerstone of classical evolutionary genetics, is the limit, as population size and resource abundance tends to infinity of the entropic selection principle. The Malthusian tenet is an approximation to the entropic selection principle-an approximation whose validity increases with increasing population size and increasing resource abundance. Evolutionary entropy is a generic concept that characterizes the interaction dynamics of metabolic entities at several levels of biological organization: cellular, organismic and ecological. Accordingly, the entropic selection principle represents a general rule for explaining the processes of adaptation and evolution at each of these levels.

Predator foraging behaviour drives food-web topological structure.

1. The structure and dynamics of prey populations are shaped by the foraging behaviours of their predators. Yet, there is still little documentation on how distinct predator foraging types control biodiversity, food-web architecture and ecosystem functioning. 2. We experimentally compared the effects of model fish species of two major foraging types of lake planktivores: a size-selective visual feeder (bluegill), and a filter feeder (gizzard shad). The visual feeder forages on individually captured consumer prey, whereas the filter feeder forages on various prey simultaneously, not only consumers but also primary producers. We ran a 1-month mesocosm experiment cross-classifying a biomass gradient of each predator type. We analysed the effect of each fish on food-web architecture by computing major topological descriptors over time (connectance, link density, omnivory index, etc.). These descriptors were computed from 80 predator-prey binary matrices, using taxa mostly identified at the species level. 3. We found that the visual feeder induced more trophic cul-de-sac (inedible) primary-producer species, lower link density and connectance, and lower levels of food-web omnivory and generalism than the filter feeder. Yet, predator biomass did not affect food-web topology. 4. Our results highlight that top-predator foraging behaviour is a key functional trait that can drive food-web topology and ultimately ecosystem functioning.

Evolutionary entropy: a predictor of body size, metabolic rate and maximal life span.

Body size of organisms spans 24 orders of magnitude, and metabolic rate and life span present comparable differences across species. This article shows that this variation can be explained in terms of evolutionary entropy, a statistical parameter which characterizes the robustness of a population, and describes the uncertainty in the age of the mother of a randomly chosen newborn. We show that entropy also has a macroscopic description: It is linearly related to the logarithm of the variables body size, metabolic rate, and life span. Furthermore, entropy characterizes Darwinian fitness, the efficiency with which a population acquires and converts resources into viable offspring. Accordingly, entropy predicts the outcome of natural selection in populations subject to different classes of ecological constraints. This predictive property, when integrated with the macroscopic representation of entropy, is the basis for enormous differences in morphometric and life-history parameters across species.

How is extinction risk related to population-size variability over time? A family of models for species with repeated extinction and immigration.

It is well known that for an isolated population, the probability of extinction is positively related to population size variation: more variation is associated with more extinction. What, then, is the relation of extinction to population size variation for a population embedded in a metapopulation and subjected to repeated extinction and recolonization? In this case, the extinction risk can be measured by the extinction rate, the frequency at which local extinction occurs. Using several population dynamics models with immigration, we find, in general, a negative correlation between extinction and variation. More precisely, with increasing length of the time series, an initially negative regression coefficient first becomes more negative, then becomes less negative, and eventually attains positive values before decreasing again to 0. This pattern holds under substantial variation in values of parameters representing species and environmental properties. It is also rather robust to census interval length and the fraction of missed individuals but fails to hold for high thresholds (population size values below which extinction is deemed to occur) when quasi extinction rather than true extinction is represented. The few departures from the initial negative correlation correspond to populations at risk: low growth rate or frequent catastrophes.

Life-history models of extinction: a test with island spiders.

This study analyzes extinction patterns for two species of orb spiders monitored annually on 77 islands over a continuous 20-yr period. One species, Argiope argentata, has large populations sometimes crashing quickly to extinction and a much weaker relation of extinction likelihood to population size than does the other species, Metepeira datona. Demographic models were built for both species and matched against observations. Differences between the species in life-history traits-estimated with measurements from the field-together with incorporation of demographic stochasticity, a population ceiling, and environmental stochasticity, were necessary to fit the observed extinction curves. As predicted from life-history patterns, long-term population growth rates (and hence predicted extinction probabilities) are relatively very sensitive to values of juvenile survivorship. Models are also sensitive to variation in the population ceiling and environmental noise, which tend to act in a complementary manner. A simple model with no age structure was able to fit the data on large initial population sizes but not on small initial population sizes, showing that life cycle characteristics interact with the various sources of stochasticity and hence have to be taken into account to produce a precise model of the extinction process.

Which future for the French Pyrenean brown bear (Ursus arctos) population? An approach using stage-structured deterministic and stochastic models.

The Pyrenean brown bear (Ursus arctos) population is considered as one of the most seriously threatened with extinction in Western Europe. To assess its viability and possible needs of augmentation, we develop deterministic and stochastic stage-structured demographic models. The deterministic model reveals that a bear population cannot have a high annual growth rate and is particularly sensitive to breeder survival. High demographic parameters appear to be crucial to population persistence, especially for a small population that remains vulnerable to demographic and environmental stochasticities. The Pyrenean population cannot therefore be considered as viable. Successful conservation strategies for this population would require releasing more bears in both sub-populations in the near future.

Conservation and control strategies for the wolf (Canis lupus) in western Europe based on demographic models.

Securing the long-term acceptance of large carnivores such as the wolf (Canis lupus) in Europe and North America raises a difficult challenge to conservation biologists: planning removals to reduce depredations on livestock while ensuring population viability. We use stochastic-stage-structured population models to investigate wolf population dynamics and to assess alternative management strategies. Among the various management strategies advocated by agencies, zoning that involves eliminating wolves outside a restricted area should be designed with caution, because probabilities of extinction are extremely sensitive to the maximum number of packs that a zone can support and to slight changes in stage specific survival probabilities. In a zoned population, viability is enhanced more by decreasing mortality rates in all classes than by increasing wolf zone size. An alternative to zoning is adaptive management, where there is no limit on pack number but population control can be operated whenever some predefined demographic conditions are met. It turns out that an adaptive management strategy that removes a moderate percentage (10%) of the population following each year of more than 5% of total population growth would provide visible actions addressing public concerns while keeping extinction probability low.

Demographic Stochasticity and Social Mating System in the Process of Extinction of Small Populations: The Case of Passerines Introduced to New Zealand.

Underlying the many causes of extinction of small populations is the random fate of each constituent individual or, in other words, demographic stochasticity. Demographic stochasticity is inherent to any demographic process, regardless of the environment, and its strength increases as population size gets smaller. In particular, random fluctuations in the proportion of males and females and the way they pair for reproduction (i.e., the social mating system) are usually neglected. To assess the potential importance of demographic stochasticity to the extinction process, a two-sex model with an explicit mating system was built. Extinction probabilities computed via Monte Carlo simulation were compared to real data, the case of passerines introduced to New Zealand a century ago. This minimal model of extinction allowed assessment of the importance of the mating system in the colonization process. Monogamous mating led to a higher extinction risk than did polygynous mating. Demographic uncertainty imposes high extinction probabilities on short-lived bird species as compared to long-lived bird species. Theoretical results for two-sex models are provided.