Three metrics of species diversity – species richness, the Shannon index and the Simpson index – are still widely used in ecology, despite decades of valid critiques leveled against them. Developing ...a robust diversity metric has been challenging because, unlike many variables ecologists measure, the diversity of a community often cannot be estimated in an unbiased way based on a random sample from that community. Over the past decade, ecologists have begun to incorporate two important tools for estimating diversity: coverage and Hill diversity. Coverage is a method for equalizing samples that is, on theoretical grounds, preferable to other commonly used methods such as equal‐effort sampling, or rarefying datasets to equal sample size. Hill diversity comprises a spectrum of diversity metrics and is based on three key insights. First, species richness and variants of the Shannon and Simpson indices are all special cases of one general equation. Second, richness, Shannon and Simpson can be expressed on the same scale and in units of species. Third, there is no way to eliminate the effect of relative abundance from estimates of any of these diversity metrics, including species richness. Rather, a researcher must choose the relative sensitivity of the metric towards rare and common species, a concept which we describe as ‘leverage.' In this paper we explain coverage and Hill diversity, provide guidelines for how to use them together to measure species diversity, and demonstrate their use with examples from our own data. We show why researchers will obtain more robust results when they estimate the Hill diversity of equal‐coverage samples, rather than using other methods such as equal‐effort sampling or traditional sample rarefaction.
Speed and strength of an epidemic intervention Dushoff, Jonathan; Park, Sang Woo
Proceedings - Royal Society. Biological sciences/Proceedings - Royal Society. Biological Sciences,
03/2021, Volume:
288, Issue:
1947
Journal Article
Peer reviewed
Open access
An epidemic can be characterized by its strength (i.e., the reproductive number Formula: see text) and speed (i.e., the exponential growth rate
). Disease modellers have historically placed much more ...emphasis on strength, in part because the effectiveness of an intervention strategy is typically evaluated on this scale. Here, we develop a mathematical framework for the classic, strength-based paradigm and show that there is a dual speed-based paradigm which can provide complementary insights. In particular, we note that
= 0 is a threshold for disease spread, just like Formula: see text 1, and show that we can measure the strength and speed of an intervention on the same scale as the strength and speed of an epidemic, respectively. We argue that, while the strength-based paradigm provides the clearest insight into certain questions, the speed-based paradigm provides the clearest view in other cases. As an example, we show that evaluating the prospects of 'test-and-treat' interventions against the human immunodeficiency virus (HIV) can be done more clearly on the speed than strength scale, given uncertainty in the proportion of HIV spread that happens early in the course of infection. We also discuss evaluating the effects of the importance of pre-symptomatic transmission of the SARS-CoV-2 virus. We suggest that disease modellers should avoid over-emphasizing the reproductive number at the expense of the exponential growth rate, but instead look at these as complementary measures.
The COVID-19 pandemic has caused more than 1,000,000 reported deaths globally, of which more than 200,000 have been reported in the United States as of October 1, 2020. Public health interventions ...have had significant impacts in reducing transmission and in averting even more deaths. Nonetheless, in many jurisdictions, the decline of cases and fatalities after apparent epidemic peaks has not been rapid. Instead, the asymmetric decline in cases appears, in most cases, to be consistent with plateau- or shoulder-like phenomena—a qualitative observation reinforced by a symmetry analysis of US state-level fatality data. Here we explore a model of fatality-driven awareness in which individual protective measures increase with death rates. In this model, fast increases to the peak are often followed by plateaus, shoulders, and lag-driven oscillations. The asymmetric shape of model-predicted incidence and fatality curves is consistent with observations from many jurisdictions. Yet, in contrast to model predictions, we find that population-level mobility metrics usually increased from low levels before fatalities reached an initial peak. We show that incorporating fatigue and long-term behavior change can reconcile the apparent premature relaxation of mobility reductions and help understand when post-peak dynamics are likely to lead to a resurgence of cases.
One year into the global COVID-19 pandemic, the focus of attention has shifted to the emergence and spread of SARS-CoV-2 variants of concern (VOCs). After nearly a year of the pandemic with little ...evolutionary change affecting human health, several variants have now been shown to have substantial detrimental effects on transmission and severity of the virus. Public health officials, medical practitioners, scientists, and the broader community have since been scrambling to understand what these variants mean for diagnosis, treatment, and the control of the pandemic through nonpharmaceutical interventions and vaccines. Here we explore the evolutionary processes that are involved in the emergence of new variants, what we can expect in terms of the future emergence of VOCs, and what we can do to minimise their impact.
Otto et al. review the evolutionary processes that have led to the emergence of variants of concern during the COVID-19 pandemic and describe efforts that could limit the future emergence of variants that spread faster, are more severe, or better escape immune responses.
Intraspecific variation in foraging niche can drive food web dynamics and ecosystem processes. In particular, male and female animals can exhibit different, often cascading, impacts on their ...interaction partners. Despite this, studies of plant-pollinator interaction networks have focused on the partitioning of the floral community between pollinator species, with little attention paid to intraspecific variation in plant preference between male and female bees. We designed a field study to evaluate the strength and prevalence of sexually dimorphic foraging, and particularly resource preferences, in bees.
We observed bees visiting flowers in semi-natural meadows in New Jersey, USA. To detect differences in flower use against a shared background of resource (flower) availability, we maximized the number of interactions observed within narrow spatio-temporal windows. To distinguish observed differences in bee use of flower species, which can reflect abundance patterns and sampling effects, from underlying differences in bee preferences, we analyzed our data with both a permutation-based null model and random effects models.
We found that the diets of male and female bees of the same species were often dissimilar as the diets of different species of bees. Furthermore, we demonstrate differences in preference between male and female bees. We show that intraspecific differences in preference can be robustly identified among hundreds of unique species-species interactions, without precisely quantifying resource availability, and despite high phenological turnover of both bees and plant bloom. Given the large differences in both flower use and preferences between male and female bees, ecological sex differences should be integrated into studies of bee demography, plant pollination, and coevolutionary relationships between flowers and insects.
Null hypothesis significance testing (NHST) remains popular despite decades of concern about misuse and misinterpretation. There are many recent suggestions for mitigating problems arising from NHST, ...including calls for abandoning NHST in favour of Bayesian or information‐theoretic approaches. We believe that NHST will continue to be widely used, and can be most usefully interpreted as a guide to whether a certain effect can be seen clearly in a particular context (e.g. whether we can clearly see that a correlation or between‐group difference is positive or negative).
We believe that much misinterpretation of NHST is due to language: significance testing has little to do with other meanings of the word ‘significance’. We therefore suggest that researchers describe the conclusions of null‐hypothesis tests in terms of statistical ‘clarity’ rather than ‘significance’. We illustrate our point by rewriting common misinterpretations of the meaning of statistical tests found in the literature using the language of ‘clarity’.
The meaning of statistical tests become easier to interpret and explain when viewed through the lens of ‘statistical clarity’.
Our suggestion is mild, but practical: this simple semantic change could enhance clarity in statistical communication.
Multiple epidemiological models have been proposed to predict the spread of Ebola in West Africa. These models include consideration of counter-measures meant to slow and, eventually, stop the spread ...of the disease. Here, we examine one component of Ebola dynamics that is of ongoing concern - the transmission of Ebola from the dead to the living. We do so by applying the toolkit of mathematical epidemiology to analyze the consequences of post-death transmission. We show that underlying disease parameters cannot be inferred with confidence from early-stage incidence data (that is, they are not "identifiable") because different parameter combinations can produce virtually the same epidemic trajectory. Despite this identifiability problem, we find robustly that inferences that don't account for post-death transmission tend to underestimate the basic reproductive number - thus, given the observed rate of epidemic growth, larger amounts of post-death transmission imply larger reproductive numbers. From a control perspective, we explain how improvements in reducing post-death transmission of Ebola may reduce the overall epidemic spread and scope substantially. Increased attention to the proportion of post-death transmission has the potential to aid both in projecting the course of the epidemic and in evaluating a portfolio of control strategies.
The role of asymptomatic carriers in transmission poses challenges for control of the COVID-19 pandemic. Study of asymptomatic transmission and implications for surveillance and disease burden are ...ongoing, but there has been little study of the implications of asymptomatic transmission on dynamics of disease. We use a mathematical framework to evaluate expected effects of asymptomatic transmission on the basic reproduction number R0 (i.e., the expected number of secondary cases generated by an average primary case in a fully susceptible population) and the fraction of new secondary cases attributable to asymptomatic individuals. If the generation-interval distribution of asymptomatic transmission differs from that of symptomatic transmission, then estimates of the basic reproduction number which do not explicitly account for asymptomatic cases may be systematically biased. Specifically, if asymptomatic cases have a shorter generation interval than symptomatic cases, R0 will be over-estimated, and if they have a longer generation interval, R0 will be under-estimated. Estimates of the realized proportion of asymptomatic transmission during the exponential phase also depend on asymptomatic generation intervals. Our analysis shows that understanding the temporal course of asymptomatic transmission can be important for assessing the importance of this route of transmission, and for disease dynamics. This provides an additional motivation for investigating both the importance and relative duration of asymptomatic transmission.
Quantifying diversity is of central importance for the study of structure, function and evolution of microbial communities. The estimation of microbial diversity has received renewed attention with ...the advent of large-scale metagenomic studies. Here, we consider what the diversity observed in a sample tells us about the diversity of the community being sampled. First, we argue that one cannot reliably estimate the absolute and relative number of microbial species present in a community without making unsupported assumptions about species abundance distributions. The reason for this is that sample data do not contain information about the number of rare species in the tail of species abundance distributions. We illustrate the difficulty in comparing species richness estimates by applying Chao's estimator of species richness to a set of in silico communities: they are ranked incorrectly in the presence of large numbers of rare species. Next, we extend our analysis to a general family of diversity metrics ('Hill diversities'), and construct lower and upper estimates of diversity values consistent with the sample data. The theory generalizes Chao's estimator, which we retrieve as the lower estimate of species richness. We show that Shannon and Simpson diversity can be robustly estimated for the in silico communities. We analyze nine metagenomic data sets from a wide range of environments, and show that our findings are relevant for empirically-sampled communities. Hence, we recommend the use of Shannon and Simpson diversity rather than species richness in efforts to quantify and compare microbial diversity.
Rabies is a notoriously underreported and neglected disease of low-income countries. This study aims to estimate the public health and economic burden of rabies circulating in domestic dog ...populations, globally and on a country-by-country basis, allowing an objective assessment of how much this preventable disease costs endemic countries.
We established relationships between rabies mortality and rabies prevention and control measures, which we incorporated into a model framework. We used data derived from extensive literature searches and questionnaires on disease incidence, control interventions and preventative measures within this framework to estimate the disease burden. The burden of rabies impacts on public health sector budgets, local communities and livestock economies, with the highest risk of rabies in the poorest regions of the world. This study estimates that globally canine rabies causes approximately 59,000 (95% Confidence Intervals: 25-159,000) human deaths, over 3.7 million (95% CIs: 1.6-10.4 million) disability-adjusted life years (DALYs) and 8.6 billion USD (95% CIs: 2.9-21.5 billion) economic losses annually. The largest component of the economic burden is due to premature death (55%), followed by direct costs of post-exposure prophylaxis (PEP, 20%) and lost income whilst seeking PEP (15.5%), with only limited costs to the veterinary sector due to dog vaccination (1.5%), and additional costs to communities from livestock losses (6%).
This study demonstrates that investment in dog vaccination, the single most effective way of reducing the disease burden, has been inadequate and that the availability and affordability of PEP needs improving. Collaborative investments by medical and veterinary sectors could dramatically reduce the current large, and unnecessary, burden of rabies on affected communities. Improved surveillance is needed to reduce uncertainty in burden estimates and to monitor the impacts of control efforts.
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