Measured Growth Rates Research Articles

UAV Image-Based Crop Growth Analysis of 3D-Reconstructed Crop Canopies.

Plant growth rate is an essential phenotypic parameter for quantifying potential crop productivity. Under field conditions, manual measurement of plant growth rate is less accurate in most cases. Image-based high-throughput platforms offer great potential for rapid, non-destructive, and objective estimation of plant growth parameters. The aim of this study was to assess the potential for quantifying plant growth rate using UAV-based (unoccupied aerial vehicle) imagery collected multiple times throughout the growing season. In this study, six diverse lines of lentils were grown in three replicates of 1 m2 microplots with six biomass collection time-points throughout the growing season over five site-years. Aerial imagery was collected simultaneously with each manual measurement of the above-ground biomass time-point and was used to produce two-dimensional orthomosaics and three-dimensional point clouds. Non-linear logistic models were fit to multiple data collection points throughout the growing season. Overall, remotely detected vegetation area and crop volume were found to produce trends comparable to the accumulation of dry weight biomass throughout the growing season. The growth rate and G50 (days to 50% of maximum growth) parameters of the model effectively quantified lentil growth rate indicating significant potential for image-based tools to be used in plant breeding programs. Comparing image-based groundcover and vegetation volume estimates with manually measured above-ground biomass suggested strong correlations. Vegetation area measured from a UAV has utility in quantifying lentil biomass and is indicative of leaf area early in the growing season. For mid- to late-season biomass estimation, plot volume was determined to be a better estimator. Apart from traditional traits, the estimation and analysis of plant parameters not typically collected in traditional breeding programs are possible with image-based methods, and this can create new opportunities to improve breeding efficiency mainly by offering new phenotypes and affecting selection intensity.

Complex Growth of Benzamide Form I: Effect of Additives, Solution Flow, and Surface Rugosity.

Understanding crystal growth kinetics is of great importance for the development and manufacturing of crystalline molecular materials. In this work, the impact of additives on the growth kinetics of benzamide form I (BZM-I) crystals has been studied. Using our newly developed crystal growth setup for the measurement of facet-specific crystal growth rates under flow, BZM-I growth rates were measured in the presence of various additives previously reported to induce morphological changes. The additives did not have a significant impact on the growth rates of BZM-I at low concentrations. By comparison to other systems, these additives could not be described as “effective” since BZM-I showed a high tolerance of the additives’ presence during growth, which may be a consequence of the type of growth mechanisms at play. Growth of pure BZM-I was found to be extremely defected, and perhaps those defects allow the accommodation of impurities. An alternative explanation is that at low additive concentrations, solid solutions are formed, which was indeed confirmed for a few of the additives. Additionally, the growth of BZM-I was found to be significantly affected by solution dynamics. Changes in some facet growth rates were observed with changes in the orientation of the BZM-I single crystals relative to the solution flow. Of the two sets of facets involved in the growth of the width and length of the crystal, the {10l̅} facets were found to be greatly affected by the solution flow while the {011} facets were not affected at all. Computational fluid dynamics simulations showed that solute concentration has higher gradients at the edges of the leading edge {10l̅} facets, which can explain the appearance of satellite crystals. {10l̅} facets were found to show significant structural rugosity at the molecular level, which may play a role in their mechanism of growth. The work highlights the complexities of measuring crystal growth data of even simple systems such as BZM-I, specifically addressing the effect of additives and fluid dynamics.

Measurements of cosmic expansion and growth rate of structure from voids in the Sloan Digital Sky Survey between redshift 0.07 and 1.0

ABSTRACT We present measurements of the anisotropic cross-correlation of galaxies and cosmic voids in data from the Sloan Digital Sky Survey (SDSS) Main Galaxy Sample, Baryon Oscillation Spectroscopic Survey (BOSS), and extended BOSS luminous red galaxy catalogues from SDSS Data Releases 7, 12, and 16, covering the redshift range 0.07 < z < 1.0. As in our previous work analysing voids in subsets of these data, we use a reconstruction method applied to the galaxy data before void finding in order to remove selection biases when constructing the void samples. We report results of a joint fit to the multipole moments of the measured cross-correlation for the growth rate of structure, fσ8(z), and the ratio DM(z)/DH(z) of the comoving angular diameter distance to the Hubble distance, in six redshift bins. For DM/DH, we are able to achieve a significantly higher precision than that obtained from analyses of the baryon acoustic oscillations and galaxy clustering in the same data sets. Our growth rate measurements are of lower precision but still comparable with galaxy clustering results. For both quantities, the results agree well with the expectations for a Λ cold dark matter model. Assuming a flat Universe, our results correspond to a measurement of the matter density parameter $\Omega _\mathrm{m}=0.337^{+0.026}_{-0.029}$. For more general models, the degeneracy directions obtained are consistent with and complementary to those from other cosmological probes. These results consolidate void–galaxy cross-correlation measurements as a pillar of modern observational cosmology.

Direct Measurement of the Return Current Instability in a Laser-Produced Plasma

Measurements were made of the return current instability growth rate, demonstrating its concurrence with nonlocal transport. Thomson scattering was used to measure a maximum growth rate of 5.1×10^{9} Hz, which was 3 times less than classical Spitzer-Härm theory predicts. The measured plasma conditions indicate the heat flux was nonlocal, and Vlasov-Fokker-Planck simulations that account for nonlocality reproduce the measured growth rates. Furthermore, the threshold for the return current instability was measured (δ_{T}=0.017±0.002) to be in good agreement with previous theoretical models.

Impact of intrinsic alignments on clustering constraints of the growth rate

ABSTRACT Intrinsic alignments between galaxies and the large-scale structure contaminate galaxy clustering analyses and impact constraints on galaxy bias and the growth rate of structure in the Universe. This is the result of alignments inducing a selection effect on spectroscopic samples which is correlated with the large-scale structure. In this work, we quantify the biases on galaxy bias and the growth rate when alignments are neglected. We also examine different options for the mitigation of alignments by considering external priors on the effect and different probe combinations. We find that conservative analyses that restrict to kmax = 0.1 Mpc−1 are not significantly affected. However, analyses that aim to go to higher wave numbers could evidence a significant contamination from alignments. In those cases, including a prior on alignment amplitude, or combining clustering with the position-intrinsic shape correlation of galaxies, can recover the same expected constraining power, or even inform bias and growth rate measurements.

Crack Growth Behavior in High pH Carbonate/Bicarbonate Environments: Application of Crack Tip Strain Rate Modeling

Aging pipeline infrastructure is subject to various degradation modes, in particular, there is a growing concern about stress corrosion cracking (SCC) from external environments. The current program focused on developing data in high pH carbonate/bicarbonate environments as a function of temperature, applied potential, and loading modes in three different pipeline steels. Crack growth rate (CGR) measurements indicate that the susceptibility to SCC increases with increasing temperature and is higher under low-cycle fatigue compared to constant K conditions. The CGR behavior at each temperature was a strong function of the applied potential, coinciding with the potential range of the active-passive transition in the polarization scans. The potential at which a peak in crack growth rate was observed, coincided with the peak value of the ratio of the current density from the fast to slow scans. The CGR data were fitted to a crack tip strain rate-based model to account for both the cyclic as well as static CGR. The model developed was able to successfully predict prior data in the literature generated under various loading conditions.

Neural operator learning of heterogeneous mechanobiological insults contributing to aortic aneurysms.

Thoracic aortic aneurysm (TAA) is a localized dilatation of the aorta that can lead to life-threatening dissection or rupture. In vivo assessments of TAA progression are largely limited to measurements of aneurysm size and growth rate. There is promise, however, that computational modelling of the evolving biomechanics of the aorta could predict future geometry and properties from initiating mechanobiological insults. We present an integrated framework to train a deep operator network (DeepONet)-based surrogate model to identify TAA contributing factors using synthetic finite-element-based datasets. For training, we employ a constrained mixture model of aortic growth and remodelling to generate maps of local aortic dilatation and distensibility for multiple TAA risk factors. We evaluate the performance of the surrogate model for insult distributions varying from fusiform (analytically defined) to complex (randomly generated). We propose two frameworks, one trained on sparse information and one on full-field greyscale images, to gain insight into a preferred neural operator-based approach. We show that this continuous learning approach can predict the patient-specific insult profile associated with any given dilatation and distensibility map with high accuracy, particularly when based on full-field images. Our findings demonstrate the feasibility of applying DeepONet to support transfer learning of patient-specific inputs to predict TAA progression.

Preparation and Evaluation of Siderol Amorphous Solid Dispersions: Selection of Suitable Matrix/Carrier.

The present study investigates the preparation of amorphous solid dispersions (ASD) for the ent-kaurane diterpenoid siderol (SDR). Initially, evaluation of the pure drug (isolated from Sideritis scardica) revealed that the API is a non-stable glass former, and hence the selection of a suitable ASD's matrix/carrier needs special attention. For this reason, four commonly used polymers and copolymers, namely poly(vinylpyrrolidone), copovidone, hydroxypropyl cellulose, and Soluplus® (SOL), were screenedviafilm casting and crystal growth rate measurements. Amongst them, SOL showed the highest SDR's crystal growth rate reduction, and, since it was also miscible with the drug, it was selected for further testing. In this direction, SDR-SOL ASDs were successfully preparedviamelt-quench cooling. These formulations showed full API amorphization, while good physical stability (i.e., a stable SDR amorphous dispersions) were obtained after storage for several months. Finally, evaluation of molecular interactions (with the aid of ATR-FTIR spectroscopy) showed strong H-bonds between SOL and SDR, while the use of molecular dynamics (MD) simulations unraveled the nature of these interactions. Therefore, based on the findings of the present work, SOL seems to be an appropriate matrix/carrier for the preparation of SDR ASDs, although further studies are needed in order to explore its full potentials.

A Machine-Learning Method to Assess Growth Patterns in Plants of the Family Lemnaceae.

Numerous new technologies have been implemented in image analysis methods that help researchers draw scientific conclusions from biological phenomena. Plants of the family Lemnaceae (duckweeds) are the smallest flowering plants in the world, and biometric measurements of single plants and their growth rate are highly challenging. Although the use of software for digital image analysis has changed the way scientists extract phenomenological data (also for studies on duckweeds), the procedure is often not wholly automated and sometimes relies on the intervention of a human operator. Such a constraint can limit the objectivity of the measurements and generally slows down the time required to produce scientific data. Herein lies the need to implement image analysis software with artificial intelligence that can substitute the human operator. In this paper, we present a new method to study the growth rates of the plants of the Lemnaceae family based on the application of machine-learning procedures to digital image analysis. The method is compared to existing analogical and computer-operated procedures. The results showed that our method drastically reduces the time consumption of the human operator while retaining a high correlation in the growth rates measured with other procedures. As expected, machine-learning methods applied to digital image analysis can overcome the constraints of measuring growth rates of very small plants and might help duckweeds gain worldwide attention thanks to their strong nutritional qualities and biological plasticity.

Effect of aging on the fatigue crack growth properties of carbon-polyamide 6 thermoplastic composites using the multi ΔG-control method

This paper focuses on the fatigue crack growth behavior of unidirectional C/PA6 composites subjected to hydrolytic aging at temperatures ranging from 100 to 140 °C. The fatigue crack growth properties were determined using a multi-ΔG control test method. The latter is fully automatic and allows measurement of crack growth rates at various ΔG levels. It was shown that the fatigue crack growth properties were highly affected by aging. Whatever the aging temperature, the crack growth rate was increased by about a decade after aging, and the fatigue crack growth properties are highly dependent on the molar mass. Finally, it was shown that the traditional Paris law does not allow a full description of the behaviour so the Hartman-Schijve relationship was applied to characterize the fatigue response.

Using a Lagrangian particle tracking model to evaluate impacts of El Niño-related advection on euphausiids in the southern California Current System

We propose a framework to examine the extent to which advection alone can explain spring biomass fluctuations of six euphausiid species in the southern California Current System (CCS) between 2008 and 2017. We modeled population changes as fluxes from defined source boxes using currents from the California State Estimate (CASE), a regional optimization of the MIT general circulation model. This period encompasses a Central Pacific El Niño (2009–10), Warm Anomaly (2014–15) and Eastern Pacific El Niño (2015–16). Total spring populations of all six species show strongest positive correlations with time-lagged flows from the preceding November–December. Three cool-water species (Euphausia pacifica, Nematoscelis difficilis, Thysanoessa spinifera) show opposite patterns for their calyptopis (larval) and adult phases, with strongest positive correlations of calyptopes with February–March flow suggesting periods of in situ reproduction. In contrast, three subtropical species (Nyctiphanes simplex, Euphausia eximia, Euphausia gibboides) show consistent correlation patterns with flow across the adult and calyptopis phases, suggesting advection of entire populations into the region during periods of enhanced favorable flows. We tested whether interannual variations in spring population size were influenced by different winter-origin waters during El Niño compared to non-Niño years. We found that cool-water species associate less strongly and subtropical species associate more strongly with southern-origin waters during anomalous years. Advection alone accounts for varying proportions of species fluctuations, with strongest influences for N. difficilis and T. spinifera. Explicit measurements of growth and mortality rates are needed to further resolve the additional factors influencing euphausiid populations during anomalous events, with implications for future forecasts.

Potential Contamination Of High-Speed Dental Handpiece By Spray Impact On The Mouth Surface

Portable dentistry devices allow medical dentists to perform procedures on patients in their homes. However, considering the recent pandemic context, these procedures raise concerns regarding the potential of infection since high-speed dental handpieces use water sprays to cool the rotating tool. The water spray droplets impacting the mouth of an infected patient can, thus, become a contamination source. Therefore, to produce reliable data to develop numerical models of aerosol propagation, this work uses a Phase-Doppler Interferometer to characterize the water spray before impact and the application of spray impact models indicates that 80% of droplets are in the conditions to deposit on the mouth's soft tissues and 19% of droplets should rebound. While a mere 1% expects to generate splashing events, the liquid film stripping and the complex 3D flow emerging from dragging the surrounding air generates a spray exiting the mouth. This spray is different from the original, thus, it is the result of shear-driven film stripping. The mathematical function that best describes all sprays was the Log-Normal and this work explains it as the result of an exponential drop size diversity growth rate (Φ). Therefore, while the characteristic size is reasonably understood in its physical meaning, the standard deviation (s) acquires one, i.e., it is a measure of the constant drop size diversity growth rate (s ≡ Φ). This could be a relevant insight to the physical interpretation of fitting a Log-Normal probability density function to describe the distribution of drop sizes in sprays. Finally, a scale analysis of the rebound contact time using a simple diffusion model, indicates that these droplets can also become contaminants agents.

Inferring S_8(z) and gamma (z) with cosmic growth rate measurements using machine learning

Measurements of the cosmological parameter S_8 provided by cosmic microwave background and large scale structure data reveal some tension between them, suggesting that the clustering features of matter in these early and late cosmological tracers could be different. In this work, we use a supervised learning method designed to solve Bayesian approach to regression, known as Gaussian Processes regression, to quantify the cosmic evolution of S_8 up to z sim 1.5. For this, we propose a novel approach to find firstly the evolution of the function sigma _8(z), then we find the function S_8(z). As a sub-product we obtain a minimal cosmological model-dependent sigma _8(z=0) and S_8(z=0) estimates. We select independent data measurements of the growth rate f(z) and of [fsigma _8](z) according to criteria of non-correlated data, then we perform the Gaussian reconstruction of these data sets to obtain the cosmic evolution of sigma _8(z), S_8(z), and the growth index gamma (z). Our statistical analyses show that S_8(z) is compatible with Planck Lambda CDM cosmology; when evaluated at the present time we find sigma _8(z=0) = 0.766 pm 0.116 and S_8(z=0) = 0.732 pm 0.115. Applying our methodology to the growth index, we find gamma (z=0) = 0.465 pm 0.140. Moreover, we compare our results with others recently obtained in the literature. In none of these functions, i.e. sigma _8(z), S_8(z), and gamma (z), do we find significant deviations from the standard cosmology predictions.

Parasite control and Saint Swithin's Day

Mid-summer provides a useful check point for assessing the dynamics of parasite populations, their potential impact and the need for control measures. In young cattle, measuring growth rates and faecal egg counts at this time can provide valuable prognostic information on the likely effects of parasitic gastroenteritis over the second half of the grazing season. Faecal sampling can also be used to monitor fluke infections, but may be of less value in assessing the risk of lungworm. Local weather patterns leading up to and including mid-summer can be used in conjunction with sampling and management data to generate an overall picture of the epidemiology and risk of the various protozoal, helminth and arthropod parasites that can affect cattle at grass; these in turn can be used to guide pasture management and treatment options appropriate to individual farms and farmers.

High-throughput Method for Novel Medium Development for Culture of Anaerobic Gut Bacteria.

Gut microbiota play important roles in the health of their host and detailed investigation of these organisms requires in vitro culture. Culturing strictly anaerobic bacteria can be a challenge as the gut environment they inhabit is nutritionally complex. Use of complex media containing nutritionally rich but undefined gut fluid reduces the accuracy of physiological and metabolomic studies. Here we present a high-throughput protocol for comparing growth rates of fastidiously anaerobic bacteria on different media. These protocols can be used to develop a solid medium made up of commercially sourced ingredients, providing replicable growth conditions for previously uncultured anaerobic bacteria. As many fastidious bacteria grow poorly in a liquid broth, these protocols measure bacterial growth rate on solid media. These protocols speed up and simplify the growth rate measurement process by using a multiwell format and equations in place of physical McFarland standards to calculate approximate cell density. Bacterial strains belonging to the families Erysipelotrichaceae and Lachnospiraceae (phylum Firmicutes) isolated from the hindgut of Kyphosus sydneyanus were used to demonstrate the efficacy of these protocols. Bacterial growth rates were compared between a nutritionally rich medium with gut fluid versus a novel replicable medium with mannitol. © 2022 The Authors. Current Protocols published by Wiley Periodicals LLC. Basic Protocol 1: Preparation of solid YCFA growth medium Basic Protocol 2: Collection of fish gut samples and plating to single isolates Basic Protocol 3: Genetic identification of single isolates with colony PCR and 16S rRNA gene sequencing Basic Protocol 4: Measurement of bacterial growth rates on solid media.

Role of δ-ferrite in fatigue crack growth of AISI 316 austenitic stainless steel

FF sample (nearly free of δ-ferrite) and CF sample (containing ∼4% δ-ferrite) were prepared from the AISI 316 austenitic stainless steel plate to elucidate the role of δ-ferrite in the fatigue crack growth under the solution treated and accelerated aged conditions. It is found that the fatigue crack growth resistance of the CF sample is higher than the FF sample under the solution treated condition. However, a significant deterioration of the fatigue crack growth resistance is observed in the CF sample while little variation is found in the FF sample after accelerated aging treatment at 750 °C for 10 h. In the solution treated condition, deflected crack growth path is present when the main crack encounters the δ-ferrite in the CF sample due to the differences in the fatigue responses between austenite and δ-ferrite. The measured growth rate of the deflected crack is significantly slower than that of the flat crack of the same length. After the accelerated aging treatment, microcracks are produced at the M23C6/δ interface due to the strain incompatibility between M23C6 and retained δ-ferrite when the decomposed δ-ferrite is subject to plastic deformation in the crack tip plastic zone. The preexisting microcracks in the front of crack tip provide a viable path for crack propagation, resulting in the relatively flat crack path.

Measuring competitive exclusion in non-small cell lung cancer.

In this study, we experimentally measure the frequency-dependent interactions between a gefitinib-resistant non-small cell lung cancer population and its sensitive ancestor via the evolutionary game assay. We show that cost of resistance is insufficient to accurately predict competitive exclusion and that frequency-dependent growth rate measurements are required. Using frequency-dependent growth rate data, we then show that gefitinib treatment results in competitive exclusion of the ancestor, while the absence of treatment results in a likely, but not guaranteed, exclusion of the resistant strain. Then, using simulations, we demonstrate that incorporating ecological growth effects can influence the predicted extinction time. In addition, we show that higher drug concentrations may not lead to the optimal reduction in tumor burden. Together, these results highlight the potential importance of frequency-dependent growth rate data for understanding competing populations, both in the laboratory and as we translate adaptive therapy regimens to the clinic.

Abstract 2613: A modified Luria-Delbrück assay allows quantification of colorectal cancer persister cells’ mutation rate

Abstract When cancer cells are exposed to lethal doses of targeted therapies, the emergence of a subpopulation of drug-tolerant persister cells (DTPs) is often observed. We previously reported that colorectal cancer (CRC) cells exposed to targeted therapies activate an adaptive mutability stress response, involving DNA damage induction and a switch to low-fidelity DNA replication. Therefore, targeted treatment might lead to increased mutation rate in DTPs, but mutation rates of cancer cells during treatment have not been quantitatively assessed. Here, we combined biological experiments and mathematical modelling to characterize emergence and dynamics of DTPs. From this, we extrapolated parameters governing dynamics of cancer cells populations and designed a modified Luria-Delbrück assay on mammalian cells (MC-LD) to quantify mutations rates of CRC cells under standard growth conditions and during exposure to targeted therapy. We selected mismatch repair proficient CRC cell lines sensitive to different clinically used therapeutic agents, and derived clones to be used for experiments. By monitoring cell dynamics in drug-response growth assays, we found that CRC cells exposed to targeted therapy display a biphasic killing curve reaching a stable plateau, a pattern indicative of emergence of DTPs. By fitting model estimation to population growth assays, we predicted that, even if a subgroup of DTPs predated treatment, the majority of them emerged only upon exposure to targeted therapies. We also observed that DTPs slowly replicate under treatment, as shown by Carboxy fluorescein succinimidyl ester (CFSE) analysis and staining with 5-ethynyl-2’-deoxyuridine (EdU). We used these population dynamics parameters to design the MC-LD assay. CRC clones were plated in several 96-multiwell plates each, and after an expansion phase in standard culture conditions, treatment was added. After 3-4 weeks, a minority of wells showed growth of resistant colonies: based on the measured growth rates, we could predict that the resistant cells arose before treatment by spontaneous mutation. The remaining wells contained a homogenous population of DTPs. After several weeks of treatment, when pre-treatment resistant clones would have already emerged, late-emerging resistant colonies appeared in a subset of wells in which DTPs had previously been detected. Using the number of residual DTPs and resistant colonies to infer mutation rates, we found a 7- to 50-fold increase (depending on the cell line) in DTPs’ mutation rate compared to sensitive cells.In conclusion, we developed a new assay which allows quantitative comparisons of spontaneous and drug-induced mutation rates in cancer cells and showed that adaptive mutability in DTPs leads to increased mutation rates. This approach could be used to measure whether and how a wide range of environmental conditions affect DTP phenotype and mutation rates in mammalian cells. Citation Format: Alberto Sogari, Mariangela Russo, Simone Pompei, Mattia Corigliano, Giovanni Crisafulli, Andrea Bertotti, Marco Gherardi, Federica Di Nicolantonio, Marco Cosentino Lagomarsino, Alberto Bardelli. A modified Luria-Delbrück assay allows quantification of colorectal cancer persister cells’ mutation rate [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2022; 2022 Apr 8-13. Philadelphia (PA): AACR; Cancer Res 2022;82(12_Suppl):Abstract nr 2613.

Applicability and limitations of high-throughput algal growth rate measurements using invivo fluorescence in microtiter plates

Micro-algae play important roles in primary production, nutrient cycling, and applied biotechnology. Mico-algae are phylogenetically, morphologically and physiologically diverse and often easy to grow in cultures. Growth is the key parameter of viability and crucial for survival insitu and efficiency invitro. Therefore, growth is often used in eco-physiological experiments to describe the fundamental niche and optimum conditions. Invivo chlorophyll-a fluorescence (IVCF) is a well-established proxy for the growth of micro-algae and is based on constant cell properties during exponential growth. High-throughput IVCF measurements have been applied for about 20 years for few, mostly green algal strains. Here, we tested the IVCF using microtiter plates on strains of four different algal phyla (Chlorophyceae, Cyanobacteria, Bacillariophyceae, Rhodophyceae) and compared the data with cell counts and chlorophyll contents. The microtiter plate reader based IVCF (MPR-IVCF) approach worked best for the diatom Cylindrothecaclosterium and the cyanobacterium Synechococcuselongatus. Differences between IVCF and cell count-based growth rates were found for Chlorellavulgaris and Rhodella sp. The IVCF growth rates were lower than the growth rates based on cell counts in both cases, thus underestimating absolute growth rates. The MPR-IVCF method is robust in terms of light scattering and non-photosynthetic contamination but prone to changes in light regimes and also to aggregating algal cells. Thus, we recommend using the MPR-IVCF approach (1) for diatoms and cyanobacteria as an absolute growth rate measure, (2) for relative measures of growth rates, intra and interspecific during the same experiment, also for all algal phyla except Rhodophyta.

Motivic Limits for Fano Varieties of k-Planes

Abstract We study the probability that an $(n - m)$-dimensional linear subspace in $\mathbb{P}^n$ or a collection of points spanning such a linear subspace is contained in an m-dimensional variety $Y \subset \mathbb{P}^n$. This involves a strategy used by Galkin–Shinder to connect properties of a cubic hypersurface to its Fano variety of lines via cut-and-paste relations in the Grothendieck ring of varieties. Generalizing this idea to varieties of higher codimension and degree, we can measure growth rates of weighted probabilities of k-planes contained in a sequence of varieties with varying initial parameters over a finite field. In the course of doing this, we move an identity motivated by rationality problems involving cubic hypersurfaces to a motivic statistics setting associated with cohomological stability.