acta oecologica 33 (2008) 280–290 available at www.sciencedirect.com journal homepage: www.elsevier.com/locate/actoec Original article Stochastic approach to determine spatial patterns of lizard community on a desert island Crystian Sadiel Venegas-Barrera1, Enrique Morales-Bojo´rquez*, Gustavo Arnaud Centro de Investigaciones Biolo´gicas del Noroeste (CIBNOR), Mar Bermejo 195, Col. Playa Palo de Santa Rita, La Paz, B.C.S. 23090, Mexico article info abstract Article history: One of the principal sources of error in identifying spatial arrangements is autocorrelation, Received 23 May 2007 since nearby points in space tend to have more similar values than would be expected by Accepted 30 November 2007 random change. When a Markovian approach is used, spatial arrangements can be mea- Published online 18 April 2008 sured as a transition probability between occupied and empty spaces in samples that are spatially dependent. We applied a model that incorporates first-order Markov chains to an- Keywords: alyse spatial arrangement of numerical dominance, richness, and abundance on a lizard Spatial dependence community at different spatial and temporal scales. We hypothesized that if a spatial de- Markov models pendence on abundance and richness exists in a diurnal desert community, then the Mar- Numerical dominance kov chains can predict the spatial arrangement. We found that each pair of values was Species richness dependent only on its immediate predecessor segment. In this sense, we found interge- Spatial arrangement neric differences at temporal and spatial scales of recurrence estimates. Also, in desert Nearby samples scrub, species show higher spatial aggregation and had lower species richness than at the island level; the inverse pattern occurred on rocky hillsides. At the species level, Uta stansburiana is the most abundant species in desert scrub, while Sauromalus slevini is the most abundant species on rocky hillsides. This report attempts to understand, using Mar- kovian spatial models, the effect of nearby samples on local abundance and richness on different scales and over several seasons. ª 2008 Elsevier Masson SAS. All rights reserved. 1. Introduction segregation, habitat selection, and territoriality (Legendre, 1993; Bevers and Flather, 1999). Patterns based on spatial ar- The spatial arrangement of several species in a community is rangements are a first approximation for analysing the effect not homogeneous because limiting factors that affect abun- of biotic, that is, inter- or intraspecific interactions and abiotic dance and distribution change spatially and species tend to environmental variations, such as, temperature, pH, topogra- respond differentially to environmental heterogeneity. Gener- phy, and soil on species. One of the principal sources of error ally, species predominate in habitats where conditions are in identifying spatial arrangements is autocorrelation, since suitable, and are rare in unfavourable habitats (Kneitel nearby points tend to have more similar values than would and Chase, 2004). Therefore, spatial elements play a funda- be expected by random change (Lichstein et al., 2002). When mental role in most ecological processes, including spatial a Markovian approach is used, spatial arrangements can be * Corresponding author. Tel.: þ52 612 123 8484x3351; fax: þ52 612 125 3625. E-mail address: [email protected] (E. Morales-Bojo´ rquez). 1 Present address: Laboratorio de Ecologı´a Evolutiva, Centro de Investigaciones en Recursos Bio´ ticos, Universidad Auto´ noma del Estado de Me´xico, Instituto Literario 100, 50000, Toluca, Mexico. 1146-609X/$ – see front matter ª 2008 Elsevier Masson SAS. All rights reserved. doi:10.1016/j.actao.2008.01.002 acta oecologica 33 (2008) 280–290 281 measured as a transition probability between occupied and abundance of species, then we can estimate the average dis- empty spaces in samples that are spatially dependent. tance before we again observe the same species (recurrence) A first-order Markov chain is a stochastic model in which and rate of change between species without the necessity of the future development of a system is dependent on the pres- evaluating the spatial structure of habitats. We predicted ent state of the system and is independent of the way in which high probabilities of replacement between species with simi- that state has developed (Formacion and Saila, 1994). lar habitat requirements as species with different require- In ecology, Markov chains have been used principally in ments. Also, we can compare the numerical dominance and temporal succession of ecological states (Tanner et al., 1996; richness at two spatial scales (island and landscape) to ana- Wootton, 2001a; Hill et al., 2004), time of recovery and restora- lyse the effect of scale on the estimation of spatial arrange- tion of forests (Orlo´ ci and Orlo´ ci, 1988; Hall et al., 1991; Tucker ment. Finally, we calculated the spatial arrangement for and Anand, 2004), patterns of change in parental stock and re- more abundant species on two landscapes. cruitment in fisheries (Roshchild and Mullen, 1985), estimates of bird populations (Wileyto et al., 1994), and anthropogenic impact on marine mammals (Lusseau, 2003). Markov chains 2. Materials and methods spatial models have been used to predict sequences of egg- laying in butterflies (Root and Kareiva, 1984), ontogenic 2.1. Study area change in habitat preference of cotton rats (Kincaid and Cameron, 1985), movements of Canada geese (Hestbeck Isla Coronados is a volcanic, land bridge island (260801500 N, et al., 1991), and spatial inhibition by allelopathy in plants 111160500 W) located w10 km northeast of Loreto, B.C.S., (Kenkel, 1993). These studies highlight the potential of Markov Mexico and w3 km from the closest shore of the Baja Califor- chains in the study of population dynamics and importance of nia Peninsula (Fig. 1). The climate is hot and arid in summer proximity neighbourhoods in the state of system. However, (mean July temperature 33 C) and warm in winter (mean Jan- rarely has it been used to explore spatial changes in richness, uary temperature 16 C). Summer precipitation comes from abundance, or dominance of species at a community scale, convectional storms on the Peninsula (average 190 mm/year) despite the utility of that approach to analyse spatial depen- (Grismer, 1994). Four types of habitats occur on Isla Coronado; dence between near samples and calculate the average dis- rocky hillsides, desert scrubland, a coastal zone, and a transi- tance between ecological states. tion zone between rocky hillsides and desert scrub (Venegas, The advantages of Markov chains are that: (1) such models 2003). On rocky hillsides, approximately 45% of the surface is are relatively easy to derive from continuous data; (2) the covered with rocks (ranging in diameter from 20 to 100 cm), model does not require deep insight into the mechanisms of 15% is bare soil (includes fallen leaves, soil, and gravel dynamic change; (3) the basic transition matrix summarizes <2 cm), and 40% is covered with vegetation (Jatropha cuneata, essential parameters of dynamic change in a systems in Euphorbia magdalenae, and Simmondsia chinensis). In desert a way that few others models achieve; and (4) a model has scrub, approximately 7% are rocks (<10 cm diameter), 38% is much potential for identifying recent history in dynamic com- bare soil, and 55% is covered with vegetation (principally Fou- munities and population dynamics (Formacion and Saila, quieria diguetii, Gossypium harknessii, Hibiscus denudatus, and 1994). These characteristics are ideal for calculating spatial ar- Jatropha cuneata). The coastal zone has a ground surface that rangement of species. Additionally, Markov chains can be is 5% rock (<10 cm diameter), 65% bare soil, and 30% covered used to estimate the probability of any state of abundance or with vegetation (principally Salicornia virginica, Maytenus phyl- richness occur in the space, assuming that it is dependent lanthoides, and Atriplex barclayana). The transition habitat is on the preceding area. We assumed that: (1) contagious bio- characterized by 30% rocks (5–50 cm diameter), 17% bare logical process that affect local abundance of individual spe- soil, and 53% vegetation (Jatropha cuneata, Hibiscus denudatus, cies are spatially dependent (Legendre, 1993), i.e. conditions Euphorbia magdalenae, and Lycium sp.). of growth, survival, and reproduction tend to be similar at nearby sites, (2) well-selected habitats provide high fitness po- 2.2. Species tential (Railsback et al., 2003), (3) individuals in a population do not show a random distribution, i.e. occurrence of an individ- Isla Coronados is one of four islands in the Gulf of California ual does not affect the presence of others, and (4) species with with a largest number of diurnal lizard species (Grismer, similar adaptations will tend to occur together at the same 2002). Of the ten species in the study area, four are ground- sites (Bell, 2001). In this study, we developed models that in- dwelling species: desert iguana (Dipsosaurus dorsalis), zebra- corporate first-order Markov chains to analyse spatial changes tailed lizard (Callisaurus draconoides), side-blotched lizard (Uta in states of numerical dominance (more abundant species by stanburiana), and orange-throated whiptail (Aspidoscelis hyper- unit area), richness (number of species by unit area), and ythra) and six are rock dwellers: slevin’s chuckwalla (Sauroma- abundance of one lizard community on Isla Coronados in lus slevini),