On the classification of regular systems of inbreeding

Regular systems of inbreeding are defined as those with discrete, nonoverlapping generations and with the same number of individuals and mating pattern in every generation. Given the number of individuals in a generation, there are many possible regular mating systems. A notion of when two such mating systems are equivalent is introduced, and several necessary conditions are given for such an equivalence. The use of these conditions is illustrated for N = 2, 3, 4 and 5 individuals, and a complete enumeration has been found for these cases: the numbers of inequivalent mating systems are 1, 5, 57 and 858, respectively. The maximal eigenvalue of the matrix q that specifies the recursion relations satisfied by the probabilities of identity have also been found for these cases. For N = 3 and 4 (and 2 trivially), circular mating gives the slowest rate of approach to genetic uniformity of those systems that do evolve to uniformity, but for N = 5 there are two other mating systems that have a slower rate of convergence, and for N = 6 partial results show that there are many such examples.Deceased     

A graph theoretic approach to the development of minimal phylogenetic trees

Summary The problem of determining the minimal phylogenetic tree is discussed in relation to graph theory. It is shown that this problem is an example of the Steiner problem in graphs which is to connect a set of points by a minimal length network where new points can be added. There is no reported method of solving realistically-sized Steiner problems in reasonable computing time. A heuristic method of approaching the phylogenetic problem is presented, together with a worked example with 7 mammalian cytochrome c sequences. It is shown in this case that the method develops a phylogenetic tree that has the smallest possible number of amino acid replacements. The potential and limitations of the method are discussed. It is stressed that objective methods must be used for comparing different trees. In particular it should be determined how close a given tree is to a mathematically determined lower bound. A theorem is proved which is used to establish a lower bound on the length of any tree and if a tree is found with a length equal to the lower bound, then no shorter tree can exist.     

Identifying ‘firebreaks’ to fragment dispersal networks of a marine parasite

Marine ecosystems are beset by disease outbreaks, and efficient strategies to control dispersal of pathogens are scarce. We tested whether introducing no-farming areas or ‘firebreaks’ could disconnect dispersal networks of a parasitic disease affecting the world’s largest marine fish farming industry (～1000 farms). Larval salmon lice (Lepeophtheirus salmonis) are released from and transported among salmon farms by ocean currents, creating inter-farm networks of louse dispersal. We used a state-of-the-art biophysical model to predict louse movement along the Norwegian coastline and network analysis to identify firebreaks to dispersal. At least one firebreak that fragmented the network into two large unconnected groups of farms was identified for all seasons. During spring, when wild salmon migrate out into the ocean, and louse levels per fish at farms must be minimised, two effective firebreaks were created by removing 13 and 21 farms (1.3% and 2.2% of all farms in the system) at ～61°N and 67°N, respectively. We have demonstrated that dispersal models coupled with network analysis can identify no-farming zones that fragment dispersal networks. Reduced dispersal pathways should lower infection pressure at farms, slow the evolution of resistance to parasite control measures, and alleviate infection pressure on wild salmon populations.     

基于图论模型的蛋白质结构类型的研究

提出了基于图论模型的H系数分类蛋白质结构为H结型和NH结型的方法.论述了蛋白质结构中序列不相邻的C_α原子之间的空间距离与序列相邻的C_α原子之间空间距离的关系.用此方法对PDB的66个单链蛋白质结构进行分类,结果显示H结型占18.2%.H结在全α型中出现比例较高,在全β型中出现比例较小,所以H结倾向出现在含有α螺旋的蛋白质结构中.     

A Network-based Analysis of the 1861 Hagelloch Measles Data

Summary In this article, we demonstrate a statistical method for fitting the parameters of a sophisticated network and epidemic model to disease data. The pattern of contacts between hosts is described by a class of dyadic independence exponential-family random graph models (ERGMs), whereas the transmission process that runs over the network is modeled as a stochastic susceptible-exposed-infectious-removed (SEIR) epidemic. We fit these models to very detailed data from the 1861 measles outbreak in Hagelloch, Germany. The network models include parameters for all recorded host covariates including age, sex, household, and classroom membership and household location whereas the SEIR epidemic model has exponentially distributed transmission times with gamma-distributed latent and infective periods. This approach allows us to make meaningful statements about the structure of the population-separate from the transmission process-as well as to provide estimates of various biological quantities of interest, such as the effective reproductive number, R. Using reversible jump Markov chain Monte Carlo, we produce samples from the joint posterior distribution of all the parameters of this model-the network, transmission tree, network parameters, and SEIR parameters-and perform Bayesian model selection to find the best-fitting network model. We compare our results with those of previous analyses and show that the ERGM network model better fits the data than a Bernoulli network model previously used. We also provide a software package, written in R, that performs this type of analysis.     

Charting epilepsy by searching for intelligence in network space with the help of evolving autonomous agents

The problem of demarcating neural network space is formidable. A simple fully connected recurrent network of five units (binary activations, synaptic weight resolution of 10) has 3.2 *10(26) possible initial states. The problem increases drastically with scaling. Here we consider three complementary approaches to help direct the exploration to distinguish epileptic from healthy networks. [1] First, we perform a gross mapping of the space of five-unit continuous recurrent networks using randomized weights and initial activations. The majority of weight patterns (>70%) were found to result in neural assemblies exhibiting periodic limit-cycle oscillatory behavior. [2] Next we examine the activation space of non-periodic networks demonstrating that the emergence of paroxysmal activity does not require changes in connectivity. [3] The next challenge is to focus the search of network space to identify networks with more complex dynamics. Here we rely on a major available indicator critical to clinical assessment but largely ignored by epilepsy modelers, namely: behavioral states. To this end, we connected the above network layout to an external robot in which interactive states were evolved. The first random generation showed a distribution in line with approach [1]. That is, the predominate phenotypes were fixed-point or oscillatory with seizure-like motor output. As evolution progressed the profile changed markedly. Within 20 generations the entire population was able to navigate a simple environment with all individuals exhibiting multiply-stable behaviors with no cases of default locked limit-cycle oscillatory motor behavior. The resultant population may thus afford us a view of the architectural principles demarcating healthy biological networks from the pathological. The approach has an advantage over other epilepsy modeling techniques in providing a way to clarify whether observed dynamics or suggested therapies are pointing to computational viability or dead space.     

Characteristics associated with Woolly Apple Aphid Eriosoma lanigerum, resistance of three apple rootstocks

The resistance characteristics of the apple resistance genes (Er1, Er2, and Er3) to the woolly apple aphid, Eriosoma lanigerum (Hausmann) (Homoptera: Aphididae) were studied according to the performance measured on apple cultivars containing these resistance genes. The resistance characteristics of Northern Spy (Er1), Robusta 5 (Er2), and Aotea (Er3) were compared to the susceptible cultivar Royal Gala, by measuring the aphid settlement, development, and survival rates correlated with electronically monitored probing behaviour. Er1 and Er2 had a higher level of resistance with a significantly shorter period of phloem feeding, suggesting that the resistance factors were present in the phloem tissue. Phenological measurements indicated that the aphids showed poor settlement, development, and survival on Er2. Er1 also showed low settlement and survival, although not as low as Er2. Aphid performance and feeding on Aotea (Er3) were similar to Royal Gala, suggesting that some woolly apple aphids in New Zealand may have recently overcome Er3 resistance. The differences in resistance mechanisms of Er1, Er2, and Er3 are discussed in relation to the strategy of pyramiding these genes to give a durable resistance to woolly apple aphid.     

Observations on graphing paleozoological data: Suggestions for better graphs

Paleozoologists have long used graphs of diverse styles to describe, analyze, and summarize their data. Some of these graphs provide excellent visual representations of complex data and are readily deciphered. Other graph styles require close study to be interpreted. Ease of visual decoding of information contained in a graph – graph perception – varies from graph style to graph style. Historical instances of graphing paleozoological data indicate some difficult to decipher graph styles have been used for at least a century. Graphs with three-dimensions, moiré effects, superimposed lines, or segmented bars, or which demand simultaneous decipherment of position and magnitude, are ill-advised. Temporal trends in data are best graphed following the principle of superposition such that data from old material is graphed at the bottom and data from younger material is graphed at the top of the diagram.     

Predicting impacts of climate change on habitat connectivity of Kalopanax septemlobus in South Korea

Understanding the drivers of habitat distribution patterns and assessing habitat connectivity are crucial for conservation in the face of climate change. In this study, we examined a sparsely distributed tree species, Kalopanax septemlobus (Araliaceae), which has been heavily disturbed by human use in temperate forests of South Korea. We used maximum entropy distribution modeling (MaxEnt) to identify the climatic and topographic factors driving the distribution of the species. Then, we constructed habitat models under current and projected climate conditions for the year 2050 and evaluated changes in the extent and connectivity of the K. septemlobus habitat. Annual mean temperature and terrain slope were the two most important predictors of species distribution. Our models predicted the range shift of K. septemlobus toward higher elevations under medium-low and high emissions scenarios for 2050, with dramatic reductions in suitable habitat (51% and 85%, respectively). In addition, connectivity analysis indicated that climate change is expected to reduce future levels of habitat connectivity. Even under the Representative Construction Pathway (RCP) 4.5 medium-low warming scenario, the projected climate conditions will decrease habitat connectivity by 78%. Overall, suitable habitats for K. septemlobus populations will likely become more isolated depending on the severity of global warming. The approach presented here can be used to efficiently assess species and habitat vulnerability to climate change.     

Stability and structural constraints of random brain networks with excitatory and inhibitory neural populations

The stability of brain networks with randomly connected excitatory and inhibitory neural populations is investigated using a simplified physiological model of brain electrical activity. Neural populations are randomly assigned to be excitatory or inhibitory and the stability of a brain network is determined by the spectrum of the network’s matrix of connection strengths. The probability that a network is stable is determined from its spectral density which is numerically determined and is approximated by a spectral distribution recently derived by Rajan and Abbott. The probability that a brain network is stable is maximum when the total connection strength into a population is approximately zero and is shown to depend on the arrangement of the excitatory and inhibitory connections and the parameters of the network. The maximum excitatory and inhibitory input into a structure allowed by stability occurs when the net input equals zero and, in contrast to networks with randomly distributed excitatory and inhibitory connections, substantially increases as the number of connections increases. Networks with the largest excitatory and inhibitory input allowed by stability have multiple marginally stable modes, are highly responsive and adaptable to external stimuli, have the same total input into each structure with minimal variance in the excitatory and inhibitory connection strengths, and have a wide range of flexible, adaptable, and complex behavior.