Diffusion about the mean drift location in a biased random walk

Random walks are used to model movement in a wide variety of contexts: from the movement of cells undergoing chemotaxis to the migration of animals. In a two-dimensional biased random walk, the diffusion about the mean drift position is entirely dependent on the moments of the angular distribution used to determine the movement direction at each step. Here we consider biased random walks using several different angular distributions and derive expressions for the diffusion coefficients in each direction based on either a fixed or variable movement speed, and we use these to generate a probability density function for the long-time spatial distribution. We demonstrate how diffusion is typically anisotropic around the mean drift position and illustrate these theoretical results using computer simulations. We relate these results to earlier studies of swimming microorganisms and explain how the results can be generalized to other types of animal movement.     

Ichthyofaunas of a temperate estuary and adjacent marine embayment. Implications regarding choice of nursery area and influence of environmental changes

A fine-mesh seine net was used at regular intervals to collect fishes from the entrance channel and basin of the Blackwood River Estuary (south-western Australia), from Deadwater Lagoon, which is joined to the entrance channel by a narrow and shallow water-course and thus constitutes part of this estuary, and from Flinders Bay into which the estuary discharges. Sampling was at six-weekly intervals between February and December 1994. The juveniles of some marine species, such as Pelates sexlineatus, Rhabdosargus sarba and Aldrichetta forsteri, were either found only in the estuary or were in far higher densities in the estuary than in Flinders Bay. In contrast, the juveniles of some other marine species, such as Sillago schomburgkii, were relatively abundant in both environments, while others such as S. bassensis, Pelsartia humeralis, Lesueurina platycephala and Spratelloides robustus were either far more abundant in Flinders Bay or entirely restricted to this marine embayment. The various marine species found in inshore waters thus apparently vary considerably in their “preference” for estuaries as nursery areas. Although some marine species were abundant in the shallows of the estuary, the fish fauna of these waters was dominated by the estuarine-spawning species Leptatherina wallacei, Favonigobius lateralis, L. presbyteroides and Atherinosoma elongata. The above regional differences help account␣for the very marked difference that was found between the compositions of the shallow-water␣ichthyofaunas of Flinders Bay and each of the three estuarine regions. The ichthyofaunal compositions of the basin and channel underwent pronounced changes during winter, when freshwater discharge increased markedly and salinities in the estuary thus declined precipitously. This faunal change was mainly attributable to the emigration of marine stragglers, a reduction in the densities of marine estuarine-opportunist species such as Pelates sexlineatus and R. sarba, and the immigration of large numbers of both young 0+ Aldrichetti forsteri from the sea and of L. wallacei from the river. Although most of the above species were also abundant in Deadwater Lagoon, the ichthyofaunal composition of this region did not undergo the same seasonal changes, presumably due to the lack of riverine input and thus the maintenance of relatively high salinities throughout the year. The number of marine straggler species was much lower in Deadwater Lagoon than in the estuary basin, reflecting a far more restricted tidal exchange with the entrance channel. However, the overall density of fishes was far higher in Deadwater Lagoon than in the estuary basin or entrance channel, due mainly to the far higher densities of the estuarine species Atherinosoma elongata and L. wallacei and of the 0+ age class of the marine species R. sarba. The high densities of certain species in Deadwater Lagoon are assumed to be related, at least in part, to the high level of productivity and protection that is provided by the presence of patches of Ruppia megacarpa, an aquatic angiosperm that was not present in the estuary basin or entrance channel. Received: 3 December 1996 / Accepted: 19 December 1996     

Composition and temporal fluctuations of inshore juvenile fish populations in the Kornati Archipelago, eastern middle Adriatic

Temporal fluctuations of species composition and abundance of fish juveniles in the National Park Kornati were studied over 12 months from January to December 1992. A total of 40 168 individuals, representing 24 families and 69 species, were collected using a 50 m long beach seine. The community was dominated numerically by a few species: Atherina hepsetus (45.90%), Sarpa salpa (21.21%), Diplodus vulgaris (10.49%), and Symphodus ocellatus (6.98%), constituting over 84.58% of the total catch. Similarity between patterns in the abundance of the 17 most common species were examined using correlation matrix-based principal component analysis. Results were compared to the abiotic factors leading to the conclusion that only a low amount of variation in the abundance field can be explained by temperature, salinity and dissolved oxygen. Received: 23 March 1997 / Accepted: 11 April 1997     

Temporal patterns and transport processes in recruitment of spiny lobster (Panulirus argus) postlarvae to south Florida

We used time-series analysis to identify weekly and annual patterns in the supply of spiny lobster, Panulirus argus (Latreille, 1804), postlarvae to the Florida Keys, USA, over an 8 yr period. We also investigated the relationship between postlarval influx and wind forcing as a transport mechanism using the complex vector-scalar correlation analysis. Postlarval supply had a lunar phase periodicity at 4.5 wk intervals, with postlarval abundance peaking between the new moon and first-quarter lunar phases. A distinct annual cycle of postlarval supply with two peak periods was also apparent. Cross-correlation analysis between relative postlarval abundance and a 12 mo cycle showed that the annual peak occurs in spring, centered around March. With the 12 mo periodicity removed, a smaller peak at 5 mo intervals was also well defined. Wind-forcing for 7 d prior to the time of postlarval collection was marginally correlated with postlarval abundance through the entire time-series; the association was strongest during the late fall to early spring months. The analysis indicated that postlarval supply was correlated with winds from the northeast (ca. 45°), which are associated with winter atmospheric fronts. In contrast to results reported for other spiny lobster populations, these patterns suggest that recruitment of lobster postlarvae to south Florida is predictable only at a gross level and is presumably affected by the temporally inconsistent structure of regional oceanic gyres and variability in the timing of lobster spawning in the Caribbean. Received: 24 January 1997 / Accepted: 4 March 1997     

Seasonal growth of the giant kelp Macrocystis pyrifera in New Zealand

The seasonal growth pattern of Macrocystis pyrifera (L.) C. Agardh in New Zealand was determined from measurements of blade-elongation rates between March 1986 and December 1987. Growth rates remained relatively constant throughout most of the year, but declined significantly during the summer months. Seawater nitrate levels had a marked seasonal cycle, with concentrations of 0.3 μM detected in summer. The timing of the decline in internal nitrogen concentrations varied for different-aged blades, but occurred ∼1 mo after the decrease in seawater nitrate concentrations. Sufficiently high irradiance levels and seawater nutrient concentrations support active growth for most of the year, but growth is nutrient-limited during summer. No carbon accumulation during summer was observed. Between March and August 1988, growth estimates were also derived from node-initiation rates and stipe-elongation rates to permit comparisons with previous studies from the northern and southern hemispheres. Direct comparisons of the three growth parameters determined for non-terminated canopy and sub-surface fronds were used to assess possible differential resource allocation in the two frond classes. Received: 16 May 1997 / Accepted: 28 May 1997     

Genetic Variation and the Immune Response in Natural Populations of Pocket Gophers

It is thought that genetic variation can affect the persistence of a population through its influence on disease susceptibility. We assessed genome-wide genetic variation, variation at a locus involved in the immune system, and acceptance or rejection of skin grafts in three natural populations of the pocket gopher ( Thomomys bottae ). Multilocus DNA fingerprints confirmed previous allozyme data, revealing high levels of variation among Hastings Reserve pocket gophers and almost complete within-population identity for individuals from the two Patricks Point populations (Patricks J and Patricks F), although Patricks J animals were dissimilar to animals from Patricks F despite their proximity. Individuals from the high-variation population consistently rejected within-population reciprocal skin grafts, whereas Patricks J and Patricks F individuals accepted within-population grafts. Patricks J and Patricks F individuals were found to be immunocompetent, however, as revealed by the ability of all individuals to reject between-population grafts, including those that previously accepted within-population grafts. A DNA heteroduplex analysis was then used to directly characterize variability at DQα, a locus of the immune system's major histocompatability complex. Both populations low in genetic variation were fixed for unique DQα alleles, whereas observed heterozygosity in the Hastings population was 0.43, ascribable to at least three unique alleles. These data are in accord with previous cheetah skin-graft results and confirm that skin grafts can be used to assess genetic similarity. We suggest that although many animal populations can persist with extremely low levels of genetic variation in the wild, such populations may be at a greater risk of extinction from particular pathogens because of their genetic uniformity.     

Grazing as a measure against grass encroachment in Dutch dry dune grassland: effects on vegetation and soil

A grazing experiment was started in 1984 and 1989 respectively, in two parts of a dune grassland in the nature reserve ‘Zwanenwater’, North Holland; a third part with similar geology and topography was used as a control area and not grazed. An evaluation of the effects of grazing on vegetation patterns, species composition, vegetation structure and humus form was made with the help of vegetation maps from 1986 and 1992 as well as field surveys. Dense tall-grass communities dominated byAmmophila arenaria increased over the period 1986–1992 in the grazed areas, and especially in the non-grazed area (increase in area to 20%, 22% and 50%, respectively). Open communities decreased in the grazed areas, but are still prevalent, while in the ungrazed area they virtually disappeared, with the result that the present percentage areas are 53%, 38% and 17%. Field survey data were classified by TWINSPAN producing four vegetation types. These occur more or less equally in grazed and ungrazed areas, albeit with different percentage areas: (1) open vegetation dominated byCorynephorus canescens; (2) open vegetation characteized, byKoeleria macrantha; (3) heathland dominated byEmpetrum nigrum; and (4) tall-grass communities dominated byAmmophila arenaria. Within a vegetation type, species composition was only marginally affected by grazing regime. Within the open communities the number of species, vegetation height, vegetation cover and soil organic horizons were not affected by grazing. In the tall-grass communities the number of species was significantly larger and the height of the vegetation significantly lower in the area grazed since 1984. In the heathland community the number of species and cover of the moss layer were significantly higher in the 1984 area and ectorganic and endorganic horizons significantly thicker in the ungrazed area. It is suggested that these effects are the result of an increased availability of light, but possibly also of a decreased stock of organic matter and nutrients, due to a decreased input of litter and accelerated rates of decomposition.     

Foraging in the seed-harvester ant genus Pogonomyrmex: are energy costs important?

Energy intake and expenditure on natural foraging trips were estimated for the seed-harvester ants, Pogonomyrmex maricopa and P. rugosus. During seed collection, P. maricopa foraged individually, whereas P. rugosus employed a trunk-trail foraging system. Energy gain per trip and per minute were not significantly different between species. There was also no interspecific difference in energy cost per trip, but energy cost per minute was lower for P. maricopa foragers because they spent on average 7 min longer searching for a load on each trip. Including both unsuccessful and successful foraging trips, average energy gain per trip was more than 100 times the energy cost per trip for both species. Based on this result, we suggest that time cost incurred during individual foraging trips is much more important than energy cost in terms of maximizing net resource intake over time. In addition, because energy costs are so small relative to gains, we propose that energy costs associated with foraging may be safely ignored in future tests of foraging theory with seed-harvesting ant species.     

Inter-specific variation in anti-predator behavior in sympatric species of kangaroo rat

Kangaroo rats, Dipodomys, occupy desert habitats with little cover and thus are under high predation risk from diverse predators. The behavior used to assess predation risk or to escape capture is unknown. We therefore compared anti-predator behavior of two sympatric species of kangaroo rat of different sizes, D. merriami and D. spectabilis. We first examined whether kangaroo rats use olfaction as a first line of defense against snake predation and tested the rats for their responses to scent extracted from two species of snake that live sympatrically with the kangaroo rats, the Mojave rattlesnake (Crotalus scutulatus) and the gopher snake (Pitophis melanoleucus). We also tested for species differences in anti-predator behavior through 15-min interactions between the kangaroo rats and free-moving gopher snakes. We found that D. spectabilis actively approached the scent of both rattlesnakes and gopher snakes more than controls of vegetable oil and evaporated solvent (Fig. 1). In contrast, D. merriami did not differentiate snake odors from controls in the experimental arena, but they sniffed the sand where a free-moving snake had passed more than D. spectabilis. Both species successfully avoided predation in encounters with live snakes. Although total numbers of approaches and withdrawals were similar (Fig. 2), D. spectabilis spent significantly more time within striking distance of the snake than D. merriami. D. spectabilis approached the head of the snake in 93% of its approaches and often engaged in nose to snout contact with the snake. If the snake struck, D. spectabilis jumped directly backward to avoid a strike and footdrummed at a safe distance. In contrast, D. merriami oriented to the snake more than D. spectabilis, but approached the head in only 41% of the approaches and rarely engaged in nose-to-snout contact. The snakes struck, hissed and decreased predatory approaches with D. spectabilis but not with D. merriami (Fig. 3). These results show that kangaroo rats can behaviorally influence the risk of being preyed on by snakes. The two species differ, however, in how they react to snakes. The larger D. spectabilis confronts snakes while the smaller D. merriami monitors snakes from a safe distance and avoids them.