Fronts from two-dimensional dispersal kernels: Beyond the nonoverlapping-generations model

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 80, Issue 5, 2009, Pages

  Amor, Daniel R ^a   Fort, Joaquim ^a  

^a UNIVERSITY OF GIRONA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

BIOLOGICAL INVASION; DISPERSAL KERNEL; LONG LIFE; STAGE STRUCTURE; TWO-DIMENSION;

EID: 71449123652     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.80.051918     Document Type: Article

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24. According to field observations in sites close to those where the dispersal kernel was measured, we estimate the net reproductive rate R0 of the yellow poplar (Liriodendron Tulipifera) to be in the range of 2-50 seeds/(tree yr.). The age at first reproduction (generation time in the nonstructured model) of the same species is T=20 yr. As shown in, the long-distance dispersal component of the kernel has a much more important effect on the front speed than the short-distance component (even if long-distance dispersal happens seldom). Therefore, we use for the distance between cells that from the long-distance component, Δ0 =6000 m, both in the CSRW and in the DSRW models.
25. All of the results in this paper have been calculated with square matrices □ and Φ□□ of order 130. However, we have observed that in many cases we can obtain accurate results using matrices of lower order. That can be very useful in order to reduce computation times. For instance, omitting all of the elements aij with i>65 and/or j>65, we obtain a demographic matrix of order 65. If we do the same for the dispersal kernel matrix and we solve the equations of our overlapping-generations model, we obtain the same invasion speeds (differences are under the 1%) for values of R0 >5. The reason is that very old individuals do not appear near the leading edge of the invasion front, so for high values of the fecundity R0 the front dynamics is driven by younger individuals and the contribution of older ones is not relevant. However we do not give a general description of such an approximation because it depends on the dispersal kernel and demographic characteristics of each species.
26. Calculation of each overlapping-DSRW speed in Fig. takes about 50 to 80 minutes. We used an Intel Core 2 CPU, T7400 (2,16GHz and 2GB RAM). We remark that calculation times become much longer as the order of the matrix H□□ increases. In contrast, each overlapping-model simulation takes about 10 minutes using the same computer. For nonoverlapping models, calculation times are about ten times shorter than for overlapping models.