Problem SE5

Lab experiments have been undertaken to study the dispersal ability of the alien insect Lymantria australis. To this purpose, several L. australis individuals are released from the same location and monitored for a few days. During this period there is no mortality or reproduction. Scientists observations confirm that the insects disperse randomly in all directions within the lab habitat (which can be assumed to be two-dimensional). By indicating with $R$ the radius inside which 95% of the organisms are spotted, the following results have been obtained

Day	1	4	8	13	20
R (metres)	3	6	8.5	10.5	13

Estimate the diffusion coefficient D of L. australis. Unfortunately, in 1985 the insect was inadvertently released in the natural habitat too, where it has fared quite well, expanding its spatial range and growing in numbers. The expansion radii of L. australis in the wild have been recorded. They are reported in the following table

Year	1990	1992	1997	2000	2004
Radius (metres)	100	145	237	304	383

From this information estimate the instantaneous rate of demographic increase r of the alien species.