The species-area relation II. A second model for continuous sampling

Summary A second mathematical model describing the species-area relation was proposed for continuous expanding of sample area. This model is expressed asS=λ ln(1+x/E) whereS is the number of species occurring in an areax, and λ andE are the constants termedspecific diversity andelemental area respectively. As a result of testing the validity of the model for several sets of data, it was shown that the above equation would provide an adequate fit to a group of species belonging to a single synusia which exists in an open habitat. The ecological implications of parameters involved were discussed and the characteristic area presented previously (Kobayashi, 1974) was defined in terms ofE. The relation between results obtained by discrete sampling and continuous sampling was examined and the possibility of converting one to another was suggested. Contribution from the Laboratory of Applied Zoology, Yamagata University, No. 79.     

Human Carrying Capacity Is Determined by Food Availability

Simple mathematical models have illustrated the relationship between human carrying capacity and population growth. In this study, food supply is proposed as the variable which best accounts for the human carrying capacity. The logistic equation, using food supply data as a variable carrying capacity, yields population estimates which are in accord with actual population numbers. That food supply data adequately fits the logistic model of human population dynamics provides evidence that, consistent with ecological notions typically applied only to nonhuman species, human population increases are a function of increased food availability.     

Damped oscillation of population density at equilibrium

Summary It has been theoretically assumed that the population density at the equilibrium oscillates with damping from generation to generation. In the adult population of the southern cowpea weevil,Callosobruchus maculatus, it was exemplified. But, it was not so clear in the adult population of the azuki bean weevil,C. chinensis as seen in that ofC. maculatus. This difference seems to be due to the scramble type of competition that occurs in larval stage inC. maculatus, instead of in the egg stage asC. chinensis. Comparing with the oscillation from generation to generation obtained in the present experiment to that ofLucilia population found byNicholson, the oscillation inLucilia population is composed of the cycle in a generation and the descending phase of each cycle of it is not regulated density-dependently. The present result seems to be more appropriate for the demonstration of the theory of self-adjustment of population. Contribution from the Entomological Laboratory, Kyoto University, No. 404. Supported by a grant in aid for Scientific Research from the Ministry of Education.     

A stochastic computer model for simulating population growth

Summary A model is described for investigating the interactions of age-specific birth and death rates, age distribution and density-governing factors determining the growth form of single-species populations. It employs Monte Carlo techniques to simulate the births and deaths of individuals while density-governing factors are represented by simple algebraic equations relating survival and fecundity to population density. In all respects the model’s behavior agrees with the results of more conventional mathematical approaches, including the logistic model andLotka’s Law, which predicts a relationship betwen age-specific rates, rate of increase and age distribution. Situations involving exponential growth, three different age-independent density functions affecting survival, three affecting fecundity and their nine combinations were tested. The one function meeting the assumptions of the logistic model produced a logistic growth curve embodying the correct values orr _m andK. The others generated sigmoid curves to which arbitrary logistic curves could be fitted with varying success. Because of populational time lags, two of the functions affecting fecundity produced overshoots and damped oscillations during the initial approach to the steady state. The general behavior of age-dependent density functions is briefly explored and a complex example is described that produces population fluctuations by an egg cannibalism mechanism similar to that found in the flour beetleTribolium. The model is free of inherent time lags found in other discrete time models yet these may be easily introduced. Because it manipulates separate individuals, the model may be combined readily with the Monte Carlo simulation models of population genetics to study eco-genetic phenomena.     

Theoretical studies on the role of food exploitation for the competition of scaamble type

Summary A model was made to clarify the basic processes of competition to occur among larvae by the exploitation as defined byBakker (1969). It was found that this model is applicable to the experimental results on the food exploitation amongDroshophila larvae obtained byBakker (1961). In the model the preimaginal stage is divided into two periods;T _f which is the time that a group of larvae spends in exhausting the food after hatching, andT _s which is the duration of the starvation period afterT _f .T _f and thenW _l (larval body weight) just after the end ofT _f are decided byF _s (amount of food supplied per larva at larval hatching) andF _c (amount of food consumed per larva).T _f affects on the onset ofT _s as well asR _l (rate of decrease in the individual body weight duringT _s ).W _a (weight of emerging adults) is gotten by a subtraction ofR _l fromW _l just after the end ofT _f ,R _e is affected directly by these components ofW _l andR _l . As a result,W _a andR _e are expressed by functions ofF _s . This model confirmed that the food exploitation lead to the competition of scramble type. Finally it was suggested that there exist some strategies which prevent ill-effects owing to the food exploitation.     

A laboratory study on the predatory miteTyphlodromus pyri (Acarina: Phytoseiidae): I. The effect of temperature and food consumption on the rate of development of the eggs and immature stages

Summary Development periods were determined for eggs and juvenile stages of the predatory phytoseiid miteTyphlodromus pyri at four constant temperatures and three feeding levels. For the non-feeding stages (eggs and larvae) power curve functions were fitted to development rate in terms of temperature. The results are compared to the general arthropod response to temperature. A non-linear model was fitted to nymphal development rate in terns of temperature and food, in which the weight gain over an instar is assumed to be a linear function of daily food consumption. Examples of the same shape development rate—food relationship are given for two more phytoseiid mites and for other arthropods. The results are discussed with respect toT. pyri as an integrated control agent.     

The ingestion in wolf spiders I. Capacity of gut ofLycosa pseudoannulata

Summary An wolf spider,Lycosa pseudoannulata, collected from the field were reared in test tubes supplied with fruit flies as the food, and the number and weight of fruit flies killed per unit time and the weight of residuum of killed flies were recorded. When the cumulative number of flies killed by a spider was plotted against time after the beginning of food supply, the angle of the curve obtained decreased gradually until a constant value. In this time, it seems that the gut of spider had saturated with food and the increase rate of number of flies killed reflects the rate of food disappeared from gut by assimilation and egestion. The amount of ingestion was obtained by subtracting the weight of residuum and the gain of live weight of the spider from the weight of killed flies. After the gut has saturated, the amount of food remained in the gut is considered to be equal to the capacity of gut, which is an essential factor in the study of predation. The amount of food disappearance from gut was also estimated. There was a linear relationship between the log body weight of spiders and the log capacity of gut. The linear relationship was also seen between the log total amount of ingestion and the log total amount of food disappeared from gut.     

A population dynamic model of Batesian mimicry

Summary A population dynamic model of Batesian mimicry, in which populations of both model and mimetic species were considered, was analyzed. The probability of a predator catching prey on each encouter was assumed to depend on the frequency of the mimic. The change in population size of each species was considered to have two components, growth at the intrinsic growth rate and carrying capacity, and reduction by predation. For simplicity in the analyses, three assumptions were made concerning the carrying capacities of each population: (1) with no density effects on the mimic population growth rate; (2) with no density effects on the model species; and (3) with density effects on both species. The first and second cases were solved analytically, whereas the last was, for the most part, investigated numerically. Under assumption (1), two stable equilibria are possible, in which both species either coexist or go to extinction. Under assumption (2), there are also two stable equilibria possible, in which either only the mimic persists or both go to extinction. These results explain the field records of butterflies (Pachliopta aristolochiae and its mimicPapilio polytes) in the Ryukyu Islands, Japan.     

Resource exploitation of larvae ofGastrophysa atrocyanea Motschulsky andgalerucella vittaticollis Baly (Coleoptera: Chrisomelidae) under a limited resource condition

Summary Resource exploitation by and intraspecific competition in larvae ofGastrophysa atrocyanea andGalerucella vittaticollis were investigated in field and laboratory experiments. Larvae of both species frequently suffered from food shortages in the field. WhenG. atrocyanea larvae suffered from a food shortage, severe intraspecific competition occurred because of lack of predation and parasitism. This exploitive competition was caused by a local food shortage of the host plant. Individuals survived by fast exploitation when food became abundant (contest type competition). TheG. atrocyanea larvae were wasteful of the food resource, and no mechanism by which to economize on the utilization of the resource was acquired because of their exploitation of the abundant resource. In contrast, theG. vittaticollis population probably is regulated by extrinsic factors such as predation and parasitism. Those larvae grew into smaller adults than those ofG. atrocyanea under a food shortage, so that their wasted food consumption was lower than that ofG. atrocyanea. Although intraspecific competition was similar to that forG. atrocyanea, it was not as severe. The food forG. vittaticollis was apt to be appropriated by other wasteful exploitators such asG. atrocyanea, which was superior in resource exploitation; thereforeG. vittaticollis frequently suffered a food shortage. Consequently selection in relation to tolerance to starvation became more acute forG. vittaticollis than forG. atrocyanea, and individuals ofG. vittaticollis that could endure starvation better may have been selected.     

Theoretical considerations on the C-D effect in self-thinning plant populations

A model for describing the competition–density (C-D) effect in self-thinning populations was developed on the basis of the following three basic assumptions: (1) the growth of mean phytomass follows a general logistic equation; (2) final yield is independent of initial population density; and (3) there exists a functional relationship between actual and initial population densities at any given time. The resultant equation takes the same reciprocal form as the reciprocal equation of the C-D effect derived from Shinozaki–Kira's theory (i.e., the logistic theory of the C-D effect), which deals with the density effect in nonself-thinning populations. However, one of the two time-dependent coefficients is quite different in mathematical interpretation between the two reciprocal equations. The reciprocal equation for self-thinning populations is essentially the same as the reciprocal equation assumed in the derivation of the functional relationship between actual and initial population densities. The establishment of the reciprocal equation is supported by the empirical facts that the reciprocal relationship between mean phytomass and population density is discernible in not only nonself-thinning populations but also in self-thinning populations. The present model is expected to systematically interpret underlying mechanisms between the C-D effect, which is observed at a time constant among populations with various initial densities, and self-thinning, which is observed along a time continuum in a given population. Received: August 5, 1998 / Accepted: January 7, 1999     

The effects of food and density on the nocturnal behaviour ofArion ater andAriolimax columbianus (Pulmonata: Stylommatophora)

Summary The effects of food supply and population density on the nocturnal behaviour ofArion ater andAriolimax columbianus were investigated. Density did not significantly affectA. ater's level of activity or short-term movement, resting, or feeding.A. columbianus was more active and moved, rested, and fed more frequently when slug density was high.A. ater foraged and rested more often, but fed less when good food was unavailable.Ariolimax's only response to the food regime was to feed more when good food was available. Seasonal changes in the level of activity and behaviour ofArion were evident, whereasAriolimax's activity and behavioural repertoire were not similarly affected.Arion ater's nightly activity appeared to be mainly food oriented, whileAriolimax columbianus seemed most responsive to slug density during its nocturnal activity periods.     

Malthus on Godwin’s of population

A number of the issues raised by Godwin in his Enquiry Concerning Political Justice recur in subdued form in Of Population. These are issues that Malthus himself considered only to interpret them differently. Most outstanding of the points of difference between the two were: (1) the augmentability of the food supply, which Malthus put far below Godwin’s estimate; (2) the rate of growth of population which Godwin believed to be negligible and Malthus to be potentially great; (3) man’s disposition to control his numbers when necessary, regarding which Godwin was much more optimistic than Malthus; (4) the interpretation each put upon the constraining role of institutions. The two men had more in common than is usually assumed.     

Potential for suppressingDiprion similis (Hymenoptera: Diprionidae) with pheromone trapping: A population model

Summary The virgin female introduced pine sawfly,Diprion similis (Hartig), produces a powerful sex pheromone capable of attracting males. Pending chemical identification of the substance, a pilot study in male annihilation is under consideration. A mathematical model was developed to assess the feasibility of population suppression using pheromone-baited traps. Departure from preexisting population models resulted chiefly from the arrhenotokous nature of the sawfly. The model predicts alternating sawfly generations which undergo first a large shift in the sex ratio but no population reduction, followed by a large decrease in population size with a moderating sex ratio. Four generations of intensive trapping would theoretically be sufficient to eliminate the sawfly from an isolated area.     

The feeding from edge towards inner part in soybean plot in rufous turtle dove,Streptopellia orientalis (Latham) and the estimation of passing rate of the flock

Summary Rufous turtle dove,Streptopelia orientalis, coming to the soybean field entered it from the outer part to eat soybean cotyledons. As a result, the injured plants extended from the outer to inner parts in the field. A model expressing these behaviours was constructed here, by assuming that the amount of food birds can eat in one block determines whether they stay there or move into neighbour block. As the food decrease due to exploitation of them by birds, birds enter into farther parts with the passage of time. The rate of feeding in all visiting birds (an ₀ wherea is the rate of feeding per individual andn ₀ the number of birds visiting) and the rate of staying at a block,b, was estimated from the field experimental results, using the above model. The value ofan ₀ fluctuated greatly, depending upon the season in which soybean seeds sowed. The value ofb also fluctuated inversely with that ofan ₀, suggesting the the staying rate decreases with an increase in the number of doves coming, probably because of interference among individuals.     

Stopping rule of host search by the parasitoid,Chrysocharis pentheus (Hymenoptera: Eulophidae), in host patches

Summary We studied the stopping rule obeyed by the female parasitoid,Chrysocharis pentheus, in deciding when to leave the leaflet on which she is searching for larvae ofPhytomyza ranunculi. She seemed not to employ some stopping rules that have been suggested; i.e., a fixed-number rule and a fixed-time rule and others. The stopping model formulated forDapsilarthra rufiventris parasitic on the same host species fitted well to the results. The model assumes that the searching female will deposit a marking pheromone on the leaflet at a rate proportional to the search speed and will leave the leaflet when the amount of the pheromone that has accumulated on the leaflet reaches the threshold,L. In this model,L denotes the amount of search effort spent on the leaflet. A comparison of the observed results with the predictions from the model suggested thatL increased markedly at the first encounter with the mine (host), but less at later encounters.C. pentheus appears to employ a mixed strategy of a fixed search-effort and an area-concentrated search. This would confer an adaptive advantage in foraging forP. ranunculi larvae, which are distributed in clumps among leaflets in the field.     

The biology of the voleClethrionomys rufocanus: A review

The biology of the gray-sided voleClethrionomys rufocanus in Hokkaido, concerning taxonomy, morphology, phylogeny, distribution, and natural history, is reviewed. Applied issues in forest management (damage, control and census) are also mentioned. AlthoughClethrionomys rufocanus of Hokkaido was originally identified as a distinct species,Evotomys (=nowClethrionomys) bedfordiae Thomas, 1905, current literature generally refers to the gray-sided vole of Hokkaido asClethrionomys rufocanus or asC. rufocanus bedfordiae (vernacular name, the Bedford’s red-backed vole). The gray-sided vole is the most common small mammal in Hokkaido. It inhabits open areas as well as forests, and mainly feeds on green plants. The gray-sided vole has a high reproductive potential; litter size: 4–7; gestation period: 18–19 days; maturation age: 30–60 days old. Although spring-born individuals usually attain sexual maturity in their summer/fall of birth, their maturation is sometimes suppressed under high densities. The breeding season is generally from April to October, but with some regional variation.Clethrionomys rufocanus has a rather specialized diet (folivorous), particularly during winter when it feeds on bamboo grass. Many predators specialize on the grey-sided vole in Hokkaido; even the red fox, which is a typical generalist predator, selectively feeds on this vole. Damage by voles’ eating bark used to be sever on forest plantations in Hokkaido. Censuses of small rodents have been carried out for management purpose since 1954.     

Analysis and simulation modelling of population dynamics and bioenergetics ofCryptolestes ferrugineus (Coleoptera: Cucujidae) in stored wheat

Summary The consequences of infestation of stored wheat by the rusty grain beetle,Cryptolestes ferrugineus (Stephens) was determined for 222 d at 30°C in 70-1 drums containing wheat at 13.5% moisture content. Temperature, grain moisture, seed damage, germination and weight, dust weight, fat acidity values (FAV), published data on growth, reproduction, survival and cannibalism rates and energy budget were used to develop a computer simulation model to simulate the population dynamics ofC. ferrugineus at 30°C. In the insect-free control system, the fungi,Alternaria alternata decreased,Aspergillus glaucus group andPenicillium spp. increased, probably causing a rise in FAV of the grain. In the insect-infested system,C. ferrugineus could only eat the wheat germ of kernels that had a broken bran layer; 35.7% of the wheat germ or 914.6 J per 100 kernels was consumed. Within two generations after initial introduction,C. ferrugineus reached a peak in numbers and biomass polluting the ecosystem with excreta and remains, and accelerating the deteriorative process observed in the insect-free control system by increasing respiration temperature, FAV and reducing grain germination. After 87 d, the insect population declined to low levels. The simulation model provided a close match between the observed and predicted numbers of insect life stages and bioenergetic variables during the insect population growth phase. Simulation trials suggested that cannibalism of larger compared with smaller immature stages would be more wasteful of developmental time and energy, reducing the number of individuals reaching reproductive age, and that density-dependent fecundity was probably not an important regulatory mechanism ofC. ferrugineus population dynamics in this study. Contribution No. 1314 from Agriculture Canada Research Station, Winnipeg, Manitoba, R3T 2M9, Canada     

A magical model of happiness

A model of happiness is described that is based on nonlinear mathematics. Happiness at timet+1 is given by:Hnext=M(1–H)H+I, whereH is happiness at timet, M is a person parameter, andI is an environmental impact term comprised of a prevailing component (Ip) and an episodic component (dI). Eight properties of the model are detailed and its utility illustrated for reconciling problematic issues in the literature that include the positive skew in the distribution of psychological well being (PWB) scores, the stability and change in PWB, and the relationships of emotionality with global PWB and its indicators. The operationalization of the model is described from the population level down to that of the single case.     

Crucial factors determining the spatio-temporal distribution patterns of threeAthalia sawflies feeding on common cruciferous plants

Summary ThreeAthalia sawflies,A. japonica, A. rosae andA. infumata, feeding on cruciferous plants, coexist in Japan. However, it is not known what ecological strategies they use and what environmental factors are crucial to such strategies. I attempted to explain these questions by examining the relationship between the spatio-temporal distribution patterns of threeAthalia sawflies and their habitats in three districts (Lowland, Intermediate and Mountain). The three sawflies have different spatio-temporal distribution patterns, though they usually used common cruciferous plants.A. japonica was abundant in spring and autumn but disappeared during summer in all the districts. In the Lowland, populations ofA. rosae andA. infumata, like that ofA. japonica, crashed in summer. HoweverA. rosae occurred mainly in summer in the Intermediate and Mountain. AlthoughA. infumata occurred in the same seasons asA. rosae in all districts, population levels ofA. infumata were always lower than those ofA. rosae. The crucial factors controlling their population patterns were the availability of host plants and temperature. Population crashes ofA. rosae andA. infumata were due to food depletion, and those ofA. japonica were due to heat stress. On the other hand, their population patterns may be interpreted as phenological synchronization with their original host plants, though they all existed on common cruciferous plants. The three sawflies may have evolved different strategies to escape from unfavorable habitat conditions. Such strategies are speculated to be summer diapause inA. japonica, long distance migration inA. rosae, and local dispersal inA. infumata.     

A simple model for linking life tables by survival mortality ratios

Patterns of variation in mortality can be studied by measuring changes in selected life table functions. A model is proposed in which the rate of change over time in the life table survivorship probability at any age has been assumed as proportional to the product of its own value and its complementary probability or the probability of dying by that age, where the proportion is the same for all ages and depends only on the time duration between successive life tables. The end result is that the logit functions of the survivorship probabilities at two points in time are linearly related with a slope of one. The projecting power of the model has been tested by using U.S. life tables for the years 1950 and 1970 as well as Coale and Demeny's regional model life tables. In the latter case, the model produced surprisingly close matches even when the expectations of life differed by as much as 20 years.