The generation interval is the interval between the time when an individual is infected by an infector and the time when this infector was infected. Its distribution underpins estimates of the reproductive number and hence informs public health strategies. Empirical generation-interval distributions are often derived from contact-tracing data. But linking observed generation intervals to the underlying generation interval required for modelling purposes is surprisingly not straightforward, and misspecifications can lead to incorrect estimates of the reproductive number, with the potential to misguide interventions to stop or slow an epidemic. Here, we clarify the theoretical framework for three conceptually different generation-interval distributions: the ‘intrinsic’ one typically used in mathematical models and the ‘forward’ and ‘backward’ ones typically observed from contact-tracing data, looking, respectively, forward or backward in time. We explain how the relationship between these distributions changes as an epidemic progresses and discuss how empirical generation-interval data can be used to correctly inform mathematical models.

The reproduction number R and the growth rate r are critical epidemiological quantities. They are linked by generation intervals, the time between infection and onward transmission. Because generation intervals are difficult to observe, epidemiologists often substitute serial intervals, the time between symptom onset in successive links in a transmission chain. Recent studies suggest that such substitution biases estimates of R based on r. Here we explore how these intervals vary over the course of an epidemic, and the implications for R estimation. Forward-looking serial intervals, measuring time forward from symptom onset of an infector, correctly describe the renewal process of symptomatic cases and therefore reliably link R with r. In contrast, backward-looking intervals, which measure time backward, and intrinsic intervals, which neglect population-level dynamics, give incorrect R estimates. Forward-looking intervals are affected both by epidemic dynamics and by censoring, changing in complex ways over the course of an epidemic. We present a heuristic method for addressing biases that arise from neglecting changes in serial intervals. We apply the method to early (21 January to February 8, 2020) serial interval-based estimates of R for the COVID-19 outbreak in China outside Hubei province; using improperly defined serial intervals in this context biases estimates of initial R by up to a factor of 2.6. This study demonstrates the importance of early contact tracing efforts and provides a framework for reassessing generation intervals, serial intervals, and R estimates for COVID-19.

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Genetic predisposition to obesity presents a paradox: how do genetic variants with a detrimental impact on human health persist through evolutionary time? Numerous hypotheses, such as the thrifty genotype hypothesis, attempt to explain this phenomenon yet fail to provide a justification for the modern obesity epidemic. In this critical review, we appraise existing theories explaining the evolutionary origins of obesity and explore novel biological and sociocultural agents of evolutionary change to help explain the modern-day distribution of obesity-predisposing variants. Genetic drift, acting as a form of 'blind justice,' may randomly affect allele frequencies across generations while gene pleiotropy and adaptations to diverse environments may explain the rise and subsequent selection of obesity risk alleles. As an adaptive response, epigenetic regulation of gene expression may impact the manifestation of genetic predisposition to obesity. Finally, exposure to malnutrition and disease epidemics in the wake of oppressive social systems, culturally mediated notions of attractiveness and desirability, and diverse mating systems may play a role in shaping the human genome. As an important first step towards the identification of important drivers of obesity gene evolution, this review may inform empirical research focused on testing evolutionary theories by way of population genetics and mathematical modelling.