Representing the acquisition and use of energy by individuals in agent-based models of animal populations

Summary 1. Agent-based models (ABMs) are widely used to predict how populations respond to changing environments. As the availability of food varies in space and time, individuals should have their own energy budgets, but there is no consensus as to how these should be modelled. Here, we use knowledge of physiological ecology to identify major issues confronting the modeller and to make recommendations about how energy budgets for use in ABMs should be constructed. 2. Our proposal is that modelled animals forage as necessary to supply their energy needs for maintenance, growth and reproduction. If there is sufficient energy intake, an animal allocates the energy obtained in the order: maintenance, growth, reproduction, energy storage, until its energy stores reach an optimal level. If there is a shortfall, the priorities for maintenance and growth/reproduction remain the same until reserves fall to a critical threshold below which all are allocated to maintenance. Rates of ingestion and allocation depend on body mass and temperature. We make suggestions for how each of these processes should be modelled mathematically. 3. Mortality rates vary with body mass and temperature according to known relationships, and these can be used to obtain estimates of background mortality rate. 4. If parameter values cannot be obtained directly, then values may provisionally be obtained by parameter borrowing, pattern-oriented modelling, artificial evolution or from allometric equations. 5. The development of ABMs incorporating individual energy budgets is essential for realistic modelling of populations affected by food availability. Such ABMs are already being used to guide conservation planning of nature reserves and shell fisheries, to assess environmental impacts of building proposals including wind farms and highways and to assess the effects on nontarget organisms of chemicals for the control of agricultural pests. Keywords: bioenergetics; energy budget; individual-based models; population dynamics.

Emission: a simple new technique to correct rainfall estimates from attenuation due to both the radome and heavy rainfall

We present a new technique for correcting errors in radar estimates of rainfall due to attenuation which is based on the fact that any attenuating target will itself emit, and that this emission can be detected by the increased noise level in the radar receiver. The technique is being installed on the UK operational network, and for the first time, allows radome attenuation to be monitored using the increased noise at the higher beam elevations. This attenuation has a large azimuthal dependence but for an old radome can be up to 4 dB for rainfall rates of just 2–4 mm/h. This effect has been neglected in the past, but may be responsible for significant errors in rainfall estimates and in radar calibrations using gauges. The extra noise at low radar elevations provides an estimate of the total path integrated attenuation of nearby storms; this total attenuation can then be used as a constraint for gate-by-gate or polarimetric correction algorithms.

The domain derivative in rough-surface scattering and rigorous estimates for first-order perturbation theory

We investigate Fréchet differentiability of the scattered field with respect to variation in the boundary in the case of time–harmonic acoustic scattering by an unbounded, sound–soft, one–dimensional rough surface. We rigorously prove the differentiability of the scattered field and derive a characterization of the Fréchet derivative as the solution to a Dirichlet boundary value problem. As an application of these results we give rigorous error estimates for first–order perturbation theory, justifying small perturbation methods that have a long history in the engineering literature. As an application of our rigorous estimates we show that a plane acoustic wave incident on a sound–soft rough surface can produce an unbounded scattered field.

Nonlinear saturation of baroclinic instability: part II: continuously stratified fluid

Rigorous upper bounds are derived that limit the finite-amplitude growth of arbitrary nonzonal disturbances to an unstable baroclinic zonal flow in a continuously stratified, quasi-geostrophic, semi-infinite fluid. Bounds are obtained bath on the depth-integrated eddy potential enstrophy and on the eddy available potential energy (APE) at the ground. The method used to derive the bounds is essentially analogous to that used in Part I of this study for the two-layer model: it relies on the existence of a nonlinear Liapunov (normed) stability theorem, which is a finite-amplitude generalization of the Charney-Stern theorem. As in Part I, the bounds are valid both for conservative (unforced, inviscid) flow, as well as for forced-dissipative flow when the dissipation is proportional to the potential vorticity in the interior, and to the potential temperature at the ground. The character of the results depends on the dimensionless external parameter γ = f02ξ/β0N2H, where ξ is the maximum vertical shear of the zonal wind, H is the density scale height, and the other symbols have their usual meaning. When γ ≫ 1, corresponding to “deep” unstable modes (vertical scale ≈H), the bound on the eddy potential enstrophy is just the total potential enstrophy in the system; but when γ≪1, corresponding to ‘shallow’ unstable modes (vertical scale ≈γH), the eddy potential enstrophy can be bounded well below the total amount available in the system. In neither case can the bound on the eddy APE prevent a complete neutralization of the surface temperature gradient which is in accord with numerical experience. For the special case of the Charney model of baroclinic instability, and in the limit of infinitesimal initial eddy disturbance amplitude, the bound states that the dimensionless eddy potential enstrophy cannot exceed (γ + 1)2/24&gamma2h when γ ≥ 1, or 1/6;&gammah when γ ≤ 1; here h = HN/f0L is the dimensionless scale height and L is the width of the channel. These bounds are very similar to (though of course generally larger than) ad hoc estimates based on baroclinic-adjustment arguments. The possibility of using these kinds of bounds for eddy-amplitude closure in a transient-eddy parameterization scheme is also discussed.

Quantitative estimates of glacial and Holocene temperature and precipitation change in lowland Amazonian Bolivia

Quantitative estimates of temperature and precipitation change during the late Pleistocene and Holocene have been difficult to obtain for much of the lowland Neotropics. Using two published lacustrine pollen records and a climate-vegetation model based on the modern abundance distributions of 154 Neotropical plant families, we demonstrate how family-level counts of fossil pollen can be used to quantitatively reconstruct tropical paleoclimate and provide needed information on historic patterns of climatic change. With this family-level analysis, we show that one area of the lowland tropics, northeastern Bolivia, experienced cooling (1–3 °C) and drying (400 mm/yr), relative to present, during the late Pleistocene (50,000–12,000 calendar years before present [cal. yr B.P.]). Immediately prior to the Last Glacial Maximum (LGM, ca. 21,000 cal. yr B.P.), we observe a distinct transition from cooler temperatures and variable precipitation to a period of warmer temperatures and relative dryness that extends to the middle Holocene (5000–3000 cal. yr B.P.). This prolonged reduction in precipitation occurs against the backdrop of increasing atmospheric CO2 concentrations, indicating that the presence of mixed savanna and dry-forest communities in northeastern Bolivia durng the LGM was not solely the result of low CO2 levels, as suggested previously, but also lower precipitation. The results of our analysis demonstrate the potential for using the distribution and abundance structure of modern Neotropical plant families to infer paleoclimate from the fossil pollen record.

Input type and parameter resetting: is naturalistic input necessary?

It has been argued that extended exposure to naturalistic input provides L2 learners with more of an opportunity to converge of target morphosyntactic competence as compared to classroom-only environments, given that the former provide more positive evidence of less salient linguistic properties than the latter (e.g., Isabelli 2004). Implicitly, the claim is that such exposure is needed to fully reset parameters. However, such a position conflicts with the notion of parameterization (cf. Rothman and Iverson 2007). In light of two types of competing generative theories of adult L2 acquisition – the No Impairment Hypothesis (e.g., Duffield and White 1999) and so-called Failed Features approaches (e.g., Beck 1998; Franceschina 2001; Hawkins and Chan 1997), we investigate the verifiability of such a claim. Thirty intermediate L2 Spanish learners were tested in regards to properties of the Null-Subject Parameter before and after study-abroad. The data suggest that (i) parameter resetting is possible and (ii) exposure to naturalistic input is not privileged.

Optimal convergence estimates for the trace of the polynomial L2-projection operator on a simplex

In this paper we study convergence of the L2-projection onto the space of polynomials up to degree p on a simplex in Rd, d >= 2. Optimal error estimates are established in the case of Sobolev regularity and illustrated on several numerical examples. The proof is based on the collapsed coordinate transform and the expansion into various polynomial bases involving Jacobi polynomials and their antiderivatives. The results of the present paper generalize corresponding estimates for cubes in Rd from [P. Houston, C. Schwab, E. Süli, Discontinuous hp-finite element methods for advection-diffusion-reaction problems. SIAM J. Numer. Anal. 39 (2002), no. 6, 2133-2163].

Near-optimal mean value estimates for multidimensional Weyl sums

We obtain sharp estimates for multidimensional generalisations of Vinogradov’s mean value theorem for arbitrary translation-dilation invariant systems, achieving constraints on the number of variables approaching those conjectured to be the best possible. Several applications of our bounds are discussed.

Constructing summary statistics for approximate Bayesian computation: semi-automatic approximate Bayesian computation

Many modern statistical applications involve inference for complex stochastic models, where it is easy to simulate from the models, but impossible to calculate likelihoods. Approximate Bayesian computation (ABC) is a method of inference for such models. It replaces calculation of the likelihood by a step which involves simulating artificial data for different parameter values, and comparing summary statistics of the simulated data with summary statistics of the observed data. Here we show how to construct appropriate summary statistics for ABC in a semi-automatic manner. We aim for summary statistics which will enable inference about certain parameters of interest to be as accurate as possible. Theoretical results show that optimal summary statistics are the posterior means of the parameters. Although these cannot be calculated analytically, we use an extra stage of simulation to estimate how the posterior means vary as a function of the data; and we then use these estimates of our summary statistics within ABC. Empirical results show that our approach is a robust method for choosing summary statistics that can result in substantially more accurate ABC analyses than the ad hoc choices of summary statistics that have been proposed in the literature. We also demonstrate advantages over two alternative methods of simulation-based inference.

Sequential variations of phytoplankton growth and mortality in an NPZ model: a remote-sensing-based assessment

Radiometric data in the visible domain acquired by satellite remote sensing have proven to be powerful for monitoring the states of the ocean, both physical and biological. With the help of these data it is possible to understand certain variations in biological responses of marine phytoplankton on ecological time scales. Here, we implement a sequential data-assimilation technique to estimate from a conventional nutrient–phytoplankton–zooplankton (NPZ) model the time variations of observed and unobserved variables. In addition, we estimate the time evolution of two biological parameters, namely, the specific growth rate and specific mortality of phytoplankton. Our study demonstrates that: (i) the series of time-varying estimates of specific growth rate obtained by sequential data assimilation improves the fitting of the NPZ model to the satellite-derived time series: the model trajectories are closer to the observations than those obtained by implementing static values of the parameter; (ii) the estimates of unobserved variables, i.e., nutrient and zooplankton, obtained from an NPZ model by implementation of a pre-defined parameter evolution can be different from those obtained on applying the sequences of parameters estimated by assimilation; and (iii) the maximum estimated specific growth rate of phytoplankton in the study area is more sensitive to the sea-surface temperature than would be predicted by temperature-dependent functions reported previously. The overall results of the study are potentially useful for enhancing our understanding of the biological response of phytoplankton in a changing environment.

Modeling ocean primary production: sensitivity to spectral resolution of attenuation and absorption of light

Modeling the vertical penetration of photosynthetically active radiation (PAR) through the ocean, and its utilization by phytoplankton, is fundamental to simulating marine primary production. The variation of attenuation and absorption of light with wavelength suggests that photosynthesis should be modeled at high spectral resolution, but this is computationally expensive. To model primary production in global 3d models, a balance between computer time and accuracy is necessary. We investigate the effects of varying the spectral resolution of the underwater light field and the photosynthetic efficiency of phytoplankton (α∗), on primary production using a 1d coupled ecosystem ocean turbulence model. The model is applied at three sites in the Atlantic Ocean (CIS (∼60°N), PAP (∼50°N) and ESTOC (∼30°N)) to include the effect of different meteorological forcing and parameter sets. We also investigate three different methods for modeling α∗ – as a fixed constant, varying with both wavelength and chlorophyll concentration [Bricaud, A., Morel, A., Babin, M., Allali, K., Claustre, H., 1998. Variations of light absorption by suspended particles with chlorophyll a concentration in oceanic (case 1) waters. Analysis and implications for bio-optical models. J. Geophys. Res. 103, 31033–31044], and using a non-spectral parameterization [Anderson, T.R., 1993. A spectrally averaged model of light penetration and photosynthesis. Limnol. Oceanogr. 38, 1403–1419]. After selecting the appropriate ecosystem parameters for each of the three sites we vary the spectral resolution of light and α∗ from 1 to 61 wavebands and study the results in conjunction with the three different α∗ estimation methods. The results show modeled estimates of ocean primary productivity are highly sensitive to the degree of spectral resolution and α∗. For accurate simulations of primary production and chlorophyll distribution we recommend a spectral resolution of at least six wavebands if α∗ is a function of wavelength and chlorophyll, and three wavebands if α∗ is a fixed value.

Improving real-time estimates of output and inflation gaps with multiple-vintage models

Real-time estimates of output gaps and inflation gaps differ from the values that are obtained using data available long after the event. Part of the problem is that the data on which the real-time estimates are based is subsequently revised. We show that vector-autoregressive models of data vintages provide forecasts of post-revision values of future observations and of already-released observations capable of improving estimates of output and inflation gaps in real time. Our findings indicate that annual revisions to output and inflation data are in part predictable based on their past vintages.