Integral projection models for species with complex demography

Matrix projection models occupy a central role in population and conservation biology. Matrix models divide a population into discrete classes, even if the structuring trait exhibits continuous variation ( e. g., body size). The integral projection model ( IPM) avoids discrete classes and potential artifacts from arbitrary class divisions, facilitates parsimonious modeling based on smooth relationships between individual state and demographic performance, and can be implemented with standard matrix software. Here, we extend the IPM to species with complex demographic attributes, including dormant and active life stages, cross- classification by several attributes ( e. g., size, age, and condition), and changes between discrete and continuous structure over the life cycle. We present a general model encompassing these cases, numerical methods, and theoretical results, including stable population growth and sensitivity/ elasticity analysis for density- independent models, local stability analysis in density- dependent models, and optimal/ evolutionarily stable strategy life- history analysis. Our presentation centers on an IPM for the thistle Onopordum illyricum based on a 6- year field study. Flowering and death probabilities are size and age dependent, and individuals also vary in a latent attribute affecting survival, but a predictively accurate IPM is completely parameterized by fitting a few regression equations. The online edition of the American Naturalist includes a zip archive of R scripts illustrating our suggested methods

Evolution of complex flowering strategies: an age- and size-structured integral projection model

We explore the evolution of delayed age- and size-dependent flowering in the monocarpic perennial Carlina vulgaris, by extending the recently developed integral projection approach to include demographic rates that depend on size and age. The parameterized model has excellent descriptive properties both in terms of the population size and in terms of the distributions of sizes within each age class. In Carlina the probability of flowering depends on both plant size and age. We use the parameterized model to predict this relationship, using the evolutionarily stable strategy (ESS) approach. Despite accurately predicting the mean size of flowering individuals, the model predicts a step-function relationship between the probability of flowering and plant size, which has no age component. When the variance of the flowering-threshold distribution is constrained to the observed value, the ESS flowering function contains an age component, but underpredicts the mean flowering size. An analytical approximation is used to explore the effect of variation in the flowering strategy on the ESS predictions. Elasticity analysis is used to partition the agespecific contributions to the finite rate of increase (u) of the survival-growth and fecundity components of the model. We calculate the adaptive landscape that defines the ESS and generate a fitness landscape for invading phenotypes in the presence of the observed flowering strategy. The implications of these results for the patterns of genetic diversity in the flowering strategy and for testing evolutionary models are discussed. Results proving the existence of a dominant eigenvalue and its associated eigenvectors in general size- and age-dependent integral projection models are presented

Why so variable: can genetic variance in flowering thresholds be maintained by fluctuating selection?

We use integral projection models (IPMs) and individual-based simulations to study the evolution of genetic variance in two monocarpic plant systems. Previous approaches combining IPMs with an adaptive dynamics–style invasion analysis predicted that genetic variability in the size threshold for flowering will not be maintained, which conflicts with empirical evidence. We ask whether this discrepancy can be resolved by making more realistic assumptions about the underlying genetic architecture, assuming a multilocus quantitative trait in an outcrossing diploid species. To do this, we embed the infinitesimal model of quantitative genetics into an IPM for a size-structured cosexual plant species. The resulting IPM describes the joint dynamics of individual size and breeding value of the evolving trait. We apply this general framework to the monocarpic perennials Oenothera glazioviana and Carlina vulgaris. The evolution of heritable variation in threshold size is explored in both individual-based models (IBMs) and IPMs, using a mutation rate modifier approach. In the Oenothera model, where the environment is constant, there is selection against producing genetically variable offspring. In the Carlina model, where the environment varies between years, genetically variable offspring provide a selective advantage, allowing the maintenance of genetic variability. The contrasting predictions of adaptive dynamics and quantitative genetics models for the same system suggest that fluctuating selection may be more effective at maintaining genetic variation than previously thought

Rapid evolution with generation overlap: the double-edged effect of dormancy

In life histories with generation overlap, selection that acts differently on different life-stages can produce reservoirs of genetic variation, for example, in long-lived iteroparous adults or long-lived dormant propagules. Such reservoirs provide “migration from the past” to the current population, and depending on the trend of environmental change, they have the potential either to slow adaptive evolution or accelerate it by re-introducing genotypes not affected by recent selection (e.g., through storage effect in a fluctuating environment). That is, the effect of generation overlap is a “double-edged sword,” with each edge cutting in a different direction. Here, we use sexual (quantitative trait) and asexual (clonal) models to explore the effects of generation overlap on adaptive evolution in a fluctuating environment, either with or without a trend in the mean environment state. Our analyses show that when environmental stochasticity scaled by strength of selection is intermediate and when the trend in mean environment is slow, intermediate values of generation overlap can maximize the rate of response to selection and minimize the adaptation lag between the trait mean and the environmental trend. Otherwise, increased generation overlap results in smaller selection response and larger adaptation lag. In the former case, low generation overlap results in low heritable trait variance, while high generation overlap increases the “migration load” from the past. Therefore, to understand the importance of rapid evolution and eco-evolutionary dynamics in the wild for organisms with overlapping generations, we need to understand the interaction of generation overlap, environmental stochasticity, and strength of selection

Atomic-Scale Variations of the Mechanical Response of 2D Materials Detected by Noncontact Atomic Force Microscopy

We show that noncontact atomic force microscopy (AFM) is sensitive to the local stiffness in the atomicscale limit on weakly coupled 2D materials, as graphene on metals. Our large amplitude AFM topography and dissipation images under ultrahigh vacuum and low temperature resolve the atomic and moiré patterns in graphene on Pt (111), despite its extremely low geometric corrugation. The imaging mechanisms are identified with a multiscale model based on density-functional theory calculations, where the energy cost of global and local deformations of graphene competes with short-range chemical and long-range van der Waals interactions. Atomic contrast is related with short-range tip-sample interactions, while the dissipation can be understood in terms of global deformations in the weakly coupled graphene layer. Remarkably, the observed moiré modulation is linked with the subtle variations of the local interplanar graphene-substrate interaction, opening a new route to explore the local mechanical properties of 2D materials at the atomic scaleWe thank the Marie Curie ITN Network “ACRITAS” (Grant No. FP7-PEOPLE-2012-ITN-317348) funded by the European Commission under the FP7 Marie Curie PEOPLE programme and the Spanish MINECO (Projects No. CSD2010-00024, No. MAT2011-23627, No. MAT2013-41636-P, and No. MAT2014-54484-P) for financial support. Computer time was provided by the Spanish Supercomputer Network (RES) at Marenostrum III (BSC, Barcelona) and Magerit (CesViMa, Madrid) computers. P. P. was supported by the Ramón y Cajal progra

Nutzung von Resistenzmechanismen verschiedener Rebarten als Alternative zum Einsatz von Kupfer im Ökoweinbau

Extrakte aus Wildreben bzw. Hybriden mit hoher Resistenz: Es war zu prüfen, ob durch die Applikation von Blattextrakten von Nicht-Vitis-vinifera-Rebsorten auf Qualitätsrebsorten Plasmopara viticola und andere Pathogene bekämpft, unterdrückt oder pflanzeneigene Abwehrmechanismen bei Qualitätsrebsorten durch in den Extrakten enthaltene Elicitoren aktiviert werden können resp. ob mit den Pflanzenextrakten eine direkte Bekämpfung dieser Problemschaderreger möglich ist. Kupferreduktionspotential bei Anbau neuer Vitis vinifera PIWI - Sorten: Der Anbau von PIWI’s ermöglicht einen weitgehenden Verzicht auf Pflanzenschutz und ist ökologisch und ökonomisch die nachhaltigste Form des Weinbaus überhaupt. Das Kupfereinsparungspotential durch den Anbau von PIWI’s ist vermutlich abhängig von der Resistenz der Sorte und von den klimatischen Bedingungen am Standort. Das für die jeweilige Sorte notwendige Maß an Pflanzenschutz soll in diesem Projekt erstmals ermittelt werden. Daraus lässt sich ein durchschnittliches Einsparpotential an Kupfer bestimmen. Orientierungsversuche mit geringen Stockzahlen im Freiland an Zuchtstämmen mit bereits pyramidisierten Plasmopara Resistenzen wurden in einer 2009 erstellten Prüfanlage mit Überkronenberegnung durchgeführt, in der beliebig hohe Befallsbedingungen für die Rebenperonospora geschaffen werden können

Understanding Terrorist Organizations with a Dynamic Model

Terrorist organizations change over time because of processes such as recruitment and training as well as counter-terrorism (CT) measures, but the effects of these processes are typically studied qualitatively and in separation from each other. Seeking a more quantitative and integrated understanding, we constructed a simple dynamic model where equations describe how these processes change an organization's membership. Analysis of the model yields a number of intuitive as well as novel findings. Most importantly it becomes possible to predict whether counter-terrorism measures would be sufficient to defeat the organization. Furthermore, we can prove in general that an organization would collapse if its strength and its pool of foot soldiers decline simultaneously. In contrast, a simultaneous decline in its strength and its pool of leaders is often insufficient and short-termed. These results and other like them demonstrate the great potential of dynamic models for informing terrorism scholarship and counter-terrorism policy making.Comment: To appear as Springer Lecture Notes in Computer Science v2: vectorized 4 figures, fixed two typos, more detailed bibliograph

Cryptic Population Dynamics: Rapid Evolution Masks Trophic Interactions

Trophic relationships, such as those between predator and prey or between pathogen and host, are key interactions linking species in ecological food webs. The structure of these links and their strengths have major consequences for the dynamics and stability of food webs. The existence and strength of particular trophic links has often been assessed using observational data on changes in species abundance through time. Here we show that very strong links can be completely missed by these kinds of analyses when changes in population abundance are accompanied by contemporaneous rapid evolution in the prey or host species. Experimental observations, in rotifer-alga and phage-bacteria chemostats, show that the predator or pathogen can exhibit large-amplitude cycles while the abundance of the prey or host remains essentially constant. We know that the species are tightly linked in these experimental microcosms, but without this knowledge, we would infer from observed patterns in abundance that the species are weakly or not at all linked. Mathematical modeling shows that this kind of cryptic dynamics occurs when there is rapid prey or host evolution for traits conferring defense against attack, and the cost of defense (in terms of tradeoffs with other fitness components) is low. Several predictions of the theory that we developed to explain the rotifer-alga experiments are confirmed in the phage-bacteria experiments, where bacterial evolution could be tracked. Modeling suggests that rapid evolution may also confound experimental approaches to measuring interaction strength, but it identifies certain experimental designs as being more robust against potential confounding by rapid evolution

Cryptic Population Dynamics: Rapid Evolution Masks Trophic Interactions

Trophic relationships, such as those between predator and prey or between pathogen and host, are key interactions linking species in ecological food webs. The structure of these links and their strengths have major consequences for the dynamics and stability of food webs. The existence and strength of particular trophic links has often been assessed using observational data on changes in species abundance through time. Here we show that very strong links can be completely missed by these kinds of analyses when changes in population abundance are accompanied by contemporaneous rapid evolution in the prey or host species. Experimental observations, in rotifer-alga and phage-bacteria chemostats, show that the predator or pathogen can exhibit large-amplitude cycles while the abundance of the prey or host remains essentially constant. We know that the species are tightly linked in these experimental microcosms, but without this knowledge, we would infer from observed patterns in abundance that the species are weakly or not at all linked. Mathematical modeling shows that this kind of cryptic dynamics occurs when there is rapid prey or host evolution for traits conferring defense against attack, and the cost of defense (in terms of tradeoffs with other fitness components) is low. Several predictions of the theory that we developed to explain the rotifer-alga experiments are confirmed in the phage-bacteria experiments, where bacterial evolution could be tracked. Modeling suggests that rapid evolution may also confound experimental approaches to measuring interaction strength, but it identifies certain experimental designs as being more robust against potential confounding by rapid evolution