Scaling limits of a model for selection at two scales

The dynamics of a population undergoing selection is a central topic in evolutionary biology. This question is particularly intriguing in the case where selective forces act in opposing directions at two population scales. For example, a fast-replicating virus strain outcompetes slower-replicating strains at the within-host scale. However, if the fast-replicating strain causes host morbidity and is less frequently transmitted, it can be outcompeted by slower-replicating strains at the between-host scale. Here we consider a stochastic ball-and-urn process which models this type of phenomenon. We prove the weak convergence of this process under two natural scalings. The first scaling leads to a deterministic nonlinear integro-partial differential equation on the interval $[0,1]$ with dependence on a single parameter, $\lambda$. We show that the fixed points of this differential equation are Beta distributions and that their stability depends on $\lambda$ and the behavior of the initial data around $1$. The second scaling leads to a measure-valued Fleming-Viot process, an infinite dimensional stochastic process that is frequently associated with a population genetics.

Temporal Stability of Molecular Diversity Measures in Natural Populations of Drosophila pseudoobscura and Drosophila persimilis

Many molecular ecological and evolutionary studies sample wild populations at a single point in time, failing to consider that data they collect represents genetic variation from a potentially unrepresentative snapshot in time. Variation across time in genetic parameters may occur quickly in species that produce multiple generations of offspring per year. However, many studies of rapid contemporary microevolution examine phenotypic trait divergence as opposed to molecular evolutionary divergence. Here, we compare genetic diversity in wild caught populations of Drosophila persimilis and D. pseudoobscura collected 16 years apart at the same time of year and same site at four X-linked and two mitochondrial loci to assess genetic stability. We found no major changes in nucleotide diversity in either species, but we observed a drastic shift in Tajima’s D between D. pseudoobscura timepoints at one locus associated with the increased abundance of a set of related haplotypes. Our data also suggests that D. persimilis may have recently accelerated its demographic expansion. While the changes we observed were modest, this study reinforces the importance of considering potential temporal variation in genetic parameters within single populations over short evolutionary timescales.

Dramatic variability of the carbonate system at a temperate coastal ocean site (Beaufort, North Carolina, USA) is regulated by physical and biogeochemical processes on multiple timescales.

Increasing atmospheric carbon dioxide (CO2) from anthropogenic sources is acidifying marine environments resulting in potentially dramatic consequences for the physical, chemical and biological functioning of these ecosystems. If current trends continue, mean ocean pH is expected to decrease by ~0.2 units over the next ~50 years. Yet, there is also substantial temporal variability in pH and other carbon system parameters in the ocean resulting in regions that already experience change that exceeds long-term projected trends in pH. This points to short-term dynamics as an important layer of complexity on top of long-term trends. Thus, in order to predict future climate change impacts, there is a critical need to characterize the natural range and dynamics of the marine carbonate system and the mechanisms responsible for observed variability. Here, we present pH and dissolved inorganic carbon (DIC) at time intervals spanning 1 hour to >1 year from a dynamic, coastal, temperate marine system (Beaufort Inlet, Beaufort NC USA) to characterize the carbonate system at multiple time scales. Daily and seasonal variation of the carbonate system is largely driven by temperature, alkalinity and the balance between primary production and respiration, but high frequency change (hours to days) is further influenced by water mass movement (e.g. tides) and stochastic events (e.g. storms). Both annual (~0.3 units) and diurnal (~0.1 units) variability in coastal ocean acidity are similar in magnitude to 50 year projections of ocean acidity associated with increasing atmospheric CO2. The environmental variables driving these changes highlight the importance of characterizing the complete carbonate system rather than just pH. Short-term dynamics of ocean carbon parameters may already exert significant pressure on some coastal marine ecosystems with implications for ecology, biogeochemistry and evolution and this shorter term variability layers additive effects and complexity, including extreme values, on top of long-term trends in ocean acidification.

Clinician judgment vs formal scales for predicting intracerebral hemorrhage outcomes.

OBJECTIVE: To compare the performance of formal prognostic instruments vs subjective clinical judgment with regards to predicting functional outcome in patients with spontaneous intracerebral hemorrhage (ICH). METHODS: This prospective observational study enrolled 121 ICH patients hospitalized at 5 US tertiary care centers. Within 24 hours of each patient's admission to the hospital, one physician and one nurse on each patient's clinical team were each asked to predict the patient's modified Rankin Scale (mRS) score at 3 months and to indicate whether he or she would recommend comfort measures. The admission ICH score and FUNC score, 2 prognostic scales selected for their common use in neurologic practice, were calculated for each patient. Spearman rank correlation coefficients (r) with respect to patients' actual 3-month mRS for the physician and nursing predictions were compared against the same correlation coefficients for the ICH score and FUNC score. RESULTS: The absolute value of the correlation coefficient for physician predictions with respect to actual outcome (0.75) was higher than that of either the ICH score (0.62, p = 0.057) or the FUNC score (0.56, p = 0.01). The nursing predictions of outcome (r = 0.72) also trended towards an accuracy advantage over the ICH score (p = 0.09) and FUNC score (p = 0.03). In an analysis that excluded patients for whom comfort care was recommended, the 65 available attending physician predictions retained greater accuracy (r = 0.73) than either the ICH score (r = 0.50, p = 0.02) or the FUNC score (r = 0.42, p = 0.004). CONCLUSIONS: Early subjective clinical judgment of physicians correlates more closely with 3-month outcome after ICH than prognostic scales.