Moment Closure - A Brief Review

Moment closure methods appear in myriad scientific disciplines in the modelling of complex systems. The goal is to achieve a closed form of a large, usually even infinite, set of coupled differential (or difference) equations. Each equation describes the evolution of one "moment", a suitable coarse-grained quantity computable from the full state space. If the system is too large for analytical and/or numerical methods, then one aims to reduce it by finding a moment closure relation expressing "higher-order moments" in terms of "lower-order moments". In this brief review, we focus on highlighting how moment closure methods occur in different contexts. We also conjecture via a geometric explanation why it has been difficult to rigorously justify many moment closure approximations although they work very well in practice.Comment: short survey paper (max 20 pages) for a broad audience in mathematics, physics, chemistry and quantitative biolog

Intense or Spatially Heterogeneous Predation Can Select against Prey Dispersal

Dispersal theory generally predicts kin competition, inbreeding, and temporal variation in habitat quality should select for dispersal, whereas spatial variation in habitat quality should select against dispersal. The effect of predation on the evolution of dispersal is currently not well-known: because predation can be variable in both space and time, it is not clear whether or when predation will promote dispersal within prey. Moreover, the evolution of prey dispersal affects strongly the encounter rate of predator and prey individuals, which greatly determines the ecological dynamics, and in turn changes the selection pressures for prey dispersal, in an eco-evolutionary feedback loop. When taken all together the effect of predation on prey dispersal is rather difficult to predict. We analyze a spatially explicit, individual-based predator-prey model and its mathematical approximation to investigate the evolution of prey dispersal. Competition and predation depend on local, rather than landscape-scale densities, and the spatial pattern of predation corresponds well to that of predators using restricted home ranges (e.g. central-place foragers). Analyses show the balance between the level of competition and predation pressure an individual is expected to experience determines whether prey should disperse or stay close to their parents and siblings, and more predation selects for less prey dispersal. Predators with smaller home ranges also select for less prey dispersal; more prey dispersal is favoured if predators have large home ranges, are very mobile, and/or are evenly distributed across the landscape

Can forest management based on natural disturbances maintain ecological resilience?

Given the increasingly global stresses on forests, many ecologists argue that managers must maintain ecological resilience: the capacity of ecosystems to absorb disturbances without undergoing fundamental change. In this review we ask: Can the emerging paradigm of natural-disturbance-based management (NDBM) maintain ecological resilience in managed forests? Applying resilience theory requires careful articulation of the ecosystem state under consideration, the disturbances and stresses that affect the persistence of possible alternative states, and the spatial and temporal scales of management relevance. Implementing NDBM while maintaining resilience means recognizing that (i) biodiversity is important for long-term ecosystem persistence, (ii) natural disturbances play a critical role as a generator of structural and compositional heterogeneity at multiple scales, and (iii) traditional management tends to produce forests more homogeneous than those disturbed naturally and increases the likelihood of unexpected catastrophic change by constraining variation of key environmental processes. NDBM may maintain resilience if silvicultural strategies retain the structures and processes that perpetuate desired states while reducing those that enhance resilience of undesirable states. Such strategies require an understanding of harvesting impacts on slow ecosystem processes, such as seed-bank or nutrient dynamics, which in the long term can lead to ecological surprises by altering the forest's capacity to reorganize after disturbance

The stability of multitrophic communities under habitat loss

Habitat loss (HL) affects species and their interactions, ultimately altering community dynamics. Yet, a challenge for community ecology is to understand how communities with multiple interaction types—hybrid communities—respond to HL prior to species extinctions. To this end, we develop a model to investigate the response of hybrid terrestrial communities to two types of HL: random and contiguous. Our model reveals changes in stability—temporal variability in population abundances—that are dependent on the spatial configuration of HL. Our findings highlight that habitat area determines the variability of populations via changes in the distribution of species interaction strengths. The divergent responses of communities to random and contiguous HL result from different constraints imposed on individuals’ mobility, impacting diversity and network structure in the random case, and destabilising communities by increasing interaction strength in the contiguous case. Analysis of intermediate HL suggests a gradual transition between the two extreme cases

Dispersal strategies, few dominating or many coexisting: the effect of environmental spatial structure and multiple sources of mortality.

Interspecific competition, life history traits, environmental heterogeneity and spatial structure as well as disturbance are known to impact the successful dispersal strategies in metacommunities. However, studies on the direction of impact of those factors on dispersal have yielded contradictory results and often considered only few competing dispersal strategies at the same time. We used a unifying modeling approach to contrast the combined effects of species traits (adult survival, specialization), environmental heterogeneity and structure (spatial autocorrelation, habitat availability) and disturbance on the selected, maintained and coexisting dispersal strategies in heterogeneous metacommunities. Using a negative exponential dispersal kernel, we allowed for variation of both species dispersal distance and dispersal rate. We showed that strong disturbance promotes species with high dispersal abilities, while low local adult survival and habitat availability select against them. Spatial autocorrelation favors species with higher dispersal ability when adult survival and disturbance rate are low, and selects against them in the opposite situation. Interestingly, several dispersal strategies coexist when disturbance and adult survival act in opposition, as for example when strong disturbance regime favors species with high dispersal abilities while low adult survival selects species with low dispersal. Our results unify apparently contradictory previous results and demonstrate that spatial structure, disturbance and adult survival determine the success and diversity of coexisting dispersal strategies in competing metacommunities

Methylation of the 4q35 D4Z4 repeat defines disease status in facioscapulohumeral muscular dystrophy.

Genetic diagnosis of facioscapulohumeral muscular dystrophy (FSHD) remains a challenge in clinical practice as it cannot be detected by standard sequencing methods despite being the third most common muscular dystrophy. The conventional diagnostic strategy addresses the known genetic parameters of FSHD: the required presence of a permissive haplotype, a size reduction of the D4Z4 repeat of chromosome 4q35 (defining FSHD1), or a pathogenic variant in an epigenetic suppressor gene (consistent with FSHD2). Incomplete penetrance and epistatic effects of the underlying genetic parameters as well as epigenetic parameters (D4Z4 methylation) pose challenges to diagnostic accuracy and hinder prediction of clinical severity. In order to circumvent the known limitations of conventional diagnostics and to complement genetic parameters with epigenetic ones, we developed and validated a multistage diagnostic workflow that consists of a haplotype analysis and a high throughput methylation profile analysis (FSHD-MPA). FSHD-MPA determines the average global methylation level of the D4Z4 repeat array as well as the regional methylation of the most distal repeat unit by combining bisulfite conversion with next-generation sequencing (NGS) and a bioinformatics pipeline and uses these as diagnostic parameters. We applied the diagnostic workflow to a cohort of 148 patients and compared the epigenetic parameters based on FSHD-MPA to genetic parameters of conventional genetic testing. In addition, we studied the correlation of repeat length and methylation level within the most distal repeat unit with age-corrected clinical severity and age at disease onset in FSHD patients. The results of our study show that FSHD-MPA is a powerful tool to accurately determine the epigenetic parameters of FSHD, allowing discrimination between FSHD patients and healthy individuals, while simultaneously distinguishing FSHD1 and FSHD2. The strong correlation between methylation level and clinical severity indicates that the methylation level determined by FSHD-MPA accounts for differences in disease severity among individuals with similar genetic parameters. Thus, our findings further confirm that epigenetic parameters rather than genetic parameters represent FSHD disease status and may serve as a valuable biomarker for disease status

Variations in the configuration of algae in subtidal forests: Implications for invertebrate assemblages

The definitive version may be found at www.wiley.comThe ecology of Australia's most extensive canopy-forming alga, Ecklonia radiata, is often studied with little regard as to whether it occurs in monospecific stands or as part of a mixed assemblage of canopy-forming algae. We tested the hypothesis that E. radiata does not primarily occur as monospecific stands, rather it occurs more often in stands of mixed algae. At a 1-m2 scale we recognized three main configurations within forests of algae (hereafter called stands): E. radiata that occurs as (i) monospecific stands; (ii) clumps (four or more individuals together) surrounded by species of Fucales; or (iii) individual plants (or clusters of fewer than three plants) interspersed among species of Fucales. All three types of stand occurred in similar proportions (percentage cover) across two regions of Australia's southern coastline (Western and South Australia). We also tested the hypothesis that these three types of stands (identified at 1 m2) contain different assemblages of invertebrates associated with the holdfast of E. radiata. Assemblages of invertebrates varied between monospecific and interspersed stands, but not between monospecific and clumped stands. These results suggest that variation in the configuration of subtidal algae (stands measured at a 1-m2 scale) has the potential to influence the composition and abundance of associated biota. We suggest that although studies in stands of monospecific E. radiata may provide useful information for the majority of forests containing E. radiata (monospecific and clumped stands made up 65% of forests sampled), caution must be used when extrapolating to stands of mixed, interspersed algae (>31% of forests sampled).P. J. Goodsell, M. J. Fowler-Walker, B. M. Gillanders and S. D. Connel