Uncertainty in population growth rates: determining confidence intervals from point estimates of parameters

Background

Demographic models are widely used in conservation and management, and their parameterisation often relies on data collected for other purposes. When underlying data lack clear indications of associated uncertainty, modellers often fail to account for that uncertainty in model outputs, such as estimates of population growth.

Methodology/Principal Findings

We applied a likelihood approach to infer uncertainty retrospectively from point estimates of vital rates. Combining this with resampling techniques and projection modelling, we show that confidence intervals for population growth estimates are easy to derive. We used similar techniques to examine the effects of sample size on uncertainty. Our approach is illustrated using data on the red fox, Vulpes vulpes, a predator of ecological and cultural importance, and the most widespread extant terrestrial mammal. We show that uncertainty surrounding estimated population growth rates can be high, even for relatively well-studied populations. Halving that uncertainty typically requires a quadrupling of sampling effort.

Conclusions/Significance

Our results compel caution when comparing demographic trends between populations without accounting for uncertainty. Our methods will be widely applicable to demographic studies of many species.     

Intimate Partner Femicide in South Africa in 1999 and 2009

Background

Death is the most extreme consequence of intimate partner violence. Female homicide studies with data on the perpetrator–victim relationship can provide insights. We compare the results of two South African national studies of female homicide with similar sampling done 10 y apart.

Methods and Findings

We conducted a retrospective national survey using a weighted cluster design of a proportionate random sample of 38 mortuaries to identify homicides committed in 2009. We abstracted victim data from mortuary and autopsy reports, and perpetrator data from police interviews. We compared homicides of women 14 y and older in 2009 with previously published data collected with the same methodology for homicides committed in 1999.The study found that the rate of female homicide per 100,000 female population in 2009 was 12.9 (95% confidence interval [CI]: 9.3, 16.5), compared to 24.7 (95% CI: 17.7, 31.6) in 1999. The incidence rate ratio of 0.54 (95% CI: 0.20, 0.84) reflects a significantly lower rate in 2009. The rate of intimate partner femicide was 5.6/100,000 in 2009 versus 8.8/100,000 in 1999, with an incidence rate ratio of 0.63 (95% CI: 0.24, 1.02), indicating no difference between rates. Logistic regression analysis of homicide characteristics showed that the odds ratio of suspected rape among non-intimate femicides in 2009 compared to 1999 was 2.61 (95% CI: 1.23, 4.08) and among intimate partner femicides it was 0.84 (95% CI: 0.50, 1.42). The OR of homicide by gunshot was 0.54 (95% CI: 0.30, 0.99) in 2009 versus 1999. There was a significant drop in convictions of perpetrators of non-intimate femicide in 2009 versus 1999 (OR = 0.32 [95% CI: 0.19, 0.53]). Limitations of the study include the relatively small sample size and having only two time points.

Conclusions

Female homicide in South Africa was lower in 2009 than 1999, but intimate partner femicide and suspected rape homicide rates were not statistically different. The cause of the difference is unknown. The findings suggest that South Africa needs greater efforts nationally to implement evidence-based violence prevention. Please see later in the article for the Editors'' Summary     

External validation of the Hospital-patient One-year Mortality Risk (HOMR) model for predicting death within 1 year after hospital admission

Background:

Predicting long-term survival after admission to hospital is helpful for clinical, administrative and research purposes. The Hospital-patient One-year Mortality Risk (HOMR) model was derived and internally validated to predict the risk of death within 1 year after admission. We conducted an external validation of the model in a large multicentre study.

Methods:

We used administrative data for all nonpsychiatric admissions of adult patients to hospitals in the provinces of Ontario (2003–2010) and Alberta (2011–2012), and to the Brigham and Women’s Hospital in Boston (2010–2012) to calculate each patient’s HOMR score at admission. The HOMR score is based on a set of parameters that captures patient demographics, health burden and severity of acute illness. We determined patient status (alive or dead) 1 year after admission using population-based registries.

Results:

The 3 validation cohorts (n = 2 862 996 in Ontario, 210 595 in Alberta and 66 683 in Boston) were distinct from each other and from the derivation cohort. The overall risk of death within 1 year after admission was 8.7% (95% confidence interval [CI] 8.7% to 8.8%). The HOMR score was strongly and significantly associated with risk of death in all populations and was highly discriminative, with a C statistic ranging from 0.89 (95% CI 0.87 to 0.91) to 0.92 (95% CI 0.91 to 0.92). Observed and expected outcome risks were similar (median absolute difference in percent dying in 1 yr 0.3%, interquartile range 0.05%–2.5%).

Interpretation:

The HOMR score, calculated using routinely collected administrative data, accurately predicted the risk of death among adult patients within 1 year after admission to hospital for nonpsychiatric indications. Similar performance was seen when the score was used in geographically and temporally diverse populations. The HOMR model can be used for risk adjustment in analyses of health administrative data to predict long-term survival among hospital patients.The life expectancy of individual patients can be important for both medical decision-making and research. Patients with a short life expectancy may choose to defer preventive treatments, screening interventions or interventional procedures for conditions that are currently asymptomatic. An accurate assessment of risk of death, particularly if that risk is high, could motivate and inform discussions between patients and physicians regarding goals of care. In addition, accurate prognostications are essential for adjusting statistical models that have death as an outcome (or as a competing risk for other outcomes) in both research and administration.We recently derived and internally validated a model that predicts the risk of death from any cause at 1 year after admission to hospital.¹ The Hospital-patient One-year Mortality Risk (HOMR) model consists of covariates whose values are determined at admission using routinely collected health administrative data (Figure 1). These covariates include patient demographics (age, sex and living status); health burden (measured using the Charlson Comorbidity Index score, home oxygen status and the number of visits to emergency departments and admissions to hospital by ambulance in the previous year); and acuity of illness (admission urgency and hospital service, direct admission to an intensive care unit and whether the admission was an urgent readmission to hospital). The latter category was also gauged using the Diagnostic Risk Score, which quantifies risk of death for particular diagnoses beyond that explained by the other covariates (Appendix 1, available at www.cmaj.ca/lookup/suppl/doi:10.1503/cmaj.150209/-/DC1).Open in a separate windowFigure 1:Covariates used to calculate a patient’s Hospital-patient One-year Mortality Risk (HOMR) score at the time of admission to hospital. The Diagnostic Risk Score (Appendix 1) quantifies risk of death for diagnostic groups beyond that explained by the other covariates. Points for the interacting covariates of age and Charlson Comorbidity Index score include the risk of patient age, comorbidity score and their interaction. In contrast, points for living status and admission urgency include the risk of these covariates and their interaction with admissions by ambulance in the previous year; points for the latter covariate are considered separately. See www.cmaj.ca/lookup/suppl/doi:10.1503/cmaj.150209/-/DC1)Discrete values for each covariate are given specific points, which are summed to create the HOMR score (Figure 1). In an internal validation population, the HOMR score accurately predicted the risk of death from any cause within 1 year after admission, with a C statistic of 0.92 and excellent calibration among adult residents of Ontario admitted to hospital for nonpsychiatric indications in 2011.¹Although these statistics are impressive, external validation is required to determine the true usefulness of any statistical model. External validation is necessary to prove that the model’s performance is not idiosyncratic to the patients, physicians, institutions or data systems used to derive and internally test it.^2,3 A prognostic model should remain accurate when retested with different patients (reproducibility), during different periods (historical transportability) and in different locations (geographic transportability).⁴ We conducted an external validation of the HOMR model in a multicentre study that included Canadian and American hospitals.     

Cellulosomics, a gene-centric approach to investigating the intraspecific diversity and adaptation of Ruminococcus flavefaciens within the rumen

Background

The bovine rumen maintains a diverse microbial community that serves to break down indigestible plant substrates. However, those bacteria specifically adapted to degrade cellulose, the major structural component of plant biomass, represent a fraction of the rumen microbiome. Previously, we proposed scaC as a candidate for phylotyping Ruminococcus flavefaciens, one of three major cellulolytic bacterial species isolated from the rumen. In the present report we examine the dynamics and diversity of scaC-types both within and between cattle temporally, following a dietary switch from corn-silage to grass-legume hay. These results were placed in the context of the overall bacterial population dynamics measured using the 16S rRNA.

Principal Findings

As many as 117 scaC-types were estimated, although just nineteen were detected in each of three rumens tested, and these collectively accounted for the majority of all types present. Variation in scaC populations was observed between cattle, between planktonic and fiber-associated fractions and temporally over the six-week survey, and appeared related to scaC phylogeny. However, by the sixth week no significant separation of scaC populations was seen between animals, suggesting enrichment of a constrained set of scaC-types. Comparing the amino-acid translation of each scaC-type revealed sequence variation within part of the predicted dockerin module but strong conservation in the N-terminus, where the cohesin module is located.

Conclusions

The R. flavefaciens species comprises a multiplicity of scaC-types in-vivo. Enrichment of particular scaC-types temporally, following a dietary switch, and between fractions along with the phylogenetic congruence suggests that functional differences exist between types. Observed differences in dockerin modules suggest at least part of the functional heterogeneity may be conferred by scaC. The polymorphic nature of scaC enables the relative distribution of R. flavefaciens strains to be examined and represents a gene-centric approach to investigating the intraspecific adaptation of an important specialist population.     

Effect of fire on the topsoil seed banks of rehabilitated bauxite mine sites in the jarrah forest of Western Australia

Summary Germinable seed stores of 5- and 8-year-old rehabilitated bauxite mine pits in south-west Western Australia were assessed before and after burning. These seed stores were compared to those of adjacent unmined Jarrah ( Eucalyptus marginata ) forest, to identify at what age fire can be reintroduced, in order to measure restoration success and reduce fire hazard. Soils were sampled in early summer (before fire) and late autumn (after fire). Before fire, the mean topsoil seed bank of 5-year-old sites was 2121 seeds per m² while 8-year-old sites had a mean of 1520 seeds per m². Only the 5-year-old sites were significantly different from the forest mean of 1478 seeds per m² for the same season. After summer burns (and possibly due to seasonal effects) topsoil seed banks of rehabilitated areas (sampled in autumn) decreased by an average of 53 per cent. Topsoil seed banks of 5–8-year-old sites were resistant to lower intensity burns, with 362 seeds per m² of native species surviving mild burns and 108 seeds per m² of native species surviving after an intense summer fire. The topsoil seed reserve of 5–8-year-old rehabilitated areas had a high proportion of annual weed species while the forest sites had high levels of subshrubs and native annuals. Low-intensity burns did not alter the composition of life-forms in the soil seed bank, while intense burns favoured annual weed and shrub species. The results indicate that it is not appropriate to introduce fire to rehabilitated areas before 8 years, due to limited fuel reduction benefits and possible adverse effects on obligate seeding species. The large proportion of weed species in the soil seed bank of young rehabilitated areas is a concern, and remains a major consideration for future disturbance of these areas.     

Scale and direction of adaptive introgression between black cottonwood (Populus trichocarpa) and balsam poplar (P. balsamifera)

Introgression can introduce novel genetic variation at a faster rate than mutation alone and result in adaptive introgression when adaptive alleles are maintained in the recipient genome over time by natural selection. A previous study from our group demonstrated adaptive introgression from Populus balsamifera into P. trichocarpa in a target genomic region. Here we expand our local ancestry analysis to the whole genome of both parents to provide a comprehensive view of introgression patterns and to identify additional candidate regions for adaptive introgression genomewide. Populus trichocarpa is a large, fast‐growing tree of mild coastal regions of the Pacific Northwest, whereas P. balsamifera is a smaller stature tree of continental and boreal regions with intense winter cold. The species hybridize where they are parapatric. We detected asymmetric patterns of introgression across the whole genome of these two poplar species adapted to contrasting environments, with stronger introgression from P. balsamifera to P. trichocarpa than vice versa. Admixed P. trichocarpa individuals contained more genomic regions with unusually high levels of introgression (19 regions) and also the largest introgressed genome fragment (1.02 Mb) compared with admixed P. balsamifera (nine regions). Our analysis also revealed numerous candidate regions for adaptive introgression with strong signals of selection, notably related to disease resistance, and enriched for genes that may play crucial roles in survival and adaptation. Furthermore, we detected a potential overrepresentation of subtelomeric regions in P. balsamifera introgressed into P. trichocarpa and possible protection of sex‐determining regions from interspecific gene flow.     

Reproductive biology of the endemic goby, Lentipes concolor, from Makamaka'ole Stream, Maui and Waikolu Stream, Moloka'i

Constant pressure in Hawai'i to use limited freshwater resources has resulted in increasing concern for the future of the native stream fauna. Hawaiian freshwater gobies have an amphidromous life cycle with a marine larva period and require streams which flow continuously to the ocean for the critical reproductive periods and during recruitment. As such, the stream fauna is particularly sensitive to any anthropogenic perturbations which disrupt the continuity of stream flows. The objective of this 2-year study was to compare the life cycles of the goby, Lentipes concolor, from a heavily diverted stream on Moloka'i and a relatively undisturbed stream on Maui. In Makamaka'ole Stream, Maui, the population of L. concolor was reproductively active all year with females potentially spawning 2–3 times annually. The timing of spawning did not occur consistently during the wet or dry season but coincided with high stream flow conditions regardless of time-of-year. In Waikolu Stream, Moloka'i, the reproductive pattern was more variable with the number of reproductively active females ranging from 0% to 100%. In general the number of eggs was greater and egg size smaller for female L. concolor in Waikolu Stream than in Makamaka'ole Stream. However, female reproductive condition of L. concolor from Maui was consistently higher than from fish on Moloka'i. Reproduction of L. concolor in Makamaka'ole Stream was correlated with the seasonal pattern of flow rates with peaks in female reproductive condition associated with periods of elevated discharge. No correlation between reproduction and discharge occurred in Waikolu Stream. There were considerable differences between the magnitude of discharge in the two streams. Waikolu Stream experienced prolonged periods of extremely low flows which have become common since the Moloka'i Irrigation System began diverting water from the stream in 1960. In Makamaka'ole Stream, L. concolor was capable of reproducing throughout the year and adjusting fecundity in response to stream flow conditions. In contrast, the population in Waikolu Stream appeared to have a ‘boom or bust’ reproductive pattern; the population had reduced or no reproduction when stream flow conditions reached extreme low levels, but the population succesfully reproduced during higher flow months. The diversion structure in Waikolu Stream has dampened the natural seasonal discharge cycle, exacerbated natural low flow conditions, and increased the likelihood of prolonged periods of extremely low flow. Stream management practices in the Hawaiian Islands must take into account the complex life cycles and sensitivity to variable stream flow conditions of the native fauna. This revised version was published online in July 2006 with corrections to the Cover Date.