Seed germination experiments are conducted in a wide variety of biological disciplines. Numerous methods of analysing the resulting data have been proposed, most of which fall into three classes: intuition-based germination indexes, classical non-linear regression analysis and time-to-event analysis (also known as survival analysis, failure-time analysis and reliability analysis). This paper briefly reviews all three of these classes, and argues that time-to-event analysis has important advantages over the other methods but has been underutilized to date. It also reviews in detail the types of time-to-event analysis that are most useful in analysing seed germination data with standard statistical software. These include non-parametric methods (life-table and Kaplan–Meier estimators, and various methods for comparing two or more groups of seeds) and semi-parametric methods (Cox proportional hazards model, which permits inclusion of categorical and quantitative covariates, and fixed and random effects). Each method is illustrated by applying it to a set of real germination data. Sample code for conducting these analyses with two standard statistical programs is also provided in the supplementary material available online (athttp://journals.cambridge.org/). The methods of time-to-event analysis reviewed here can be applied to many other types of biological data, such as seedling emergence times, flowering times, development times for eggs or embryos, and organism lifetimes.

Streambank erosion is difficult to quantify; models and field methods are needed to assess this important sediment source to streams. Our objectives were to (1) evaluate and compare three techniques for quantifying streambank erosion: erosion pins, total station, and laser scanning, (2) spatially assess streambank erosion rates in the Indian Mill Creek watershed of Michigan, USA, and (3) relate results with modeling of nonpoint source pollution. We found large absolute and relative errors between the different measurement techniques. However, we were unable to determine any statistically significant differences between techniques and only observed a correlation between total station and laser scanner. This suggests that the three methods have limited comparability and differences between measurements were largely not systemic. Further, the application of each technique should be dependent on site conditions, project goals, desired resolution, and resources. The laser scanner collected high-resolution data on clear, barren streambanks, but the erosion pin and total station were more representative of complex vegetated banks. Streambank erosion rates varied throughout the watershed and were influenced by fluvial processes. We estimate that streambank erosion contributed 28.5% of the creek’s total sediment load. These findings are important to address sources of watershed impairments related to sedimentation, as choosing an applicable technique for individual purposes can help reduce the challenges and costs of a streambank erosion study.

Draft method C is a standardized method for quantifying E. coli densities in recreational waters using quantitative polymerase chain reaction (qPCR). The method includes a Microsoft Excel workbook that automatically screens for poor-quality data using a set of previously proposed acceptance criteria, generates weighted linear regression (WLR) composite standard curves, and calculates E. coli target gene copies in test samples. We compared standard curve parameter values and test sample results calculated with the WLR model to those from a Bayesian master standard curve (MSC) model using data from a previous multi-lab study. The two models’ mean intercept and slope estimates from twenty labs’ standard curves were within each other’s 95% credible or confidence intervals for all labs. E. coli gene copy estimates of six water samples analyzed by eight labs were highly overlapping among labs when quantified with the WLR and MSC models. Finally, we compared multiple labs’ 2016–2018 composite curves, comprised of data from individual curves where acceptance criteria were not used, to their corresponding composite curves with passing acceptance criteria. Composite curves developed from passing individual curves had intercept and slope 95% confidence intervals that were often narrower than without screening and an analysis of covariance test was passed more often. The Excel workbook WLR calculation and acceptance criteria will help laboratories implement draft method C for recreational water analysis in an efficient, cost-effective, and reliable manner.

The polymerase chain reaction (PCR) is a molecular biology tool with diverse applications in the aquatic sciences. Classical PCR is a nonquantitative method that can be used to detect target DNA sequences that are characteristic of particular microbial taxa but cannot determine their concentrations in water samples. Various quantitative forms of PCR have been developed to remove this limitation. Of these, the two that currently are used most widely are real-time quantitative PCR (qPCR) and droplet digital PCR (ddPCR). Several outlines of the mathematical and statistical basis of these methods for estimating target sequence concentrations are available in the literature, but we are aware of no thorough and rigorous derivation of the theoretical underpinnings of either. The purpose of this review is to provide such derivations, and to identify and compare the main strengths and weaknesses of the two methods. We find that both estimation methods are sound, provided careful attention is paid to specific details that differ between the two. With qPCR, it is especially important to reduce any significant PCR inhibition by sample constituents and to properly fit the standard curve to heteroskedastic calibration data. With ddPCR, it is important to ensure that the value of the mean droplet volume used in calculating concentrations is correct for the particular combination of droplet generator and master mix used. The advantages of qPCR include lower instrument and per-sample costs, a shorter turnaround time for obtaining results, a higher upper limit of quantification, and a wider dynamic range. The advantages of ddPCR include freedom from dependence on a standard curve, an inherently lower sensitivity to PCR inhibitors, a lower limit of quantification, a simpler theoretical basis, and simpler data analysis. We suggest qPCR often will be preferable in laboratory studies where investigators have significant control over the range of target sequence concentrations in samples, concentrations are sufficiently high so proper calibration does not require standards with concentrations low enough to exhibit exaggerated variability in the threshold cycle, and no significant inhibition is present, or more generally, in studies where funding levels do not permit the higher cost of instrumentation and supplies required by ddPCR or where the shorter turnaround time for qPCR is essential. If sufficient funds are available, ddPCR often will be preferable when the ability to quantify low concentrations is important, especially if inhibitors are likely to be present at concentrations that are problematic for qPCR.