Sloppy model analysis identifies bifurcation parameters without normal form analysis

Bifurcation phenomena are common in multidimensional multiparameter dynamical systems. Normal form theory suggests that bifurcations are driven by relatively few combinations of parameters. Models of complex systems, however, rarely appear in normal form, and bifurcations are controlled by nonlinear combinations of the bare parameters of differential equations. Discovering reparameterizations to transform complex equations into a normal form is often very difficult, and the reparameterization may not even exist in a closed form. Here we show that information geometry and sloppy model analysis using the Fisher information matrix can be used to identify the combination of parameters that control bifurcations. By considering observations on increasingly long timescales, we find those parameters that rapidly characterize the system's topological inhomogeneities, whether the system is in normal form or not. We anticipate that this novel analytical method, which we call time-widening information geometry (TWIG), will be useful in applied network analysis.

Modification of the structural stability of human serum albumin in rheumatoid arthritis

Differential scanning calorimetry (DSC) can indicate changes in structure and/or concentration of the most abundant proteins in a biological sample via heat denaturation curves (HDCs). In blood serum for example, HDC changes result from either concentration changes or altered thermal stabilities for 7-10 proteins and has previously been shown capable of differentiating between sick and healthy human subjects. Here, we compare HDCs and proteomic profiles of 50 patients experiencing joint-inflammatory symptoms, 27 of which were clinically diagnosed with rheumatoid arthritis (RA). The HDC of all 50 subjects appeared significantly different from expected healthy curves, but comparison of additional differences between the RA and the non-RA subjects allowed more specific understanding of RA samples. We used mass spectrometry (MS) to investigate the reasons behind the additional HDC changes observed in RA patients. The HDC differences do not appear to be directly related to differences in the concentrations of abundant serum proteins. Rather, the differences can be attributed to modified thermal stability of some fraction of the human serum albumin (HSA) proteins in the sample. By quantifying differences in the frequency of artificially induced post translational modifications (PTMs), we found that HSA in RA subjects had a much lower surface accessibility, indicating potential ligand or protein binding partners in certain regions that could explain the shift in HSA melting temperature in the RA HDCs. Several low abundance proteins were found to have significant changes in concentration in RA subjects and could be involved in or related to binding of HSA. Certain amino acid sites clusters were found to be less accessible in RA subjects, suggesting changes in HSA structure that may be related to changes in protein-protein interactions. These results all support a change in behavior of HSA which may give insight into mechanisms of RA pathology.

Utilizing Nonequilibrium Isotope Enrichments to Dramatically Increase Turnover Measurement Ranges in Single Biopsy Samples from Humans

The synthesis of new proteins and the degradation of old proteins in vivo can be quantified in serial samples using metabolic isotope labeling to measure turnover. Because serial biopsies in humans are impractical, we set out to develop a method to calculate the turnover rates of proteins from single human biopsies. This method involved a new metabolic labeling approach and adjustments to the calculations used in previous work to calculate protein turnover. We demonstrate that using a nonequilibrium isotope enrichment strategy avoids the time dependent bias caused by variable lag in label delivery to different tissues observed in traditional metabolic labeling methods. Turnover rates are consistent for the same subject in biopsies from different labeling periods, and turnover rates calculated in this study are consistent with previously reported values. We also demonstrate that by measuring protein turnover we can determine where proteins are synthesized. In human subjects a significant difference in turnover rates differentiated proteins synthesized in the salivary glands versus those imported from the serum. We also provide a data analysis tool, DeuteRater-H, to calculate protein turnover using this nonequilibrium metabolic 2H2O method.

Invader or resident? Ancient-DNA reveals rapid species turnover in New Zealand little penguins

The expansion of humans into previously unoccupied parts of the globe is thought to have driven the decline and extinction of numerous vertebrate species. In New Zealand, human settlement in the late thirteenth century AD led to the rapid demise of a distinctive vertebrate fauna, and also a number of 'turnover' events where extinct lineages were subsequently replaced by closely related taxa. The recent genetic detection of an Australian little penguin (Eudyptula novaehollandiae) in southeastern New Zealand may potentially represent an additional 'cryptic' invasion. Here we use ancient-DNA (aDNA) analysis and radiocarbon dating of pre-human, archaeological and historical Eudyptula remains to reveal that the arrival of E. novaehollandiae in New Zealand probably occurred between AD 1500 and 1900, following the anthropogenic decline of its sister taxon, the endemic Eudyptula minor. This rapid turnover event, revealed by aDNA, suggests that native species decline can be masked by invasive taxa, and highlights the potential for human-mediated biodiversity shifts.

Extinction and recolonization of coastal megafauna following human arrival in New Zealand

Extinctions can dramatically reshape biological communities. As a case in point, ancient mass extinction events apparently facilitated dramatic new evolutionary radiations of surviving lineages. However, scientists have yet to fully understand the consequences of more recent biological upheaval, such as the megafaunal extinctions that occurred globally over the past 50 kyr. New Zealand was the world's last large landmass to be colonized by humans, and its exceptional archaeological record documents a vast number of vertebrate extinctions in the immediate aftermath of Polynesian arrival approximately AD 1280. This recently colonized archipelago thus presents an outstanding opportunity to test for rapid biological responses to extinction. Here, we use ancient DNA (aDNA) analysis to show that extinction of an endemic sea lion lineage (Phocarctos spp.) apparently facilitated a subsequent northward range expansion of a previously subantarctic-limited lineage. This finding parallels a similar extinction-replacement event in penguins (Megadyptes spp.). In both cases, an endemic mainland clade was completely eliminated soon after human arrival, and then replaced by a genetically divergent clade from the remote subantarctic region, all within the space of a few centuries. These data suggest that ecological and demographic processes can play a role in constraining lineage distributions, even for highly dispersive species, and highlight the potential for dynamic biological responses to extinction.

Tangled trees: the challenge of inferring species trees from coalescent and noncoalescent genes

Phylogenies based on different genes can produce conflicting phylogenies; methods that resolve such ambiguities are becoming more popular, and offer a number of advantages for phylogenetic analysis. We review so-called species tree methods and the biological forces that can undermine them by violating important aspects of the underlying models. Such forces include horizontal gene transfer, gene duplication, and natural selection. We review ways of detecting loci influenced by such forces and offer suggestions for identifying or accommodating them. The way forward involves identifying outlier loci, as is done in population genetic analysis of neutral and selected loci, and removing them from further analysis, or developing more complex species tree models that can accommodate such loci.

Bayesian estimation of the timing and severity of a population bottleneck from ancient DNA

In this first application of the approximate Bayesian computation approach using the serial coalescent, we demonstrated the estimation of historical demographic parameters from ancient DNA. We estimated the timing and severity of a population bottleneck in an endemic subterranean rodent, Ctenomys sociabilis, over the last 10,000 y from two cave sites in northern Patagonia, Argentina. Understanding population bottlenecks is important in both conservation and evolutionary biology. Conservation implications include the maintenance of genetic variation, inbreeding, fixation of mildly deleterious alleles, and loss of adaptive potential. Evolutionary processes are impacted because of the influence of small populations in founder effects and speciation. We found a decrease from a female effective population size of 95,231 to less than 300 females at 2,890 y before present: a 99.7% decline. Our study demonstrates the persistence of a species depauperate in genetic diversity for at least 2,000 y and has implications for modes of speciation in the incredibly diverse rodent genus Ctenomys. Our approach shows promise for determining demographic parameters for other species with ancient and historic samples and demonstrates the power of such an approach using ancient DNA.

Modern genetic variation can be used to reconstruct past events in a population's history, such as severe population declines (population bottlenecks). However, ancient DNA has the potential to improve our ability to estimate the timing and severity of such events, increasing our understanding of their causes and consequences. The authors apply a method for estimating historical demography, approximate Bayesian computation, to modern and ancient genetic variation sampled over the last 10,000 y, in order to estimate the timing and severity of a population bottleneck in an endemic Patagonian rodent. Their method shows promise for determining demographic parameters for other species with ancient and historic samples and demonstrates the power of such an approach using ancient DNA.

Serial SimCoal: A population genetics model for data from multiple populations and points in time

We present Serial SimCoal, a program that models population genetic data from multiple time points, as with ancient DNA data. An extension of SIMCOAL, it also allows simultaneous modeling of complex demographic histories, and migration between multiple populations. Further, we incorporate a statistical package to calculate relevant summary statistics, which, for the first time allows users to investigate the statistical power provided by, conduct hypothesis-testing with, and explore sample size limitations of ancient DNA data.

AVAILABILITY

Source code and Windows/Mac executables at http://www.stanford.edu/group/hadlylab/ssc.html

CONTACT

senka@stanford.edu.