Leslie matrix

The number nx at time t + 1 of all other age classes is calculated by multiplying the number of individuals in the preceding age class, nt v by the survival rate of those individuals into the next age class,, S for example 2,+i = in The other age classes of the population vector cannot contribute to n2. Thus, the transition or Leslie matrix in Equation 3.1 has a typical structure age-dependent fecundities in the first row and age-dependent survival rates in the subdiagonal (Caswell 2001 Chapter 5). 

The most commonly used age- or stage-based population models are based on the Leslie matrix (Leslie 1945). With the Leslie matrix, the population contains n ages or stages and is described by a column vector, as shown next. I present a hypothetical insect in this example, which has an egg, a nymph, and an adult stage. Furthermore, all individuals in this example are females. 

As this example illustrates, the population starts with 16 individuals and after 1 time step (1 week) consists of 22.5 individuals. Obviously, you can t have 0.5 individual, and this number will be rounded off as the multiplications continue. Therefore, the Leslie matrix model projects population abundance and population structure into the future based on starting conditions. In Figure 5.1 we see results of the matrix model after 52 multiplications. 

Therefore, the data necessary to develop a simple Leslie matrix model are a measure of survival and fecundity. These data can be developed in the field through sampling of wild populations or in the laboratory with life table experiments. 

Byers JA, Castle SJ. 2005. Areawide models comparing synchronous versus asynchronous treatments for control of dispersing insect pests. J Econ Entomol 98 1763-1773. Chandler GT, Cary TL, Bejarano AC, Pender J, Ferry JL. 2004. Population consequences of fipronil and degradates to copepods at field concentrations an integration of life cycle testing with Leslie matrix population modeling. Environ Sci Technol 38 6407-6414. 

Leslie Orgel and co-workers took up this problem and studied the non-enzymatic polymerisation of mononucleotides, i.e., the question as to whether single nucleic acid building blocks can undergo polycondensation on a corresponding complementary matrix. The substrates used were the 5 -phosphoimidazolides of adenosine (ImpA) and guanosine (ImpG), the matrices poly(U) and poly(C). 

The second rank viscous stress tensor found by Leslie for the incompressible nematic phase consists of nine matrix elements, each of them having the form ... 

Synthesis of cobalt nanoparticles in a polystyrene/triphenylphosphine polymer matrix was reported by Leslie-Pelecky et al. [39] who showed that magnetic properties of the as-synthesized nanocomposites ranged from super-paramagnetic to ferromagnetic with coercivities on the order of 130 Oe. They found that annealing in vacuiun produced coercivities of up to 600 Oe and remanence ratios of up to 0.4. 

In the case under investigations, which includes nematic (anisotropic) phase environments, we shall assume the usual approximation of considering isotropic local friction, and the macroscopic local viscosity is taken equal to half of the fourth Leslie-Ericksen coefficient 1/4 [92-95]. The diffusion tensor of the system is obtained, neglecting translational contributions, as a 4 x 4 matrix, that is. 

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