Gompertz’s empirical equation remains the most popular one in describing cancer cell population growth in a wide spectrum of bio-medical situations due to its good fit to data and simplicity. Many efforts were documented in the literature aimed at understanding the mechanisms that may support Gompertz’s elegant model equation. One of the most convincing efforts was carried out by Gyllenberg and Webb. They divide the cancer cell population into the proliferative cells and the quiescent cells. In their two dimensional model, the dead cells are assumed to be removed from the tumor instantly. In this paper, we modify their model by keeping track of the dead cells remaining in the tumor. We perform mathematical and computational studies on this three dimensional model and compare the model dynamics to that of the model of Gyllenberg and Webb. Our mathematical findings suggest that if an avascular tumor grows according to our three-compartment model, then as the death rate of quiescent cells decreases to zero, the percentage of proliferative cells also approaches to zero. Moreover, a slow dying quiescent population will increase the size of the tumor. On the other hand, while the tumor size does not depend on the dead cell removal rate, its early and intermediate growth stages are very sensitive to it.

The sensitivity of Earth’s wetlands to observed shifts in global precipitation and temperature patterns and their ability to produce large quantities of methane gas are key global change questions. We present a microwave satellite-based approach for mapping fractional surface water (FW) globally at 25-km resolution. The approach employs a land cover-supported, atmospherically-corrected dynamic mixture model applied to 20+ years (1992–2013) of combined, daily, passive/active microwave remote sensing data. The resulting product, known as Surface Water Microwave Product Series (SWAMPS), shows strong microwave sensitivity to sub-grid scale open water and inundated wetlands comprising open plant canopies. SWAMPS’ FW compares favorably (R² = 91%–94%) with higher-resolution, global-scale maps of open water from MODIS and SRTM-MOD44W. Correspondence of SWAMPS with open water and wetland products from satellite SAR in Alaska and the Amazon deteriorates when exposed wetlands or inundated forests captured by the SAR products were added to the open water fraction reflecting SWAMPS’ inability to detect water underneath the soil surface or beneath closed forest canopies. Except for a brief period of drying during the first 4 years of observation, the inundation extent for the global domain excluding the coast was largely stable. Regionally, inundation in North America is advancing while inundation is on the retreat in Tropical Africa and North Eurasia. SWAMPS provides a consistent and long-term global record of daily FW dynamics, with documented accuracies suitable for hydrologic assessment and global change-related investigations.

A warming climate is altering land-atmosphere exchanges of carbon, with a potential for increased vegetation productivity as well as the mobilization of permafrost soil carbon stores. Here we investigate land-atmosphere carbon dioxide (CO₂) cycling through analysis of net ecosystem productivity (NEP) and its component fluxes of gross primary productivity (GPP) and ecosystem respiration (ER) and soil carbon residence time, simulated by a set of land surface models (LSMs) over a region spanning the drainage basin of Northern Eurasia. The retrospective simulations cover the period 1960–2009 at 0.5° resolution, which is a scale common among many global carbon and climate model simulations. Model performance benchmarks were drawn from comparisons against both observed CO₂ fluxes derived from site-based eddy covariance measurements as well as regional-scale GPP estimates based on satellite remote-sensing data.

The site-based comparisons depict a tendency for overestimates in GPP and ER for several of the models, particularly at the two sites to the south. For several models the spatial pattern in GPP explains less than half the variance in the MODIS MOD17 GPP product. Across the models NEP increases by as little as 0.01 to as much as 0.79 g C m^-2 yr^-2, equivalent to 3 to 340 % of the respective model means, over the analysis period. For the multimodel average the increase is 135 % of the mean from the first to last 10 years of record (1960–1969 vs. 2000–2009), with a weakening CO₂ sink over the latter decades. Vegetation net primary productivity increased by 8 to 30 % from the first to last 10 years, contributing to soil carbon storage gains. The range in regional mean NEP among the group is twice the multimodel mean, indicative of the uncertainty in CO₂ sink strength.

The models simulate that inputs to the soil carbon pool exceeded losses, resulting in a net soil carbon gain amid a decrease in residence time. Our analysis points to improvements in model elements controlling vegetation productivity and soil respiration as being needed for reducing uncertainty in land-atmosphere CO₂ exchange. These advances will require collection of new field data on vegetation and soil dynamics, the development of benchmarking data sets from measurements and remote-sensing observations, and investments in future model development and intercomparison studies.

Soil temperature (T_s) change is a key indicator of the dynamics of permafrost. On seasonal and interannual timescales, the variability of T_s determines the active-layer depth, which regulates hydrological soil properties and biogeochemical processes. On the multi-decadal scale, increasing T_s not only drives permafrost thaw/retreat but can also trigger and accelerate the decomposition of soil organic carbon. The magnitude of permafrost carbon feedbacks is thus closely linked to the rate of change of soil thermal regimes. In this study, we used nine process-based ecosystem models with permafrost processes, all forced by different observation-based climate forcing during the period 1960–2000, to characterize the warming rate of T_s in permafrost regions. There is a large spread of T_s trends at 20 cm depth across the models, with trend values ranging from 0.010 ± 0.003 to 0.031 ± 0.005 °C yr^-1. Most models show smaller increase in T_s with increasing depth. Air temperature (Tsub>a) and longwave downward radiation (LWDR) are the main drivers of T_s trends, but their relative contributions differ amongst the models. Different trends of LWDR used in the forcing of models can explain 61 % of their differences in T_s trends, while trends of T_a only explain 5 % of the differences in T_s trends. Uncertain climate forcing contributes a larger uncertainty in T_s trends (0.021 ± 0.008 °C yr^-1, mean ± standard deviation) than the uncertainty of model structure (0.012 ± 0.001 °C yr^-1), diagnosed from the range of response between different models, normalized to the same forcing. In addition, the loss rate of near-surface permafrost area, defined as total area where the maximum seasonal active-layer thickness (ALT) is less than 3 m loss rate, is found to be significantly correlated with the magnitude of the trends of T_s at 1 m depth across the models (R = −0.85, P = 0.003), but not with the initial total near-surface permafrost area (R = −0.30, P = 0.438). The sensitivity of the total boreal near-surface permafrost area to T_s at 1 m is estimated to be of −2.80 ± 0.67 million km²°C^-1. Finally, by using two long-term LWDR data sets and relationships between trends of LWDR and T_s across models, we infer an observation-constrained total boreal near-surface permafrost area decrease comprising between 39 ± 14  ×  10³ and 75 ± 14  ×  10³km²yr^-1 from 1960 to 2000. This corresponds to 9–18 % degradation of the current permafrost area.

A realistic simulation of snow cover and its thermal properties are important for accurate modelling of permafrost. We analyse simulated relationships between air and near-surface (20  cm) soil temperatures in the Northern Hemisphere permafrost region during winter, with a particular focus on snow insulation effects in nine land surface models, and compare them with observations from 268 Russian stations. There are large cross-model differences in the simulated differences between near-surface soil and air temperatures (ΔT; 3 to 14 °C), in the sensitivity of soil-to-air temperature (0.13 to 0.96 °C °^C-1), and in the relationship between ΔT and snow depth. The observed relationship between ΔT and snow depth can be used as a metric to evaluate the effects of each model's representation of snow insulation, hence guide improvements to the model's conceptual structure and process parameterisations. Models with better performance apply multilayer snow schemes and consider complex snow processes. Some models show poor performance in representing snow insulation due to underestimation of snow depth and/or overestimation of snow conductivity. Generally, models identified as most acceptable with respect to snow insulation simulate reasonable areas of near-surface permafrost (13.19 to 15.77 million  km²). However, there is not a simple relationship between the sophistication of the snow insulation in the acceptable models and the simulated area of Northern Hemisphere near-surface permafrost, because several other factors, such as soil depth used in the models, the treatment of soil organic matter content, hydrology and vegetation cover, also affect the simulated permafrost distribution.

A data set of observed daily precipitation, maximum and minimum temperature, gridded to a 1/16° (~6 km) resolution, is described that spans the entire country of Mexico, the conterminous U.S. (CONUS), and regions of Canada south of 53° N for the period 1950-2013. The dataset improves previous products in spatial extent, orographic precipitation adjustment over Mexico and parts of Canada, and reduction of transboundary discontinuities. The impacts of adjusting gridded precipitation for orographic effects are quantified by scaling precipitation to an elevation-aware 1981-2010 precipitation climatology in Mexico and Canada. Differences are evaluated in terms of total precipitation as well as by hydrologic quantities simulated with a land surface model. Overall, orographic correction impacts total precipitation by up to 50% in mountainous regions outside CONUS. Hydrologic fluxes show sensitivities of similar magnitude, with discharge more sensitive than evapotranspiration and soil moisture. Because of the consistent gridding methodology, the current product reduces transboundary discontinuities as compared with a commonly used reanalysis product, making it suitable for estimating large-scale hydrometeorologic phenomena.

The ongoing Zika virus (ZIKV) epidemic in the Americas poses a major global public health emergency. While ZIKV is transmitted from human to human by bites of Aedes mosquitoes, recent evidence indicates that ZIKV can also be transmitted via sexual contact with cases of sexually transmitted ZIKV reported in Argentina, Canada, Chile, France, Italy, New Zealand, Peru, Portugal, and the USA. Yet, the role of sexual transmission on the spread and control of ZIKV infection is not well-understood. We introduce a mathematical model to investigate the impact of mosquito-borne and sexual transmission on the spread and control of ZIKV and calibrate the model to ZIKV epidemic data from Brazil, Colombia, and El Salvador. Parameter estimates yielded a basic reproduction number R_0 = 2.055 (95% CI: 0.523–6.300), in which the percentage contribution of sexual transmission is 3.044% (95% CI: 0.123–45.73). Our sensitivity analyses indicate that R_0 is most sensitive to the biting rate and mortality rate of mosquitoes while sexual transmission increases the risk of infection and epidemic size and prolongs the outbreak. Prevention and control efforts against ZIKV should target both the mosquito-borne and sexual transmission routes.

Background: Androgens bind to the androgen receptor (AR) in prostate cells and are essential survival factors for healthy prostate epithelium. Most untreated prostate cancers retain some dependence upon the AR and respond, at least transiently, to androgen ablation therapy. However, the relationship between endogenous androgen levels and cancer etiology is unclear. High levels of androgens have traditionally been viewed as driving abnormal proliferation leading to cancer, but it has also been suggested that low levels of androgen could induce selective pressure for abnormal cells. We formulate a mathematical model of androgen regulated prostate growth to study the effects of abnormal androgen levels on selection for pre-malignant phenotypes in early prostate cancer development.

Results: We find that cell turnover rate increases with decreasing androgen levels, which may increase the rate of mutation and malignant evolution. We model the evolution of a heterogeneous prostate cell population using a continuous state-transition model. Using this model we study selection for AR expression under different androgen levels and find that low androgen environments, caused either by low serum testosterone or by reduced 5α-reductase activity, select more strongly for elevated AR expression than do normal environments. High androgen actually slightly reduces selective pressure for AR upregulation. Moreover, our results suggest that an aberrant androgen environment may delay progression to a malignant phenotype, but result in a more dangerous cancer should one arise.

Conclusions: The model represents a useful initial framework for understanding the role of androgens in prostate cancer etiology, and it suggests that low androgen levels can increase selection for phenotypes resistant to hormonal therapy that may also be more aggressive. Moreover, clinical treatment with 5α-reductase inhibitors such as finasteride may increase the incidence of therapy resistant cancers.