Difficulties in summing log-normal distributions for abundance and potential solutions.

The log-normal distribution, often used to model animal abundance and its uncertainty, is central to ecological modeling and conservation but its statistical properties are less intuitive than those of the normal distribution. The right skew of the log-normal distribution can be considerable for highly uncertain estimates and the median is often chosen as a point estimate. However, the use of the median can become complicated when summing across populations since the median of the sum of log-normal distributions is not the sum of the constituent medians. Such estimates become sensitive to the spatial or taxonomic scale over which abundance is being summarized and the naive estimate (the median of the distribution representing the sum across populations) can become grossly inflated. Here we review the statistical issues involved and some alternative formulations that might be considered by ecologists interested in modeling abundance. Using a recent estimate of global avian abundance as a case study (Callaghan et al. 2021), we investigate the properties of several alternative methods of summing across species' abundance, including the sorted summing used in the original study (Callaghan et al. 2021) and the use of shifted log-normal distributions, truncated normal distributions, and rectified normal distributions. The appropriate method of summing across distributions was intimately tied to the use of the mean or median as the measure of central tendency used as the point estimate. Use of the shifted log-normal distribution, however, generated scale-consistent estimates for global abundance across a spectrum of contexts. Our paper highlights how seemingly inconsequential decisions regarding the estimation of abundance yield radically different estimates of global abundance and its uncertainty, with conservation consequences that are underappreciated and require careful consideration.

Variability, skipped breeding and heavy-tailed dynamics in an Antarctic seabird.

The population dynamics of many colonially breeding seabirds are characterized by large interannual fluctuations that cannot be explained by environmental conditions alone. This variation may be particularly confounded by the use of skipped breeding by seabirds as a life-history strategy, which directly impacts the number of breeding pairs and may affect the accuracy of breeding abundance as a metric of population health. Additionally, large fluctuations in time series may suggest that the underlying population dynamics are heavy tailed, allowing for a higher likelihood of extreme events than expected under Gaussian dynamics. Here, we investigated the effect of demography on time series for abundance of the Adélie penguin Pygoscelis adeliae and explored the occurrence of heavy-tailed dynamics in observed Adélie time series. We focus this study on the Adélie penguin as it is an important bellwether species long used to track the impacts of climate change and fishing on the Southern Ocean ecosystem and shares life-history traits with many colonial seabirds. We quantified the impacts of demographic rates, including skipped breeding, on time series of Adélie abundance simulated using an age-structured model. We also used observed time series of Adélie breeding abundance at all known Antarctic colonies to classify distributions for abundance as Gaussian or non-Gaussian heavy tailed. We then identified the cause of such heavy-tailed dynamics in simulated time series and linked these to spatial patterns in Adélie food resource variability. We found that breeding propensity drives observed breeding fluctuations more than any other vital rate, with high variability in skipped breeding decoupling true abundance from observed breeding abundance. We also found several Antarctic regions characterized by heavy-tailed dynamics in abundance. These regions were often also characterized by high variability in zooplankton availability. In simulated time series, heavy-tailed dynamics were strongly linked to high variability in adult survival. Our results illustrate that stochastic variability in abundance dynamics, particularly the presence of variable rates of skipped breeding, can challenge our interpretation of fluctuations in abundance through time and obscure the relationship between key environmental drivers and population abundance.

Zika virus dynamics: When does sexual transmission matter?

The Zika virus (ZIKV) has captured worldwide attention with the ongoing epidemic in South America and its link to severe birth defects, most notably microcephaly. ZIKV is spread to humans through a combination of vector and sexual transmission, but the relative contribution of these transmission routes to the overall epidemic remains largely unknown. Furthermore, a disparity in the reported number of infections between males and females has been observed. We develop a mathematical model that describes the transmission dynamics of ZIKV to determine the processes driving the observed epidemic patterns. Our model reveals a 4.8% contribution of sexual transmission to the basic reproductive number, R0. This contribution is too minor to independently sustain an outbreak but suggests that vector transmission is the main driver of the ongoing epidemic. We also find a minor, yet statistically significant, difference in the mean number of cases in males and females, both at the peak of the epidemic and at equilibrium. While this suggests an intrinsic disparity between males and females, the differences do not account for the vastly greater number of reported cases for females, indicative of a large reporting bias. In addition, we identify conditions under which sexual transmission may play a key role in sparking an epidemic, including temperate areas where ZIKV mosquito vectors are less prevalent.