Simulation study of territory size distributions in subterranean termites

In this study, on the basis of empirical data, we have simulated the foraging tunnel patterns of two subterranean termites, Coptotermes formosanus Shiraki and Reticulitermes flavipes (Kollar), using a two-dimensional model. We have defined a territory as a convex polygon containing a tunnel pattern and explored the effects of competition among termite territory colonies on the territory size distribution in the steady state that was attained after a sufficient simulation time. In the model, territorial competition was characterized by a blocking probability P_block that quantitatively describes the ease with which a tunnel stops its advancement when it meets another tunnel; higher P_block values imply easier termination. In the beginning of the simulation run, N=10, 20,…,100 territory seeds, representing the founding pair, were randomly distributed on a square area. When the territory density was less (N=20), the differences in the territory size distributions for different P_block values were small because the territories had sufficient space to grow without strong competitions. Further, when the territory density was higher (N>20), the territory sizes increased in accordance with the combinational effect of P_block and N. In order to understand these effects better, we introduced an interference coefficient γ. We mathematically derived γ as a function of P_block and N: γ(N,P_block)=a(N)P_block/(P_block+b(N)). a(N) and b(N) are functions of N/(N+c) and d/(N+c), respectively, and c and d are constants characterizing territorial competition. The γ function is applicable to characterize the territoriality of various species and increases with both the P_block values and N; higher γ values imply higher limitations of the network growth. We used the γ function, fitted the simulation results, and determined the c and d values. In addition, we have briefly discussed the predictability of the present model by comparing it with our previous lattice model that had been used to explain the territory size distributions of mangrove termites on the Atlantic coast of Panama.     

Exploring landscape structure effect on termite territory size using a model approach

The foraging territory of the Formosan subterranean termite, Coptotermes formosanus Shiraki, was simulated by using a lattice model in order to study how landscape structure affects the foraging territory. Three kinds of landscape were generated on lattice space: ideal, random and fractal landscape. Each lattice cell had a value ranging from 0.0 to 1.0, interpreted as transition probability, P_trans, which represents spatially distributed property of the landscapes. The heterogeneity of the fractal landscape was characterized by a parameter, H, controlling aggregation of lattice cells with higher value of P_trans. Higher H values corresponded to higher aggregation levels. The model made use of minimized local rules based on empirical data that determines the development of the foraging territory. Additionally, seasonal cycle (summer and winter season), and obstacles which hinder the growth of the territory were incorporated in the model as environmental variables. Territory size was largest in the ideal landscape while it was larger in the random landscape than in the fractal landscape. As obstacle density increased, the territory size decreased. In the fractal landscape, the territory size increased, decreased, and increased again as H increased.     

Food encounter rates of simulated termite tunnels with variable food size/distribution pattern and tunnel branch length

Subterranean termites excavate tunnels in a search pattern to encounter food in soil. To investigate the effect of food size, food distribution and the branch length of tunnels on food encounter rate we used a lattice gas model to simulate tunnels of the Formosan subterranean termite, Coptotermes formosanus Shiraki. The model made use of minimized local rules derived from empirical data to simulate termite tunnel patterns in featureless soil. Food distributions with three types (uniform, random, and clumped) were defined by using an I-index proposed by Zimmer and Johnson (1985). The food encounter rate was higher in a clumped than in non-clumped (uniform and random) distribution of food particles. When food particle size was varied in random distributions of food particles a maximum encounter rate was found, with particles of larger or smaller size being encountered less frequently. We also discussed the relationship between the branch tunnel length and the tunnel search pattern in minimizing the redundancy of overlapping branches.     

Effects of environmental perturbation on the territory size of subterranean termites: A simulation study

Disruptions to an ecological system can have profound effects on the use of that system by various species. Such effects are often studied in terrestrial or aquatic species, but subterranean species are equally affected. To investigate how environmental perturbation affects the territory size of subterranean termites, a lattice model was designed based using seasonal and behavioral data to simulate the foraging behavior of the Formosan subterranean termite Coptotermes formosanus Shiraki. This computer model was then used to subject a given number of founding pairs (N = 20, 40, 60, 80, 100 at t = 0) to several levels of environmental perturbations (H = 0.0–1.0) once initial territory growth had reached saturation for a fixed area (t = 5). At lower values of H, territories were reduced to localized holdings randomly distributed over the entire model area. As H increased, the size of surviving territories increased while the total number of territories decreased. Analysis of territory size post-disruption (t = 10) indicated a trend towards larger overall territorial size when both N and H were high, whereas no such increase was seen when N was low. These results can be used to improve modeling systems to determine survival of subterranean populations in environmental disasters.     

A field study investigating effects of landmarks on territory size and shape

Few studies have examined how landmarks affect territories'' fundamental characteristics. In this field study, we investigated effects of landmarks on territory size, shape and location in a cichlid fish (Amatitlania siquia). We provided cans as breeding sites and used plastic plants as landmarks. During 10 min trials, we recorded locations where residents chased intruders and used those locations to outline and measure the territory. In two experiments, we observed pairs without landmarks and with either a point landmark (one plant) or linear landmark (four plants) placed near the nest can. We alternated which trial occurred first and performed the second trial 24 h after the first. Territories were approximately round without landmarks or with a point landmark but were significantly more elongated when we added a linear landmark. Without landmarks, nests were centrally located; however, with any landmark, pairs set territory boundaries closer to the landmark and thus the nest. Territory size was significantly reduced in the presence of any landmark. This reduction suggests that a smaller territory with well-defined boundaries has greater benefits than a larger territory with less well-defined borders.     

Spatial distribution and habitats of useful plants: an initial assessment for conservation on an indigenous territory, Panama

In order to examine the spatial distribution of forest resources on local territories and to understand the factors controlling such distributions, we studied the spatial patterns of a group of 23 useful plant species on the territory of a Kuna community in the province of Darien, Panama. A stratified random sampling scheme was used to survey the distribution and abundance of the species across a 3500 ha area around the village. Data on the physical environment as well as the geographic coordinates of the sample plots were also obtained. A series of canonical analyses was conducted to evaluate the species–environment relationships and to identify spatial structures in the species distributions left unexplained by the environmental variables. Four distinct distribution patterns were identified among the species; these were most strongly explained by land-use, the degree of canopy closure and topography. Significant spatial structures, independent of the measured environmental variables, were related to anthropogenic pressure and an edaphic gradient, and the habitat associations of the individual species were described. The results obtained from this case study suggest that land-use dynamics may play a predominant role in structuring inhabited landscapes, and that diversity in distribution patterns and habitat associations will require a combination of spatially explicit management strategies to ensure the local resource base.     

Growth and size distribution of some large brown algae in Ohori,east coast of Korea

About fifty individuals of four dominant large brown algae were collected by random sampling at monthly intervals using SCUBA. Size frequencies of Sargassum confusum and S. horneri were concentrated mainly in the small size classes during the initial growth phase, but were more or less evenly distributed in most size classes during the fast growing phase. Undaria pinnatifida and Costaria costata showed the same tendency as Sargassum spp., that frequency distribution became even when the plants reached their maximum growth. The kelp species recorded their maximum lengths in March, whereas Sargassum spp. showed their peaks in early summer. The relationships between the length and weight in different growth phases appeared to be dependent on the phenology of each species.     

Global asymptotic stability of the size distribution in probabilistic models of the cell cycle

Probabilistic models of the cell cycle maintain that cell generation time is a random variable given by some distribution function, and that the probability of cell division per unit time is a function only of cell age (and not, for instance, of cell size). Given the probability density, f(t), for time spent in the random compartment of the cell cycle, we derive a recursion relation for _n(x), the probability density for cell size at birth in a sample of cells in generation n. For the case of exponential growth of cells, the recursion relation has no steady-state solution. For the case of linear cell growth, we show that there exists a unique, globally asymptotically stable, steady-state birth size distribution, _*(x). For the special case of the transition probability model, we display _*(x) explicitly.This work was supported by the National Science Foundation under grants MCS8301104 (to J.J.T.) and MCS8300559 (to K.B.H.), and by the National Institutes of Health under grant GM27629 (to J.J.T.).     

Niche differentiation depends on body size in a cichlid fish: a model system of a community structured according to size regularities

1. Communities of different species are often structured according to niche differentiation associated with competitive interactions. We show that similar principles may apply on an ecological time-scale when individuals of a species having a wide size variation compete for resources, using the Lake Tanganyika cichlid Lobochilotes labiatus (5-30 cm). This species has a mouth especially adapted to suck up invertebrates from rock crevices. 2. Individuals defended feeding territories against similar-sized conspecifics, but not against different-sized ones. Thus, territories of similar-sized fish rarely overlapped, but up to a total of seven individuals (of seven size-ranks) had broadly overlapping territories with dissimilar-sized individuals. Comparison with expectation from the null model demonstrated clearly that observed size ratios between adjacent size rank were determined non-randomly regardless of sexual combinations. 3. Larger individuals took larger prey types of larger average size, but more importantly used wider rock crevices from which to suck food than smaller individuals. We calculated pairwise values of Schoener's index of diet overlap C(d) and the values of Levin's index of diet breadth B(d) (prey type and prey size) and the same for the width of the rock crevices used for foraging (C(r) and B(r)). C(d) remained high among all combinations of the seven ranks. In contrast, C(r) declined strongly in combinations of adjacent ranks (to 0.27), and was low or zero among further different size ranks. This shows that fish with overlapping territories divided the food resources largely through foraging site partitioning. Accordingly, B(d) did not depend on the size difference to the nearest two coinhabiting fish, whereas B(r) did. 4. We conclude that this L. labiatus community is structured non-randomly: body size-dependent effects on foraging site usage result in competition with, and territorial exclusion of, similar-sized individuals, but not of dissimilar-sized individuals that were accepted as coinhabitants. Accordingly, mean body size ratios (large/small) between two adjacent ranks were consistently approximately 1.28 [standard deviation (SD) = 0.07, n = 104], while approximately 1.34 from the null model (SD = 0.34, n = 10 400 simulations). We discuss our results as an example of Hutchinson's rule, applied originally to size ratios of different species.     

The asymptotic final size distribution of reducible multitype Reed-Frost processes

The asymptotic final size distribution of a multitype Reed-Frost process, a chain-binomial model for the spread of infection in a finite, closed multitype population, is derived in the case of reducible contact pattern between types. The results are obtained using techniques developed for the irreducible case.     

The influence of particle size distribution and composition on seasonal sedimentation rates in a temperate lake

To evaluate the effect of particle size and composition on seasonal changes in the sedimentation rate, suspended and sedimenting particles were collected from Trout Lake, Wisconsin, USA during the 2002 ice-free season. Particles were characterized with regard to particulate biogenic silicon (PBSi) concentration and distribution between four size classes. The concentration of particulate chlorophyll and chlorophyll degradation products was also measured in water column particles and sediment trap material collected during the first half of the sampling period. The highest rates of mass sedimentation during the stratified period were measured in spring and early summer. Seasonal increases in sedimentation are related to the presence of large colonial diatoms in the water column as indicated by elevated PBSi concentrations. The majority of particulate matter in the water column was found in the smallest (<20 m) size fraction while most of the mass of sediment trap material was in larger size fractions (>20 m). Smaller cells appear to carry out most of the photosynthesis in Trout Lake but larger cells are responsible for seasonal trends in sedimentation. These results may explain how pelagic photosynthesis and sedimentation rates can be quantitatively decoupled across a range of trophic conditions but appear correlated when based on mid-summer measurements.     

A model explaining the size distribution of gene and protein families

This article deals with the theoretical size distribution of gene and protein families in complete genomes. A simple evolutionary model for the development of such families in which genes in a family are formed or selected against independently and at random, and in which new families are formed by the random splitting of existing families, is used to derive the resulting size distribution. Mathematically this turns out to be the distribution of the state of a homogeneous birth-and-death process after an exponentially distributed time, which it is shown will under certain conditions exhibit the power-law behaviour observed for gene and protein family sizes.     

A model of drop size distribution for a system with evaporation

Abstract. The size and shape of drops on leaf surfaces strongly affect their persistence. The relationship between volume and exposed surface area of drops on wheat leaves and the log-normal drop size distribution in a wheat canopy after rain are used to derive equations to describe how the total volume and drop number change with evaporation. Firstly, the behaviour of a single drop as it evaporates is considered and then equations describing the change in a population of drops with an initial log-normal distribution are derived. The time taken for all the drops to reach complete dryness is about thirty times that for the same volume of water spread uniformly over the surface with the same potential evaporation rate.     

Effect of habitat types on survival, spatial distribution and production of an allopatric cohort of Atlantic salmon, Salmo salar L., under conditions of low competition

An allopatric cohort of Atlantic salmon, Salmo salar L., introduced to a small previously fishless stream was studied from parr to the smolt stages. In May 3900 0+ parr (mean total length 30mm) were planted at three different densities in habitats with slow, intermediate and fast water velocities. During the first year, high mortality occurred during the first 7 weeks after planting in May, and in September–October. Survival from May 1985 to April 1986, before the smolt emigration, was24.8%. The smolt yield 1 year after planting was 15.5%. It is suggested that the high survival was caused by low competition. Most of the redistribution of the fish took place during the first months. Type of planting habitat affected the timing of redistribution. The parr left slow-flowing, deep habitats with fine substrate soon after planting, while redistribution was slowest in the fastest flowing habitats with coarse substrate. The observed avoidance of slow, deep habitat types in the absence of interspecific competition, suggests that this may be a fixed behavioural response, and not due to competition. Long movements, up to 800 m, were recorded only within the first 7 weeks after planting. The effect of planting densities on population density was most pronounced immediately after planting in the fast and also intermediate habitats. Planting density effects declined and were not detectable after 1 year. The effect of habitat type on fish numbers and biomass was pronounced irrespective of planting densities. Growth was fastest in the intermediate habitat, and at the lower planting densities. Production was 7.2 g m⁻² the first summer-autumn. Due to smolt emigration, few fish remained in the stream the second summer-autumn, and the production was 1.0 g m⁻².     

A preliminary study of two species of flatfish (family: Bothidae) from the south-west Atlantic

Two species of the family Bothidae (lefteye flounders), Mancopsetta maculata metadata and M. milfordi occur in the south-west Atlantic but are caught rarely by commercial bottom trawlers. Little is therefore known about their general biology from this area. A total of 251 M. maculata and 276 M. milfordi were sampled during deep-water exploratory fishing conducted in November 1994 within the Falkland Islands Interim and Outer Conservation Zones, at depths of 400-1000 m, using standard commercial bottom trawling gear. The two species were found to have similar geographical distributions between 48.30'-53.30'S and 55°-62° W and were often obtained at the same stations in depths of 400-900 m on the continental slope. Mancopsetta maculata maculata showed a uni-modal cohort structure with a modal length at the 29-cm total length size-class. Males of M. m. maculata outnumbered females in a ratio of 3.5 : 1. Mancopsetta milfordi showed a tri-modal length distribution, the main mode at the 37-cm total length size-class, with females outnumbering males in a ratio of 1.1 : 1. Length-weight relationships and length-at-age information are presented for the two species. Diet was determined from the analysis of stomach contents and, although the major prey type for both species consisted of crustaceans, the morid fish Austrophycis marginata also formed an important part of the diet of M. milfordi. Key words: Mancopsetta maculata maculata; Mancopsetta milfordi; distribution; south-west Atlantic; size; diet.     

中国十字花科(Cruciferae)的地理分布

在评述十字花科（Cruciferae）分类系统,分析主要性状演化趋势和科、属分布的基础上,提出中国十字花科植物可能是本土起源的观点,其起源中心和分布中心可能在以青藏高原为主体的西部高山和丘陵地区,起源时间至少在第三纪晚期以前,并认为中国十字花科植物自起源地（青藏高原）可能有3条主要的散布途径：第1条是自青藏高原向东北部,沿宁夏、陕西、内蒙古、山西、河北,到达东北大小兴安岭一带,并在蒙古高原及东北山地形成次分布中心;第2条自青藏高原向东,经重庆、湖南、湖北,沿长江流域分布,到达东部沿海一带;第3条自青藏高原向东南部,经贵州、广西、广东、福建,延伸到台湾。     

A Lyapunov function for piecewise-independent differential equations: stability of the ideal free distribution in two patch environments

In this article we construct Lyapunov functions for models described by piecewise-continuous and independent differential equations. Because these models are described by discontinuous differential equations, the theory of Lyapunov functions for smooth dynamical systems is not applicable. Instead, we use a geometrical approach to construct a Lyapunov function. Then we apply the general approach to analyze population dynamics describing exploitative competition of two species in a two-patch environment. We prove that for any biologically meaningful parameter combination the model has a globally stable equilibrium and we analyze this equilibrium with respect to parameters.      

A test of neutrality and constant population size based on the mismatch distribution

Several factors including demographic changes, selection, and recombination are known to affect the distribution of the number of pairwise differences between DNA sequences. The effects of each of these forces have previously been used to estimate population parameter values using various assumptions about other factors. In this article, we use the predictions of the mismatch distribution under a standard neutral equilibrium model to design a coalescent simulation-based test and detect any deviation from this equilibrium. When reliable independent estimates are available for the intragenic recombination rate, this test can be used as a neutrality test or a population expansion test in actual studies, under reasonable assumptions.