Extinction probabilities

Beyond the gel point, the bonds Issuing from a monomer unit can have finite or Infinite continuation. If the continuation Is finite, the Issuing subtree Is also only finite If the continuation Is Infinite, the unit Is bound via this bond to the "infinite" gel. The classification of bonds with respect to whether they have finite or Infinite continuation enables a relatively detailed statistical description of the gel structure. The probability of finite continuation of a bond Is called the extinction probability. The extinction probability Is obtained In a simple way from the distribution of units In generation g>0. This distribution Is obtained from the distribution of units In the root g-0 (for more details see Ref. 6). 

Ludwig D. 1996. Uncertainty and the assessment of extinction probabilities. Ecol Appl 6 1067-1076. 

The reader familiar with the cascade theory will notice that the root 0 < < 1 is related to the extinction probability, v, i.e., the probability of a unit chosen at random to belong to a sol molecule [ 14,55]. This probability is [53]... 

Reduction in habitat quality by persistent pollutants can decrease the survival and reproduction of individuals that predominantly dwell on or near the polluted site and, in this way, increase the extinction probability of populations. This can become effective through direct exposure or through transfer of the pollutants through the food web. In mobile species, this also depends on the relative proportion of contaminated sites in the total range of landscape elements that individuals use to forage... 

Beyond the gel point, some units belong to finite molecules in the sol and some are a part of the (infinite) gel. That means that units in the sol must issue none and units in the gel at least one bond that has (via a sequence of bonds) a continuation to infinity. The key quantity which determines the probability that a bond has no continuation to infinity is called extinction probability v. The extinction probability is defined as the root of the equation... 

The extinction probabilities necessary for obtaining the structural characteristics beyond the gel point are defined by Eq. (20). For the diamine-diepoxide system we have... 

The following trends, also demonstrated in the figure, are observed regarding to the extinction probability Po(t), i.e., the probability that the population will eventually die out by time L The trends are obtained from Eq.(2-173b) by letting t -> oo. 

Raimondo S, McKenney CLJ. 2005. Projected population-level effects of thiobencarb exposure on the mysid, Americamysis bahia, and extinction probability in a concentration-decay exposure system. Environ Toxicol Chem 24 564-572. 

V/e recall that the extinction probability v., i.e. the chance that a link to an i-tyj >e unit leads to at most a finite sul mole-cule, is found easily from the equations... 

M. Gordon The basic topological idea by Case and by Scanlan is that a network chain is active if at least three links issuing from each of the two teiminal junction points lead to paths through the network which can be continued to the surface of the specimen. In the statistical theory, the surface is projected to infinity, and the extinction probability of a link is used in the calculation. The basic theory is reviewed in reference 25 of our paper, and extended in a forthcoming paper. Coll. Czech. Communications, Gordon, Kuch rik and Ward, late 1970. 

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