The sloppy model universality class and the Vandermonde matrix

In a variety of contexts, physicists study complex, nonlinear models with many unknown or tunable parameters to explain experimental data. We explain why such systems so often are sloppy; the system behavior depends only on a few `stiff' combinations of the parameters and is unchanged as other `sloppy' parameter combinations vary by orders of magnitude. We contrast examples of sloppy models (from systems biology, variational quantum Monte Carlo, and common data fitting) with systems which are not sloppy (multidimensional linear regression, random matrix ensembles). We observe that the eigenvalue spectra for the sensitivity of sloppy models have a striking, characteristic form, with a density of logarithms of eigenvalues which is roughly constant over a large range. We suggest that the common features of sloppy models indicate that they may belong to a common universality class. In particular, we motivate focusing on a Vandermonde ensemble of multiparameter nonlinear models and show in one limit that they exhibit the universal features of sloppy models.Comment: New content adde

Linking stoichiometric homeostasis with ecosystem structure, functioning, and stability

Ecosystem structure, functioning, and stability have been a focus of ecological and environmental sciences during the past two decades. The mechanisms underlying their relationship, however, are not well understood. Based on comprehensive studies in Inner Mongolia grassland, here we show that species-level stoichiometric homeostasis was consistently positively correlated with dominance and stability on both 2-year and 27-year temporal scales and across a 1200-km spatial transect. At the community level, stoichiometric homeostasis was also positively correlated with ecosystem function and stability in most cases. Thus, homeostatic species tend to have high and stable biomass; and ecosystems dominated by more homeostatic species have higher productivity and greater stability. By modulating organism responses to key environmental drivers, stoichiometric homeostasis appears to be a major mechanism responsible for the structure, functioning, and stability of grassland ecosystems

Soil pH, ecological stoichiometry, and allometric scaling in soil biota

The factors regulating the structure of food webs are a central focus of community and
ecosystem ecology, as trophic interactions among species have important impacts on
nutrient storage and cycling in many ecosystems. For soil invertebrates in grassland
ecosystems in the Netherlands, the site-specific slopes of the faunal biomass to organism body mass relationships reflected basic biochemical and biogeochemical processes associated with soil acidity and soil C:N:P stoichiometry. That is, the higher the phosphorus availability in the soil, the higher, on average, the slope of the faunal biomass size spectrum (i.e., the higher the biomass of large-bodied invertebrates relative to the biomass of small invertebrates). While other factors may also be involved, these results are consistent with the growth rate hypothesis from biological stoichiometry that relates phosphorus demands to ribosomal RNA and protein production. Thus our data represent the first time that ecosystem phosphorus availability has been associated with allometry in soil food webs (supporting information available online). Our results have broad implications, as soil invertebrates of different size have different effects on soil processes

Stoichiometry and the New Biology: The Future Is Now

There is a call for biological science to move away from the reductionist focus of the past, but there are large-scale integrative efforts already underway; biological stoichiometry provides one such example

Coherent diffraction of single Rice Dwarf virus particles using hard X-rays at the Linac Coherent Light Source

Single particle diffractive imaging data from Rice Dwarf Virus (RDV) were recorded using the Coherent X-ray Imaging (CXI) instrument at the Linac Coherent Light Source (LCLS). RDV was chosen as it is a wellcharacterized model system, useful for proof-of-principle experiments, system optimization and algorithm development. RDV, an icosahedral virus of about 70 nm in diameter, was aerosolized and injected into the approximately 0.1 mu m diameter focused hard X-ray beam at the CXI instrument of LCLS. Diffraction patterns from RDV with signal to 5.9 angstrom ngstrom were recorded. The diffraction data are available through the Coherent X-ray Imaging Data Bank (CXIDB) as a resource for algorithm development, the contents of which are described here.11Ysciescopu

Fine sediment reduces vertical migrations of Gammarus pulex (Crustacea: Amphipoda) in response to surface water loss

Surface and subsurface sediments in river ecosystems are recognized as refuges that may promote invertebrate survival during disturbances such as floods and streambed drying. Refuge use is spatiotemporally variable, with environmental factors including substrate composition, in particular the proportion of fine sediment (FS), affecting the ability of organisms to move through interstitial spaces. We conducted a laboratory experiment to examine the effects of FS on the movement of Gammarus pulex Linnaeus (Crustacea: Amphipoda) into subsurface sediments in response to surface water loss. We hypothesized that increasing volumes of FS would impede and ultimately prevent individuals from migrating into the sediments. To test this hypothesis, the proportion of FS (1–2 mm diameter) present within an open gravel matrix (4–16 mm diameter) was varied from 10 to 20% by volume in 2.5% increments. Under control conditions (0% FS), 93% of individuals moved into subsurface sediments as the water level was reduced. The proportion of individuals moving into the subsurface decreased to 74% at 10% FS, and at 20% FS no individuals entered the sediments, supporting our hypothesis. These results demonstrate the importance of reducing FS inputs into river ecosystems and restoring FS-clogged riverbeds, to promote refuge use during increasingly common instream disturbances

Stoichiometric Plant-Herbivore Models and Their Interpretation

The purpose of this note is to mechanistically formulate amathematically tractable model that specifically deals with thedynamics of plant-herbivore interaction in a closedphosphorous (P) limiting environment. The key to our approach isthe employment of the plant cell P quota and the Droopequation for its growth. Our model takes the simple form of asystem of two autonomous ordinary differential equations. It canbe shown that our model includes the LKE model (Loladze, Kuang and Elser (2000)) as a special case. Our study reveals that the details of ecological stoichiometry models really matter for quantitativepredictions of plant-herbivore dynamics, especially atintermediate ranges of the carrying capacity

Population structure and ecological effects of the crayfish \u3ci\u3ePacifastacus leniusculus\u3c/i\u3e in Castle Lake, California

The recent appearance of the California crayfish, Pacifastacus leniusculus, in Castle Lake, California, and interest in its potential impacts on the lake ecosystem provided motivation for a study of the population structure and habitat use of this species and its effects on aquatic macrophytes. Mark-recapture studies indicated that the total number of adult (3+ yr or older) crayfish in the lake was ca 10,100 individuals, yielding an estimate of lakewide crayfish density in preferred crayfish habitats of 0.13 adults m−2. Using mean body mass of individuals, we estimated that ambient biomass density was 5.9 g m−2. Length-weight relationships determined for captured individuals were sex dependent, with males having greater body mass for a given carapace length. Length-frequency and weight-frequency diagrams indicated that P. leniusculus reaches larger sizes in Castle Lake than do populations of P. leniusculus in ultraoligotrophic Lake Tahoe. Population-wide, males were significantly larger in both carapace length and body mass than females. We also examined sex dependence of interhabitat differences in crayfish body size by comparing animals trapped in rocky areas with those from areas with macrophytes and soft sediments. No significant differences in overall body size were found between habitats, but a significant habitat-sex interaction term occurred because the sex-dependent size differences were more pronounced in sediment than in rocky areas. Exclosure and enclosure experiments indicated that crayfish had large but differential impacts on Castle Lake macrophyte species, as the abundance of two of the dominant species (Chara sp., Potamogeton richardsonii) declined in the presence of crayfish and, in one case, increased in exclosures. These effects occurred via both consumptive and nonconsumptive mechanisms. These studies indicate that an expanding population of P. leniusculus in Castle Lake may be producing sizable impacts on the littoral zone habitat

Biological Stoichiometry in Human Cancer

A growing tumor in the body can be considered a complex ecological and evolutionary system. A new eco-evolutionary hypothesis (the "Growth Rate Hypothesis", GRH) proposes that tumors have elevated phosphorus (P) demands due to increased allocation to P-rich nucleic acids, especially ribosomal RNA, to meet the protein synthesis demands of accelerated proliferation.We determined the elemental (C, N, P) and nucleic acid contents of paired malignant and normal tissues from colon, lung, liver, or kidney for 121 patients. Consistent with the GRH, lung and colon tumors were significantly higher (by approximately two-fold) in P content (fraction of dry weight) and RNA content and lower in nitrogen (N):P ratio than paired normal tissue, and P in RNA contributed a significantly larger fraction of total biomass P in malignant relative to normal tissues. Furthermore, patient-specific differences for %P between malignant and normal tissues were positively correlated with such differences for %RNA, both for the overall data and within three of the four organ sites. However, significant differences in %P and %RNA between malignant and normal tissues were not seen in liver and kidney and, overall, RNA contributed only approximately 11% of total tissue P content.Data for lung and colon tumors provide support for the GRH in human cancer. The two-fold amplification of P content in colon and lung tumors may set the stage for potential P-limitation of their proliferation, as such differences often do for rapidly growing biota in ecosystems. However, data for kidney and liver do not support the GRH. To account for these conflicting observations, we suggest that local environments in some organs select for neoplastic cells bearing mutations increasing cell division rate ("r-selected," as in colon and lung) while conditions elsewhere may select for reduced mortality rate ("K-selected," as in liver and kidney)