Probabilities of extinction

More recently, studies have applied the probability of extinction as an endpoint to extrapolate short-term effects on long-term population consequences. Based on population viability analysis (Boyce 1992 Groom and Pascual 1997), population size is projected into the future using demographic rates and models that incorporate stochastic effects (Snell and Serra 2000). In practice, it would be difficult to determine extinction rates experimentally due to the need to conduct experiments over multiple generations. Thus, the probability of extinction is typically modeled using the instantaneous rate of increase (Snell and Serra 2000). 

Snell TW, Serra M. 2000. Using probability of extinction to evaluate the ecological significance of toxicant effects. Environ Toxicol Chem 19 2357-2363. 

Population parameters population density productivity mating success alterations in genetic structure competitive alterations probability of extinctions... 

One of the difficulties in the quantification of the stressor-response profile is that many of the extrapolations are qualitative in nature. Phylogenetic extrapolations are rarely quantified or assisted with structure-activity relationships. Quantification of population level effects is likewise difficult and in some cases probabilities of extinction have been used as the quantified variable, not a subtle population endpoint. 

The advantage of stochastic matrix models over deterministic models is that stochastic models can give you probabilities of extinction, risk of decline, and probability of recovery. Furthermore, they are more realistic than deterministic models because factors such as carrying capacities, competition, and immigration can also be incorporated. 

As was mentioned in Subsection 5.6.2, stochastic versions of the Lotka-Volterra model lead to qualitatively different results from the deterministic model. The occurrence of a similar type of results is not too surprising. A simple model for random predator-prey interactions in a varying environment has been studied, staring from generalised Lotka-Volterra equations (De, 1984). The transition probability of extinction is to be determined. The standard procedure is to convert the problem to a Fokker-Planck equation (adopting continuous approximation) and to find an approximation procedure for evaluating the transition probabilities of extinction and of survival. 

Expression (13AS), which must of course be evaluated numerically, is capable of accommodating any objective of the irradiation process. Suppose, for example, we want to be 1 % certain that all the cancerous cells have been killed. This implies that the left-hand side of (7.3.48) is 0.01. If the irradiation intensity / is known, then (7.3.48) can be used to calculate the irradiation time tjr- Another alternative is to calculate the irradiation intensity for a fixed time of irradiation. A third even more interesting alternative is the manipulation of the initial distribution which will imply some form of pretreatment of the tumor, so that one can maximize the probability of extinction at the end of irradiation. Clearly, this is an open problem that has several possibilities for future research. 

The vector v of the Nz probabilities of extinction (the fractions of finite pendent... 

These concentrations can be easily predicted, given the probabilities of extinction and the moments with respect to the numbers of pendent chains as previously defined. Defining Xz as the count of infinite pendent chains and the correspondent dummy Laplace variable as Sz , its pgf for the chains stemming out of a monomer unit X is F [v + Sz (Inz v)> Ina] and so and can be computed using Eqs. (90) and (91). 

After computing the probabilities of extinction, the moments in Eq. (96) can be evaluated. 

One of the most challenging aspects of modeling turbulent combustion is the accurate prediction of finite-rate chemistry effects. In highly turbulent flames, the local transport rates for the removal of combustion radicals and heat may be comparable to or larger than the production rates of radicals and heat from combustion reactions. As a result, the chemistry cannot keep up with the transport and the flame is quenched. To illustrate these finite-rate chemistry effects, we compare temperature measurements in two piloted, partially premixed CH4/air (1/3 by vol.) jet flames with different turbulence levels. Figure 7.2.4 shows scatter plots of temperature as a function of mixture fraction for a fully burning flame (Flame C) and a flame with significant local extinction (Flame F) at a downstream location of xld = 15 [16]. These scatter plots provide a qualitative indication of the probability of local extinction, which is characterized... 

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. 

If it would be possible to increase the accuracy of the determination of extinction angles so that measurements could be carried out at very low flow rates q, it probably would be possible to show that, at low values, the measuring points for the high molecular weight fractions of... 

All upward radiative transitions in Figure 3.23 are absorptions which can promote a molecule from the ground state to an excited state, or from an excited state to a higher excited state. We have seen that the probability of these transitions is related ultimately to the transition moment between the two states and thereby to the Einstein coefficient A. In practice two other related quantities are used to define the intensity5 of an absorption, the oscillator strength f and the molar decadic extinction coefficient e. 

Experimentally, we can determine the probability of a certain transition by measuring its extinction coefficient, e. When a beam of monochromatic radiation passes through an absorbing system, the intensity of the transmitted beam, It, is given by the Beer-Lambert law (Equation 13.6), where I0 is the intensity of... 

For organic materials, ultraviolet absorption spectra are substantially determined by the presence of functional groups. Identical functional groups in different molecules may not absorb at precisely the same wavelength due to different structural environments which modify the local electric field. The magnitude of the molar extinction coefficient ( e ) for a particular absorption is directly proportional to the probability of occurrence of the particular electronic transition. Spectral features of some isolated chromophoric groups are presented in Table 2... 

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... 

The long-wave bands of 182a and 183a (which are probably due, as in the azulenium ion,129 for example, to electron transfer from the phenyl group to the 1,2-dithiolium or tropylium ion) are very similar in position and maximum extinction they suffer bathochromic shifts of similar magnitudes when identical donor substituents such as OCHs or N(CHS)2 are introduced into the p-positions of the phenyl groups, with a consequent increase in the probability of electron transfer. 

---