A Diffusion Model for Dispersal of Opuntia Imbricata (Cholla) on Rangeland

Abstract

The dispersal of Opuntia imbricata (cholla) on rangeland may be directly or indirectly affected by the presence of livestock and wildlife. Overgrazing creates gaps or open spaces for seeds or stems that fall to the ground to become established (passive dispersal). In addition, livestock or wildlife may cause stems and fruits to fall to the ground (active dispersal). (2) A theoretical model is formulated for the dispersal of plants based on the diffusion equation which assumes one or more mechanisms of dispersal (e.g. passive and active dispersal). The x2 goodness-of-fit test is used to determine whether the data may be explained by one or by two mechanisms of dispersal. Methods for estimating the model parameters are presented based on the x2 method and the method of moments. (3) The model and analytical techniques are applied to field data on the spatial distribution of Opuntia imbricata in four different pastures. (4) The results indicate that dispersal of cholla can be attributed to two dispersal mechanisms. Passive dispersal alone cannot account for the current spread of cholla on some of the pastures.

Recruiting mechanisms of Cylindropuntia leptocaulis (Cactaceae) in the Southern Chihuahuan Desert

“…Furthermore, the threshold at which temperatures begin to affect the capacity of photosynthetic tissue decreases along with stem segment volume (Smith et al, 1984). This inability to establish in intercanopy areas contrasts with the results of studies done in the Chihuahuan Desert (Allen et al, 1991;Mandujano et al, 1998Mandujano et al, , 2007 that showed that pad rooting allows clonal propagation in O. rastrera, Opuntia macrocentra, and Cylindropuntia imbricata under the stressful environmental conditions found in intercanopy areas. Nevertheless, it is noteworthy that the pad volumes of these Opuntia species (272.98 AE 22.9 cm 3 , 65.26 AE 4.2 cm 3 y 28.69 AE 1.4 cm 3 respectively, n ¼ 45 in all cases, Flores-Torres and Montaña, unpublished data) are far higher than that reported above for C. leptocaulis.…”

“…Observational data on the spatial association between C. leptocaulis genets and ramets and shrub cover show that most C. leptocaulis terminal stem segments root under adult L. tridentata plants, unlike some Opuntia species whose vegetative propagules favor establishment under the plant from which they originated (Allen et al, 1991;Palleiro et al, 2006). Intercanopy space represents the worst site for rooting due to its extreme climatic conditions and the lack of protection from herbivores.…”

“…Ramet establishment is a frequent event in Opuntia and Cylindropuntia, but between species and between genera, variability has been reported (Allen et al, 1991;Bobich and Nobel, 2001;Ebert, 2006;Evans et al, 2004;Mandujano et al, 1998Mandujano et al, , 2007. Evans et al (2004) analyzed the establishment of stem segmentsdalso known as terminal joints, in the terminology of Bobich and Nobel (2001)din ten Cylindropuntia species and in the pads of 15 Opuntia species in the southwestern United States; the terminal joints of the former were shown to have a lower rooting percentage than Opuntia pads (32 vs. 71%, respectively).…”

“…Furthermore, some authors (Allen et al, 1991;Mandujano et al, 1998Mandujano et al, , 2007 have observed that several Opuntia species in the Chihuahuan Desert undergo clonal propagation in highly stressful sites, such as intercanopy space, without the need for nurse plants. To date, however, no published study has assessed the association between ramets and nurse plants in Cylindropuntia.…”

Patterns of spread in biological invasions dominated by long-distance jump dispersal: Insights from Argentine ants

“…Skellam (2) advanced models based on reactiondiffusion equations that have been used commonly by ecologists to predict asymptotic rate of invasion. Predicted rates of spread are often in agreement with observed rates, demonstrating the value of this approach (1,(3)(4)(5)(6). These models are often based on two parameters: the intrinsic rate of growth and the diffusion coefficient (2,7).…”