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Results for “Journal of Nonlinear Science”

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USGS2011

A predator-prey model with a holling type I functional response including a predator mutual interference

The most widely used functional response in describing predator-prey relationships is the Holling type II functional response, where per capita predation is a smooth, increasing, and saturating function of prey density. Beddington and DeAngelis modified the Holling type II response to include interference of predators that increases with predator density. Here we introduce a predator-interference term into a Holling type I functional response. We explain the ecological rationale for the response and note that the phase plane configuration of the predator and prey isoclines differs greatly from that of the Beddington-DeAngelis response; for example, in having three possible interior equilibria rather than one. In fact, this new functional response seems to be quite unique. We used analytical and numerical methods to show that the resulting system shows a much richer dynamical behavior than the Beddington-DeAngelis response, or other typically used functional responses. For example, cyclic-fold, saddle-fold, homoclinic saddle connection, and multiple crossing bifurcations can all occur. We then use a smooth approximation to the Holling type I functional response with predator mutual interference to show that these dynamical properties do not result from the lack of smoothness, but rather from subtle differences in the functional responses. ?? 2011 Springer Science+Business Media, LLC.

Journal of Nonlinear Science↗

USGS1996

Numerical evaluation of static-chamber measurements of soil-atmospheric gas exchange--Identification of physical processes

The exchange of gases between soil and atmosphere is an important process that affects atmospheric chemistry and therefore climate. The static-chamber method is the most commonly used technique for estimating the rate of that exchange. We examined the method under hypothetical field conditions where diffusion was the only mechanism for gas transport and the atmosphere outside the chamber was maintained at a fixed concentration. Analytical and numerical solutions to the soil gas diffusion equation in one and three dimensions demonstrated that gas flux density to a static chamber deployed on the soil surface was less in magnitude than the ambient exchange rate in the absence of the chamber. This discrepancy, which increased with chamber deployment time and air-filled porosity of soil, is attributed to two physical factors: distortion of the soil gas concentration gradient (the magnitude was decreased in the vertical component and increased in the radial component) and the slow transport rate of diffusion relative to mixing within the chamber. Instantaneous flux density to a chamber decreased continuously with time; steepest decreases occurred so quickly following deployment and in response to such slight changes in mean chamber headspace concentration that they would likely go undetected by most field procedures. Adverse influences of these factors were reduced by mixing the chamber headspace, minimizing deployment time, maximizing the height and radius of the chamber, and pushing the rim of the chamber into the soil. Nonlinear models were superior to a linear regression model for estimating flux densities from mean headspace concentrations, suggesting that linearity of headspace concentration with time was not necessarily a good indicator of measurement accuracy.

Soil Science Society of America Journal↗

USGS2011

Multimodel inference and adaptive management

Ecology is an inherently complex science coping with correlated variables, nonlinear interactions and multiple scales of pattern and process, making it difficult for experiments to result in clear, strong inference. Natural resource managers, policy makers, and stakeholders rely on science to provide timely and accurate management recommendations. However, the time necessary to untangle the complexities of interactions within ecosystems is often far greater than the time available to make management decisions. One method of coping with this problem is multimodel inference. Multimodel inference assesses uncertainty by calculating likelihoods among multiple competing hypotheses, but multimodel inference results are often equivocal. Despite this, there may be pressure for ecologists to provide management recommendations regardless of the strength of their study’s inference. We reviewed papers in the Journal of Wildlife Management (JWM) and the journal Conservation Biology (CB) to quantify the prevalence of multimodel inference approaches, the resulting inference (weak versus strong), and how authors dealt with the uncertainty. Thirty-eight percent and 14%, respectively, of articles in the JWM and CB used multimodel inference approaches. Strong inference was rarely observed, with only 7% of JWM and 20% of CB articles resulting in strong inference. We found the majority of weak inference papers in both journals (59%) gave specific management recommendations. Model selection uncertainty was ignored in most recommendations for management. We suggest that adaptive management is an ideal method to resolve uncertainty when research results in weak inference.

Journal of Environmental Management↗

USGS2011

Nutrient fluxes and the recent collapse of coastal California salmon populations

Migratory salmon move nutrients both in and out of fresh waters during the different parts of their life cycle. We used a mass-balance approach to quantify recent changes in phosphorus (P) fluxes in six coastal California, USA, watersheds that have recently experienced dramatic decreases in salmon populations. As adults, semelparous Chinook ( Oncorhynchus tshawytscha ) and coho ( Oncorhynchus kisutch ) salmon imported 8.3 and 10.4 times more P from the ocean, respectively, than they exported as smolts, while iteroparous steelhead (i.e., sea-run rainbow trout, Oncorhynchus mykiss ) imported only 1.6 times more than they exported as kelts and smolts. Semelparous species whose life histories led them to import more nutrients were also the species whose populations decreased the most dramatically in California in recent years. In addition, the relationship between import and export was nonlinear, with export being proportionally more important at lower levels of import. This pattern was driven by two density-dependent processes — smolts were larger and disproportionately more abundant at lower spawner abundances. In fact, in four of our six streams we found evidence that salmon can drive net export of P at low abundance, evidence for the reversal of the "conveyor belt" of nutrients.

California↗

USGS2002

Improving the analysis of slug tests

This paper examines several techniques that have the potential to improve the quality of slug test analysis. These techniques are applicable in the range from low hydraulic conductivities with overdamped responses to high hydraulic conductivities with nonlinear oscillatory responses. Four techniques for improving slug test analysis will be discussed: use of an extended capability nonlinear model, sensitivity analysis, correction for acceleration and velocity effects, and use of multiple slug tests. The four-parameter nonlinear slug test model used in this work is shown to allow accurate analysis of slug tests with widely differing character. The parameter ?? represents a correction to the water column length caused primarily by radius variations in the wellbore and is most useful in matching the oscillation frequency and amplitude. The water column velocity at slug initiation (V0) is an additional model parameter, which would ideally be zero but may not be due to the initiation mechanism. The remaining two model parameters are A (parameter for nonlinear effects) and K (hydraulic conductivity). Sensitivity analysis shows that in general ?? and V0 have the lowest sensitivity and K usually has the highest. However, for very high K values the sensitivity to A may surpass the sensitivity to K. Oscillatory slug tests involve higher accelerations and velocities of the water column; thus, the pressure transducer responses are affected by these factors and the model response must be corrected to allow maximum accuracy for the analysis. The performance of multiple slug tests will allow some statistical measure of the experimental accuracy and of the reliability of the resulting aquifer parameters. ?? 2002 Elsevier Science B.V. All rights reserved.

Journal of Hydrology↗

USGS2013

Salmon-mediated nutrient flux in selected streams of the Columbia River basin, USA

Salmon provide an important resource subsidy and linkage between marine and land-based ecosystems. This flow of energy and nutrients is not uni-directional (i.e., upstream only); in addition to passive nutrient export via stream flow, juvenile emigrants actively export nutrients from freshwater environments. In some cases, nutrient export can exceed import. We evaluated nutrient fluxes in streams across central Idaho, USA using Chinook salmon (Oncorhynchus tshawytscha) adult escapement and juvenile production data from 1998 to 2008. We found in the majority of stream-years evaluated, adults imported more nutrients than progeny exported; however, in 3% of the years, juveniles exported more nutrients than their parents imported. On average, juvenile emigrants exported 22 ± 3% of the nitrogen and 30 ± 4% of the phosphorus their parents imported. This relationship was density dependent and nonlinear; during periods of low adult abundance juveniles were larger and exported up to 194% and 268% of parental nitrogen and phosphorus inputs, respectively. We highlight minimum escapement thresholds that appear to 1) maintain consistently positive net nutrient flux and 2) reduce the average proportional rate of export across study streams. Our results suggest a state-shift occurs when adult spawner abundance falls below a threshold to a point where the probability of juvenile nutrient exports exceeding adult imports becomes increasingly likely.

Idaho↗

USGS2017

Deleterious effects of net clogging on the quantification of stream drift

Drift studies are central to stream and river ecological research. However, a fundamental aspect of quantifying drift — how net clogging affects the accuracy of results — has been widely ignored. Utilizing approaches from plankton and suspended sediment studies in oceanography and hydrology, we examined the rate and dynamics of net clogging across a range of conditions. We found that nets clog nonlinearly over time and that suspended solid concentrations and net mesh size exerted a strong effect on clogging rates. Critically, net clogging introduced unpredictable biases in resultant data due to the inaccuracies in water volume estimates introduced by progressive clogging. This renders the widespread approach to linearly “correct” for clogging inadequate. Using a meta-analysis of 77 drift studies spanning 25 years, we demonstrate that the detrimental effects of net clogging are routinely unappreciated, even though the results of most of these studies were likely affected by clogging. We close by describing an approach for avoiding net clogging, which will increase the accuracy and reproducibility of results in future freshwater, lotic drift studies.

Canadian Journal of Fisheries and Aquatic Sciences↗

USGS2010

Seasonal H2O and CO2 ice cycles at the Mars Phoenix landing site: 1. Prelanding CRISM and HiRISE observations

The condensation, evolution, and sublimation of seasonal water and carbon dioxide ices were characterized at the Mars Phoenix landing site from Martian northern midsummer to midspring (L s ∼ 142° – L s ∼ 60°) for the year prior to the Phoenix landing on 25 May 2008. Ice relative abundances and grain sizes were estimated using data from the Compact Reconnaissance Imaging Spectrometer for Mars and High Resolution Imaging Science Experiment aboard Mars Reconnaissance Orbiter and a nonlinear mixing model. Water ice first appeared at the Phoenix landing site during the afternoon in late summer (L s ∼ 167°) as an optically thin layer on top of soil. CO 2 ice appeared after the fall equinox. By late winter (L s ∼ 344°), the site was covered by relatively pure CO 2 ice (∼30 cm thick), with a small amount of ∼100 μ m diameter water ice and soil. As spring progressed, CO 2 ice grain sizes gradually decreased, a change interpreted to result from granulation during sublimation losses. The combined effect of CO 2 sublimation and decreasing H 2 O ice grain sizes allowed H 2 O ice to dominate spectra during the spring and significantly brightened the surface. CO 2 ice disappeared by early spring (L s ∼ 34°) and H 2 O ice by midspring (L s ∼ 59°). Spring defrosting was not uniform and occurred more rapidly over the centers of polygons and geomorphic units with relatively higher thermal inertia values.

Journal of Geophysical Research E: Planets↗

USGS2018

Degradation of 100‐m‐scale rocky ejecta craters at the InSight Landing Site on Mars and implications for surface processes and erosion rates in the hesperian and amazonian

Rocky ejecta craters (RECs) at the Interior Exploration using Seismic Investigations, Geodesy and Heat Transport (InSight) landing site on Elysium Planitia, Mars, provide constraints on crater modification and rates for the Hesperian and Amazonian. The RECs are between 10 m and 1.2 km in diameter and exhibit five classes of preservation. Class 1 represents pristine craters with sharp rims and abundant ejected rocks. From Classes 2 to 5, rims become more subdued, craters are infilled, and the ejecta become discontinuously distributed. High‐Resolution Imaging Science Experiment digital elevation models indicate a maximum depth to diameter ratio of ~0.15, which is lower than pristine models for craters of similar size. The low ratio is related to the presence of a loosely consolidated regolith and early‐stage eolian infill. Rim heights have an average height to diameter ratio of ~0.03 for the most pristine class. The size‐frequency distribution of RECs, plotted using cumulative and differential methods, indicates that crater classes within the diameter range of 200 m to 1.2 km are separated by ~100 to 200 Myr. Smaller craters degrade faster, with classes separated by <100 Myr. Rim erosion can be entirely modeled by nonlinear diffusional processes using the calculated timescales and a constant diffusivity of 8 × 10 −7 m 2 /year for craters 200 to 500 m in diameter. Diffusion models only partly capture depth‐related degradation, which requires eolian infill. Depth degradation and rim erosion rates are 10 −2 to 10 −3 m/Myr, respectively. The rates are consistent with relatively slow modification that is typical of the last two epochs of Martian history.

Journal of Geophysical Research - Planets↗

USGS1997

Gillnet selectivity for lake trout ( Salvelinus namaycush ) in Lake Superior

Gillnet selectivity for lake trout (Salvelinus namaycush) was estimated indirectly from catches in nets of 102-, 114-, 127-, 140-, and 152-mm stretch measure. Mesh selectivity was modeled as a nonlinear response surface that describes changes in the mean, standard deviation, and skewness of fish lengths across mesh sizes. Gillnet selectivity for lake trout was described by five parameters that explained 88% of the variation in wedged and entangled catches, 81% of the variation in wedged catches, and 82% of the variation in entangled catches. Combined catches of wedged and entangled lake trout were therefore described more parsimoniously than separate catches of wedged and entangled lake trout. Peak selectivity of wedged and entangled fish increased from 588 to 663 mm total length as mesh size increased from 102 to 152 mm, and relative selectivity peaked at a total length of 638 mm. The estimated lake trout population size-frequency indicated that gillnet catches were negatively biased toward both small and large lake trout. As a consequence of this bias, survival of Lake Superior lake trout across ages 9-11 was underestimated by about 20% when the catch curve was not adjusted for gillnet selectivity.

Canadian Journal of Fisheries and Aquatic Sciences↗

USGS2021

Techniques to improve ecological interpretability of black box machine learning models

Statistical modeling of ecological data is often faced with a large number of variables as well as possible nonlinear relationships and higher-order interaction effects. Gradient boosted trees (GBT) have been successful in addressing these issues and have shown a good predictive performance in modeling nonlinear relationships, in particular in classification settings with a categorical response variable. They also tend to be robust against outliers. However, their black-box nature makes it difficult to interpret these models. We introduce several recently developed statistical tools to the environmental research community in order to advance interpretation of these black-box models. To analyze the properties of the tools, we applied gradient boosted trees to investigate biological health of streams within the contiguous USA, as measured by a benthic macroinvertebrate biotic index. Based on these data and a simulation study, we demonstrate the advantages and limitations of partial dependence plots (PDP), individual conditional expectation (ICE) curves and accumulated local effects (ALE) in their ability to identify covariate–response relationships. Additionally, interaction effects were quantified according to interaction strength (IAS) and Friedman’s H 2 "> H 2 statistic. Interpretable machine learning techniques are useful tools to open the black-box of gradient boosted trees in the environmental sciences. This finding is supported by our case study on the effect of impervious surface on the benthic condition, which agrees with previous results in the literature. Overall, the most important variables were ecoregion, bed stability, watershed area, riparian vegetation and catchment slope. These variables were also present in most identified interaction effects. In conclusion, graphical tools (PDP, ICE, ALE) enable visualization and easier interpretation of GBT but should be supported by analytical statistical measures. Future methodological research is needed to investigate the properties of interaction tests. Supplementary materials accompanying this paper appear on-line.

Journal of Agricultural, Biological, and Environme↗