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Information-theoretic (IT) and multi-model averaging (MMA) statistical approaches are widely used but suboptimal tools for pursuing a multifactorial approach (also known as the method of multiple working hypotheses) in ecology. (1) Conceptually, IT encourages ecologists to perform tests on sets of artificially simplified models. (2) MMA improves on IT model selection by implementing a simple form of shrinkage estimation (a way to make accurate predictions from a model with many parameters relative to the amount of data, by “shrinking” parameter estimates toward zero). However, other shrinkage estimators such as penalized regression or Bayesian hierarchical models with regularizing priors are more computationally efficient and better supported theoretically. (3) In general, the procedures for extracting confidence intervals from MMA are overconfident, providing overly narrow intervals. If researchers want to use limited data sets to accurately estimate the strength of multiple competing ecological processes along with reliable confidence intervals, the current best approach is to use full (maximal) statistical models (possibly with Bayesian priors) after making principled, a priori decisions about model complexity.

Abstract The Cox proportional hazards model is commonly used in evaluating risk factors in cancer survival data. The model assumes an additive, linear relationship between the risk factors and the log hazard. However, this assumption may be too simplistic. Further, failure to take time-varying covariates into account, if present, may lower prediction accuracy. In this retrospective, population-based, prognostic study of data from patients diagnosed with cancer from 2008 to 2015 in Ontario, Canada, we applied machine learning-based time-to-event prediction methods and compared their predictive performance in two sets of analyses: (1) yearly-cohort-based time-invariant and (2) fully time-varying covariates analysis. Machine learning-based methods—gradient boosting model (gbm), random survival forest (rsf), elastic net (enet), lasso and ridge—were compared to the traditional Cox proportional hazards (coxph) model and the prior study which used the yearly-cohort-based time-invariant analysis. Using Harrell’s C index as our primary measure, we found that using both machine learning techniques and incorporating time-dependent covariates can improve predictive performance. Gradient boosting machine showed the best performance on test data in both time-invariant and time-varying covariates analysis.

Predicting the combined effects of predators on shared prey has long been a focus of community ecology, yet quantitative predictions often fail. Failure to account for nonlinearity is one reason for this. Moreover, prey depletion in multiple predator effects (MPE) studies generates biased predictions in applications of common experimental and quantitative frameworks. Here, we explore additional sources of bias stemming from nonlinearities in prey predation risk. We show that in order to avoid bias, predictions about the combined effects of independent predators must account for nonlinear size-dependent risk for prey as well as changes in prey risk driven by nonlinear predator functional responses and depletion. Historical failure to account for biases introduced by well-known nonlinear processes that affect predation risk suggest that we may need to reevaluate the general conclusions that have been drawn about the ubiquity of emergent MPEs over the past three decades.

Abstract Background Patient age is one of the most salient clinical indicators of risk from COVID-19. Age-specific distributions of known SARS-CoV-2 infections and COVID-19-related deaths are available for many regions. Less attention has been given to the age distributions of serious medical interventions administered to COVID-19 patients, which could reveal sources of potential pressure on the healthcare system should SARS-CoV-2 prevalence increase, and could inform mass vaccination strategies. The aim of this study is to quantify the relationship between COVID-19 patient age and serious outcomes of the disease, beyond fatalities alone. Methods We analysed 277,555 known SARS-CoV-2 infection records for Ontario, Canada, from 23 January 2020 to 16 February 2021 and estimated the age distributions of hospitalizations, Intensive Care Unit admissions, intubations, and ventilations. We quantified the probability of hospitalization given known SARS-CoV-2 infection, and of survival given COVID-19-related hospitalization. Results The distribution of hospitalizations peaks with a wide plateau covering ages 60–90, whereas deaths are concentrated in ages 80+. The estimated probability of hospitalization given known infection reaches a maximum of 27.8% at age 80 (95% CI 26.0%–29.7%). The probability of survival given hospitalization is nearly 100% for adults younger than 40, but declines substantially after this age; for example, a hospitalized 54-year-old patient has a 91.7% chance of surviving COVID-19 (95% CI 88.3%–94.4%). Conclusions Our study demonstrates a significant need for hospitalization in middle-aged individuals and young seniors. This need is not captured by the distribution of deaths, which is heavily concentrated in very old ages. The probability of survival given hospitalization for COVID-19 is lower than is generally perceived for patients over 40. If acute care capacity is exceeded due to an increase in COVID-19 prevalence, the distribution of deaths could expand toward younger ages. These results suggest that vaccine programs should aim to prevent infection not only in old seniors, but also in young seniors and middle-aged individuals, to protect them from serious illness and to limit stress on the healthcare system.

Abstract Background Mathematical and statistical models are used to project the future time course of infectious disease epidemics and the expected future burden on health care systems and economies. Influenza is a particularly important disease in this context because it causes annual epidemics and occasional pandemics. In order to forecast health care utilization during epidemics—and the effects of hospitalizations and deaths on the contact network and, in turn, on transmission dynamics—modellers must make assumptions about the lengths of time between infection, visiting a physician, being admitted to hospital, leaving hospital, and death. More reliable forecasts could be be made if the distributions of times between these types of events (“delay distributions”) were known. Methods We estimated delay distributions in the province of Ontario, Canada, between 2006 and 2010. To do so, we used encrypted health insurance numbers to link 1.34 billion health care billing records to 4.27 million hospital inpatient stays. Because the four year period we studied included three typical influenza seasons and the 2009 influenza pandemic, we were able to compare the delay distributions in non-pandemic and pandemic settings. We also estimated conditional probabilities such as the probability of hospitalization within the year if diagnosed with influenza. Results In non-pandemic [pandemic] years, delay distribution medians (inter-quartile ranges) were: Service to Admission 6.3 days (0.1–17.6 days) [2.4 days (-0.3–13.6 days)], Admission to Discharge 3 days (1.4–5.9 days) [2.6 days (1.2–5.1 days)], Admission to Death 5.3 days (2.1–11 days) [6 days (2.6–13.1 days)]. (Service date is defined as the date, within the year, of the first health care billing that included a diagnostic code for influenza-like-illness.) Among individuals diagnosed with either pneumonia or influenza in a given year, 19% [16%] were hospitalized within the year and 3% [2%] died in hospital. Among all individuals who were hospitalized, 10% [12%] were diagnosed with pneumonia or influenza during the year and 5% [5%] died in hospital. Conclusion Our empirical delay distributions and conditional probabilities should help facilitate more accurate forecasts in the future, including improved predictions of hospital bed demands during influenza outbreaks, and the expected effects of hospitalizations on epidemic dynamics.

Abstract Background West Nile virus (WNV) is a mosquito-transmitted disease of birds that has caused bird population declines and can spill over into human populations. Previous research has identified bird species that infect a large fraction of the total pool of infected mosquitoes and correlate with human infection risk; however, these analyses cover small spatial regions and cannot be used to predict transmission in bird communities in which these species are rare or absent. Here we present a mechanistic model for WNV transmission that predicts WNV spread (R0) in any bird community in North America by scaling up from the physiological responses of individual birds to transmission at the level of the community. We predict unmeasured bird species’ responses to infection using phylogenetic imputation, based on these species’ phylogenetic relationships with bird species with measured responses. Results We focused our analysis on Texas, USA, because it is among the states with the highest total incidence of WNV in humans and is well sampled by birders in the eBird database. Spatio-temporal patterns: WNV transmission is primarily driven by temperature variation across time and space, and secondarily by bird community composition. In Texas, we predicted WNV R0 to be highest in the spring and fall when temperatures maximize the product of mosquito transmission and survival probabilities. In the most favorable months for WNV transmission (April, May, September and October), we predicted R0 to be highest in the “Piney Woods” and “Oak Woods & Prairies” ecoregions of Texas, and lowest in the “High Plains” and “South Texas Brush County” ecoregions. Dilution effect: More abundant bird species are more competent hosts for WNV, and predicted WNV R0 decreases with increasing species richness. Keystone species: We predicted that northern cardinals (Cardinalis cardinalis) are the most important hosts for amplifying WNV and that mourning doves (Zenaida macroura) are the most important sinks of infection across Texas. Conclusions Despite some data limitations, we demonstrate the power of phylogenetic imputation in predicting disease transmission in heterogeneous host communities. Our mechanistic modeling framework shows promise both for assisting future analyses on transmission and spillover in heterogeneous multispecies pathogen systems and for improving model transparency by clarifying assumptions, choices and shortcomings in complex ecological analyses.

We use two modelling approaches to forecast synthetic Ebola epidemics in the context of the RAPIDD Ebola Forecasting Challenge. The first approach is a standard stochastic compartmental model that aims to forecast incidence, hospitalization and deaths among both the general population and health care workers. The second is a model based on the renewal equation with latent variables that forecasts incidence in the whole population only. We describe fitting and forecasting procedures for each model and discuss their advantages and drawbacks. We did not find that one model was consistently better in forecasting than the other. Keywords: Forecasting, Epidemics, Renewal equation, Compartmental model

Abstract Beta diversity describes how species composition varies across space and through time. Current estimators of beta diversity typically ignore the effects of within‐patch sample size, determined jointly by local abundance and sampling effort. Many ecological processes such as immigration, predation, or nutrient limitation affect abundance and asymptotic beta diversity concurrently; thus, existing metrics may confound changes in asymptotic beta diversity with changes that result from differences in abundance or sampling. Results from a stochastic simulation model illustrate how decreasing within‐patch sample size may either increase or decrease observed beta diversity, depending on the type of metric, sample size, and community properties; these changes are easy to understand, and predict, by considering the effects of sampling on variance. A modified, patch‐level form of rarefaction controls for variation in within‐patch sample size; two case studies illustrate the utility of this approach. Studies seeking a mechanistic link between ecological process and beta diversity will continue to benefit from explicit consideration of sampling effects.

In most ecological studies, within-group variation is a nuisance that obscures patterns of interest and reduces statistical power. However, patterns of within-group variability often contain information about ecological processes. In particular, such patterns can be used to detect positive growth autocorrelation (consistent variation in growth rates among individuals in a cohort across time), even in samples of unmarked individuals. Previous methods for detecting autocorrelated growth required data from marked individuals. We propose a method that requires only estimates of within-cohort variance through time, using maximum likelihood methods to obtain point estimates and confidence intervals of the correlation parameter. We test our method on simulated data sets and determine the loss in statistical power due to the inability to identify individuals. We show how to accommodate nonlinear growth trajectories and test the effects of size-dependent mortality on our method's accuracy. The method can detect significant growth autocorrelation at moderate levels of autocorrelation with moderate-sized cohorts (for example, statistical power of 80% to detect growth autocorrelation ρ (2) = 0.5 in a cohort of 100 individuals measured on 16 occasions). We present a case study of growth in the red-eyed tree frog. Better quantification of the processes driving size variation will help ecologists improve predictions of population dynamics. This work will help researchers to detect growth autocorrelation in cases where marking is logistically infeasible or causes unacceptable decreases in the fitness of marked individuals.

Costs and benefits for partners in mutualistic interactions can vary greatly, but surprisingly little is known about the factors that drive this variation across systems. We conducted a meta-analysis of ant-plant protective mutualisms to quantify the effects of ant defenders on plant reproductive output, to evaluate if reproductive effects were predicted from reductions in herbivory and to identify characteristics of the plants, ants and environment that explained variation in ant protection. We also compared our approach with two other recent meta-analyses on ant-plant mutualisms, emphasizing differences in our methodology (using a weighted linear mixed effects model) and our focus on plant reproduction rather than herbivore damage. Based on 59 ant and plant species pairs, ant presence increased plant reproductive output by 49% and reduced herbivory by 62%. The effects on herbivory and reproduction within systems were positively correlated, but the slope of this relationship (0.75) indicated that tolerance to foliar herbivory may be a common plant response to absence of ant guards. Furthermore, the relationship between foliar damage and reproduction varied substantially among systems, suggesting that herbivore damage is not a reliable surrogate for fitness consequences of ant protection. Studies that experimentally excluded ants reported a smaller effect of ant protection on plant reproduction than studies that relied upon natural variation in ant presence, suggesting that study methods can affect results in these systems. Of the ecological variables included in our analysis, only plant life history (i.e., annual or perennial) explained variation in the protective benefit of mutualistic ants: presence of ants benefitted reproduction of perennials significantly more than that of annuals. These results contrast with other quantitative reviews of these relationships that did not include plant life history as an explanatory factor and raise several questions to guide future research on ant-plant protection mutualisms.

Tree cover is a fundamental structural characteristic and driver of ecosystem processes in terrestrial ecosystems, and trees are a major global carbon (C) sink. Fire and herbivores have been hypothesized to play dominant roles in regulating trees in African savannas, but the evidence for this is conflicting. Moving up a trophic scale, the factors that regulate fire occurrence and herbivores, such as disease and predation, are poorly understood for any given ecosystem. We used a Bayesian state-space model to show that the wildebeest population eruption that followed disease (rinderpest) eradication in the Serengeti ecosystem of East Africa led to a widespread reduction in the extent of fire and an ongoing recovery of the tree population. This supports the hypothesis that disease has played a key role in the regulation of this ecosystem. We then link our state-space model with theoretical and empirical results quantifying the effects of grazing and fire on soil carbon to predict that this cascade may have led to important shifts in the size of pools of C stored in soil and biomass. Our results suggest that the dynamics of herbivores and fire are tightly coupled at landscape scales, that fire exerts clear top-down effects on tree density, and that disease outbreaks in dominant herbivores can lead to complex trophic cascades in savanna ecosystems. We propose that the long-term status of the Serengeti and other intensely grazed savannas as sources or sinks for C may be fundamentally linked to the control of disease outbreaks and poaching.

BACKGROUND: Matrix models are widely used to study the dynamics and demography of populations. An important but overlooked issue is how the number of individuals sampled influences estimates of the population growth rate (lambda) calculated with matrix models. Even unbiased estimates of vital rates do not ensure unbiased estimates of lambda-Jensen's Inequality implies that even when the estimates of the vital rates are accurate, small sample sizes lead to biased estimates of lambda due to increased sampling variance. We investigated if sampling variability and the distribution of sampling effort among size classes lead to biases in estimates of lambda. METHODOLOGY/PRINCIPAL FINDINGS: Using data from a long-term field study of plant demography, we simulated the effects of sampling variance by drawing vital rates and calculating lambda for increasingly larger populations drawn from a total population of 3842 plants. We then compared these estimates of lambda with those based on the entire population and calculated the resulting bias. Finally, we conducted a review of the literature to determine the sample sizes typically used when parameterizing matrix models used to study plant demography. CONCLUSIONS/SIGNIFICANCE: We found significant bias at small sample sizes when survival was low (survival = 0.5), and that sampling with a more-realistic inverse J-shaped population structure exacerbated this bias. However our simulations also demonstrate that these biases rapidly become negligible with increasing sample sizes or as survival increases. For many of the sample sizes used in demographic studies, matrix models are probably robust to the biases resulting from sampling variance of vital rates. However, this conclusion may depend on the structure of populations or the distribution of sampling effort in ways that are unexplored. We suggest more intensive sampling of populations when individual survival is low and greater sampling of stages with high elasticities.