Why high seed densities within buried mesh bags may overestimate depletion rates of soil seed banks

1. Estimates of seed bank depletion rates are essential for modelling and management of plant populations. The seed bag burial method is often used to measure seed mortality in the soil. However, the density of seeds within seed bags is higher than densities in natural seed banks, which may elevate levels of pathogens and influence seed mortality. The aim of this study was to quantify the effects of fungi and seed density within buried mesh bags on the mortality of seeds. Striga hermonthica was chosen as the study species because it has been widely studied but different methods for measuring seed mortality in the soil have yielded contradictory estimates. 2. Seed bags were buried in soil and exhumed at regular time intervals to monitor mortality of the seeds in three field experiments during two rainy seasons. The effect of fungal activity on seed mortality was evaluated in a fungi exclusion experiment. Differences in seed-to-seed interaction were obtained by using two and four densities within the seed bags in consecutive years. Densities were created by mixing 1000 seeds with 0, 10, 100 or 1000 g of coarse sand. 3. The mortality rate was significantly lower when fungi were excluded, indicating the possible role of pathogenic fungi. 4. Decreasing the density of seeds in bags significantly reduced seed mortality, most probably because of decreased seed-to-seed contamination by pathogenic fungi. 5. Synthesis and applications. Models of plant populations in general and annual weeds in particular often use values from the literature for seed bank depletion rates. These depletion rates have often been estimated by the seed bag burial method, yet seed density within seed bags may be unrealistically high. Consequently, estimates of seed mortality rates may be too high because of an overestimation of the effects of soil or seed-borne pathogens. Species that have been classified from such studies as having short-lived seed banks may need to be re-assessed using realistic densities either within seed bags or otherwise. Similarly, models of seed bank dynamics based on such overestimated depletion rates may lead to incorrect conclusions regarding the seed banks and, perhaps, the management of weeds and rare species.

Equitability revisited: why the “equitable threat score” is not equitable

In the forecasting of binary events, verification measures that are “equitable” were defined by Gandin and Murphy to satisfy two requirements: 1) they award all random forecasting systems, including those that always issue the same forecast, the same expected score (typically zero), and 2) they are expressible as the linear weighted sum of the elements of the contingency table, where the weights are independent of the entries in the table, apart from the base rate. The authors demonstrate that the widely used “equitable threat score” (ETS), as well as numerous others, satisfies neither of these requirements and only satisfies the first requirement in the limit of an infinite sample size. Such measures are referred to as “asymptotically equitable.” In the case of ETS, the expected score of a random forecasting system is always positive and only falls below 0.01 when the number of samples is greater than around 30. Two other asymptotically equitable measures are the odds ratio skill score and the symmetric extreme dependency score, which are more strongly inequitable than ETS, particularly for rare events; for example, when the base rate is 2% and the sample size is 1000, random but unbiased forecasting systems yield an expected score of around −0.5, reducing in magnitude to −0.01 or smaller only for sample sizes exceeding 25 000. This presents a problem since these nonlinear measures have other desirable properties, in particular being reliable indicators of skill for rare events (provided that the sample size is large enough). A potential way to reconcile these properties with equitability is to recognize that Gandin and Murphy’s two requirements are independent, and the second can be safely discarded without losing the key advantages of equitability that are embodied in the first. This enables inequitable and asymptotically equitable measures to be scaled to make them equitable, while retaining their nonlinearity and other properties such as being reliable indicators of skill for rare events. It also opens up the possibility of designing new equitable verification measures.