A statistical model of the reproduction of aphids

1. The logistic function has been generally used to describe the reproductive process of a “population” of animal. However, this model can not give us any information about the reproductive process of “individuals” in the population. In this study a statistical model on the basis of the reproduction of individuals of barley aphid is presented to find the proportion of the mature individuals, the heterogeneity in reproductive ability of the aphids, etc.
2. The model is constructed as follows:
3. The probability that j insects are found on a plant at time t₀ is represented as Q(j).
4. The probability that h individuals of j have reproductive ability, say, mature individuals, in the period t₀ to t₁ is represented as B(h/j)=_jC_hw^h(1−w)^j−h, where w is the proportion of mature individuals.
5. In a population with a homogeneous reproductive ability, the probability that each parent lays i offspring in the period t₀ to t₁ is represented as P(i/m)=e^−mmⁱ/i!, where m is mean. And, in a population, m changes according to the gamma distribution. Hence the probability that a parent lays i offspring between t₀ and t₁ is represented as , where p and k are parameters of negative binomial distribution. The probability that h parents on a plant lays s offspring is represented as .
6. From the assumptions mentioned above, the probability that s offspring are to be found at time t₁ on a plant with the original j individuals at time t₀ is represented by
7. The experimental populations were demonstrated to fit well to the model.

     

A model of the plant-to-plant movement of aphids I. Description of the model

The plant-to-plant movement of insects in one of the factors determining the distribution of individuals in insect populations. In this report the movement of barley aphids was analyzed by a statistical model. The model is represented as the convolution of three probability functions:

1. The probability that s individuals are found on a plant at time t₀:Q(s);
2. The probability that i individuals leave the plant and remain on the ground from time t₀ to t₁:_sC_ipⁱq^s−i and p+q=1, where p and q are the proportions of individuals which do not leave a plant and which leave it once or more, respectively;
3. The probability that j individuals climb a plant between time t₀ to t₁ and stay there at time t₁:e^−λλ^j/λ^!, where λ is the mean of the individuals.

The probability that l individuals are located on a plant at time t₁ is represented by the following equation It was shown by simple experiments that the experimental populations were well fitted to the model.     

Tiller population dynamics of reciprocally transplanted Eriophorum vaginatum L. ecotypes in a changing climate

Moist tussock tundra, dominated by the sedge Eriophorum vaginatum L., covers approximately 3.36 × 10⁸ km² of arctic surface area along with large amounts of subarctic land area. Eriophorum vaginatum exhibits ecotypic differentiation along latitudinal gradients in Alaska. While ecotypic differentiation may be beneficial during periods of climate stability, it may be detrimental as climate changes, causing adaptational lag. Following harvest of a 30-year reciprocal transplant experiment, age-specific demographic data on E. vaginatum tillers were collected to parameterize a Leslie matrix. Yellow Taxi analysis, based on Tukey's Jackknife, was used to determine mean pseudovalues of tiller population growth rate () for four source populations of E. vaginatum tussocks that were transplanted to each of three gardens along a latitudinal gradient. Source populations responded differentially along the latitudinal gradient. Survival and daughter tiller production influenced differences seen at the mid-latitude garden, and the overall tiller population performance was generally improved by northward transplanting relative to southward transplanting. A comparison of home-source and away-source within the same transplant garden indicates no home-site advantage. Although populations were still growing when transplanted to home-sites ( = 1.056), tiller population growth rate increased as ΔGDD became more negative relative to the home site (i.e., as tussocks were transplanted north). These results imply that populations are affected by climate gradients in a manner consistent with adaptational lag. This study documenting the response of high-latitude ecotypes to climate gradients may be an indication of the possible future effects of climate shift in more southern latitudes.     

Estimation of the attraction range of a human bait forAedes albopictus (Diptera,culicidae) adults and its absolute density by a new removal method applicable to populations with immigrants

The attraction range of a human bait for Aedes albopictus (Diptera, Culicidae) adults and its absolute density in the range were estimated by a new removal method which is applicable to populations with immigrants. In this model, the number of mosquitoes removed during the kth collection unit y_k, is expressed as where x₀ is the initial number of mosquitoes in the attraction range, a is an index directly proportional to collection efficiency, b is the number of immgirants per collection unit and s(=e^−a) is the survival rate of mosquitoes in the attraction range per collection unit. From the result of successive two collections with various interval distances, it was considered that Aedes albopictus adults are attracted to a human bait from the distance of 4–5 m in the bamboo forest on the calm day. The applicability of this method for the population census of forest mosquitoes was discussed.     

A new proposal for measurement of the adjusted mean crowding through consideration of size variability in habitat units

The mean crowding has previously been measured under the assumption that all quadrats or habitat units have the same size, even though the actual habitat units such as seeds or leaves are generally variable in size. A new index, ‘adjusted mean crowding’, which is adjusted for this variability can be given as where Q is the total number of habitat units in the whole area, x_j the number of individuals in the jth habitat unit, and a_j is defined as the ‘relative size’ of the jth habitat unit, i.e. a_y=y_y/(∑y_j/Q) where y_j is the actually measured size of the jth habitat unit. It is expected that and for the uniform distribution and the random distribution ‘per unit size’, respectively. The comparison between and regressions ( analysis) for the egg distribution pattern of Callosobruchus chinensis or C. maculatus proved that the regression is biased by a positive correlation between the egg number per seed and seed size rather than by a density-dependent change in the ovipositional behavior.     

Application of the\mathop m\limits^* - m method to the analysis of spatial patterns by changing the quadrat sizemethod to the analysis of spatial patterns by changing the quadrat size

A method for the analysis of spatial pattern using quadrats of different sizes is developed on the basis of the relationship of mean crowding () to mean density (m). The -on-m regression obtained by successive changes in quadrat size in a single population (unit-size relation) shows a characteristic pattern according to the type of distribution. By aid of the ρ-index proposed here, we can distinguish the random, aggregated and uniform distributions of the basic components (individual or group of individuals). The ρ serves as an index of spatial correlation between neighbouring quadrats, and it also provides information on the approximate area occupied by clump (colony), distribution pattern of individuals within clumps, and possibly the distribution pattern of clumps themselves. Even in a specified type of distribution, the unit-size relation is not necessarily identical with the relation for a series of populations at a particular quadrat size (series relation). The changes in the series relationship with successive changes of quadrat sizes are also considered for some basic patterns of distributions. The combined use of the unit-size and the series relations for a set of populations of the species under study may provide a satisfactory picture of the spatial pattern characteristic of the species. Application of the method is illustrated by using distribution data of several species of animals and plants. The advantage of the present method over other methods are discussed, and the formulae for determining the optimum quadrat unit in sampling surveys are given.     

Detection of,and sampling procedures for,the citrus blackfly in urban southern Florida

The dispersion pattern of the citrus blackfly (CBF)Aleurocanthus woglumi Ashby on urban citrus trees was studied in southern Florida. There was no usable correlation (r²=0.41) between the % of older leaves infested with CBF versus that on the newest mature flush, but there was a strong correlation (r²=0.87) between the % of leaves in the newest mature flush infested with CBF and log_e, where is the number of egg spirals of CBF/leaf on the same leaves. CBF egg spirals are distributed among the flushes in groups rather than singly and the flushes are not over-dispersed. Visual surveys proved superior to sticky traps for the detection of CBF at low densities (<5% leaves infested) on citrus trees in an urban setting. A sampling procedure is described herein based upon visual surveys.     

Estimation of the stage-specific survival rate in the insect population with overlapping stages

An application ofHokyo andKiritani 's method (1967) was attempted to estimate the stage specific survival rates of the population with overlapping stages. This method can be written as follows assuming a constant daily survival rate (K) throughout the life: where, and F refer respectively to the total incidence of ith instar nymphs and that of individuals after ith instar inclusive, and α_i refers to the developmental period of ith instar. Application of this model to caged and natural populations of the southern green stink bug, Nezara viridula, was made to test its validity. The estimates of the initial number of successive stages obtained from the present method were compared with those fromRichards andWaloff 's method (1954) for the caged populations of 1st, 2nd and 3rd generations. The superiority of the present method to theRichards andWaloff 's in estimating adult numbers was shown in all the generations examined. When different daily survival rates are involved in the course of population decrease, application of the revised method proposed byHokyo andKiritani (1967), gives much reliable estimate as compared with one before correction. The present method is useful in constructing life table of such species as scale insects which complete their life cycle within a defined space, but their successive stages overlap considerably.     

Analysis of spatial association between two species based on the interspecies mean crowding

The measurement of spatial association between two species is considered on the basis of interspecies mean crowding. Two indices of overlapping, γ and C_p, are derived as geometric and weighted arithmetic means of the same component ratios related to inter-and intraspecies mean crowdings. Both indices behave in a similar way, ranging from 1 when the distributions of two species are completely overlapped to 0 when they are completely exclusive with each other. The former is essentially identical with indices proposed byKuno (1968) andPianka (1973), and the latter is a modified form ofMorisita's (1959)C_σ index. Indices to measure the degree of spatial correlation between species, Ω and R_μ, are then derived for both kinds of overlapping indices, which vary from 1 in complete overlapping, through 0 in independent occurrence, to −1 in complete exclusion. Various kinds of interspecies association are analyzed using these indices and an extended form of the regression graph which provides a convenient way of indicating the spatial interrelation between two species as well as distribution patterns of respective species. The method presented in this paper may also be applicable to compare temporal distribution patterns between species, similarity between communities, etc. For such a wider application which includes continuous as well as discrete distributions, the interpretation of intra-and interspecies mean crowdings is not necessarily appropriate, and hence the concept of mean concentration with the symbols and for intraspecies relation and and for interspecies relation is suggested.     

Conversion of NaHCO3 to Na2CO3 with a growth of Arthrospira platensis cells in 660 m2 raceway ponds with a CO2 bicarbonation absorber

The weight ratio of Na₂CO₃/NaHCO₃ was investigated in order to improve microalgal productivity in large-scale industrial operations by converting NaHCO₃ to Na₂CO₃ with a growth of Arthrospira platensis cells in 660 m² raceway ponds. Two microalgal cultivation systems with a NaHCO₃ by-product (SPBP) and a CO₂ bicarbonation absorber (CBAP) were firstly thoroughly introduced. There was a 13.3% decrease in the initial weight ratio of Na₂CO₃/NaHCO₃ resulting in a 25.3% increase in the biomass growth rate with CBAP, compared to that of SPBP. Increased sunlight intensity, solution temperature and pH all resulted in both a higher absorbance and release, thereby increasing the weight ratio of Na₂CO₃/NaHCO₃ during the growth of A. platensis. The biomass growth rate was peaked at 39.9 g m⁻² day⁻¹ when the weight ratio of Na₂CO₃/NaHCO₃ was 3.7. Correspondingly, the cell pigments (chlorophyll a and carotenoid) and trichome size (helix pitch and trichome length) reached to a maximum state of 8.47 mg l⁻¹, 762 μg l⁻¹, 57 and 613 μm under the CBAP system.     

Diel Division Cycle and Growth Rates of Synechococcus in Lakes Huron and Michigan1

A clone of Synechococcus isolated from Lake Huron and natural populations of Synechococcus from lakes Huron and Michigan were studied in 1989 to examine the diel division cycle and to provide estimates of the in situ growth rate based on the frequency of dividing cells (FDC) method. Cultured populations of Synechococcus exhibited a consistent diel division pattern with a midday/afternoon (1100–1800 h) peak in the percent of dividing cells. The maximum percent of dividing cells varied among cultures (8-27%) and was related to the growth rate. A small fraction of dividing cells (3-5%) remained throughout the dark period, suggesting that some cells were arrested in the doublet stage prior to division. The duration of division (t_d) ranged from 2.6-4.9 h, with a 3.7 h mean for cultures with growth rates ≥0.34 d⁻¹ but increased to 8 h at a lower growth rate of 0.20 d⁻¹. The diel division pattern for natural populations was very similar to the laboratory clone; an afternoon peak (1400-2100 h) in dividing cells and a small fraction of dividing cells (2-5%) remained during the dark period. The maximum percent of dividing cells for natural populations ranged from 6-10%. In situ growth rates, determined from the FDC and assuming a constant t_d of 3.7 h, ranged from 0.30-0.42 d⁻¹. The FDC method may provide accurate estimates of in situ growth, particularly in environments where the growth rate is >0.34 d⁻¹, but in lakes Huron and Michigan where growth rates can be lower and t_d values may increase, FDC-growth rates must be viewed with caution.     

The importance of non-linearity: A comment on the views of Taylor

Taylor's (1984) view that his power law is better measurement of the distribution pattern of animals than 1/k, I_ρ and relation because almost all the data on means and variances of given species could be fitted by the power low, was critisized. Changes in values of 1/k, I_ρ and suggest the change of distribution pattern of the species, but the data can still be fitted by the power law because of the great linearizing power of log-log plots, and, using the power law only, we shall overlook the information on the meaningful changes in the distribution pattern.     

An index of spatial distribution

The index , which takes the value of −1 for a perfectly regular distribution, +1 for a highly aggregated distribution and 0 for the distribution implied by the theoretical varianceσ², is proposed and a significance table provided.     

A distance measure of spatial pattern in a biological population

Suppose that n individuals locate independently and randomly on a segment of line of finite length (habitat). Let the theoretical and observed ranges of the sites of the individuals on the segment be μ_n-1 and r_n-1, respectively. Then, the degree of dispersion of the individual sites is measured by the ratio, T_n=n_n-1/μ_n-1, as follows: A random spatial pattern for I_r−1=1 An aggregated spatial pattern for 0≤I_r<1 A uniform spatial pattern for (n+1)/(n−1)≥I_r>1. Another method was derived. Let the probability that an observed range is less than r_n−1 be I_p, under the hypothesis of a Beta distribution. Then indicates A random spatial pattern for I_p=1/2 An aggregated spatial pattern for I_p<1/2 A uniform spatial pattern for I_p>1/2. The first index can be used for comparing populations having the same number of individuals, whereas the second one can be used for comparing populations with different numbers of individuals.     

The effects of hurricanes on the stochastic population growth of the endemic epiphytic orchid Broughtonia cubensis living in Cuba

We carried out a posthurricane evaluation of Broughtonia cubensis (Lindl.) Cogn., an endemic Cuban epiphytic orchid, after Hurricane Ivan (2004). We studied the transient responses in the stochastic dynamics of the species at three different sites over 13 successive years (2006–2019), monitored plot inventories (464 individuals in 10 transects) and built stochastic population models. The deterministic stochastic growth rate values () did not significantly differ (F = 2.76; p > 0.076) among the three sites over the 2006–2019 period. The long-term stochastic growth rate was 0.973 [0.932, 1.034]. The matrix elements that had the largest effect on were the transition to and stasis within the largest size class. Transient responses explained an average of 86% of the variation in the observed population growth rates , compared to 4% of the variation in the vital rates . Because transient dynamics are dependent on the population size composition, we ran extinction risk analyses under two scenarios: a population composed mainly of juveniles and another composed mainly of adults. There was little risk of falling below the quasi-extinction threshold before 25 year for both juveniles and adults. However, the risk of quasi-extinction was almost certain for both size classes by 80 year. We also simulated the effect of increasing the hurricane occurrence probability over 80 year on the population. There was little risk of extinction before 20 year in the baseline model, but there was a significant risk of extinction within 5 year when 90% of the individuals were affected by a new hurricane event.     

A preliminary study on collembolan populations in a pine forest

1. A study was made of the populations of Collembola in the pine forest. Among the eight species commonly found, Folsomia octoculataHandschin was numerically dominant.
2. Seasonal population changes of these eight species were described over a year. It was found that many species show two peaks in number. As for F. octoculata, the dominant species, the changes in number was discussed in connection with the variation in age structure.
3. The census data for each species were examined for the distribution pattern by using the regression method. None of these eight species was distributed at random in the soil and they could be classified into three groups based on the differences in the degree of aggregation in terms of coefficient β of the regression. It was suggested that such differences in the distribution pattern are largely due to differences in the response to heterogeneity of the habitat. In the case of F. octoculata, the changes of distribution pattern in the course of post-embryonic development were examined and it was found that (a) the component of distribution is a single individual rather than a colony, and (b) the degree of aggregation is decreased with the development of individuals.
4. Using the relationship, the relation of the necessary sample size to the population density was derived for a fixed level of presision (D=S.E./m=0.2) and some suggestions were given concerning sampling plans for these insects.

     

Dynamics of long-term continuous culture of Limnospira indica in an air-lift photobioreactor

MELiSSA (Microecological Life Support System Alternative) is a developing technology for regenerative life support to enable long-term human missions in Space and has developed a demonstration Pilot Plant. One of the components of the MELiSSA Pilot Plant system is an 83L external loop air-lift photobioreactor (PBR) where Limnospira indica (previously named Arthrospira sp. PC8005) is axenically cultivated in a continuous operation mode for long-periods. Its mission is to provide O₂ and consume CO₂ while producing edible material. Biological and process characterization of this PBR is performed by analysing the effect of two main variables, dilution rate (D) and PFD (Photon Flux Density) illumination. A maximum oxygen productivity () of 1.35 mmol l⁻¹ h⁻¹ is obtained at a D of 0.025 h⁻¹ and PFD of 930 µmol m⁻² s⁻¹. Photoinhibition can occur when a 1 g l⁻¹ cell density culture is exposed to PFD higher than 1700 µmol m⁻² s⁻¹. This process is reversible if the illumination is returned to dim light (150 µmol m⁻² s⁻¹), proving the cell adaptability and capacity to respond at different illumination conditions. Influence of light intensity in cell composition is also described. Specific photon flux density (qPFD) has a direct effect on phycobiliproteins and chlorophyll content causing a decrease of 62.5% and 47.8%, respectively, when qPFD increases from 6.1 to 19.2 µmol g⁻¹ s⁻¹. The same trend is observed for proteins and the opposite for carbohydrate content. Morphological and spiral structural features of L. indica are studied by confocal microscopy, and size distribution parameters are quantified. A direct effect between trichome width and CDW/OD ratio is observed. Changes in size distribution are not correlated with environmental factors, further confirms the adaptation capacity of the cells. The systematic analysis performed provides valuable insights to understand the key performance criteria of continuous culture in air-lift PBRs.     

Nutrient Requirement and Growth of a Synechococcus Species Isolated from Lake Balaton

A pico sized Synechococcus species isolated from Lake Balaton was studied in batch and continuous cultures. This picocyanobacterium had a pH optimum at 8.5 and a temperature optimum at 28-30°C. The I_k value for growth was 52 μEinstein m⁻² S⁻¹, the maximum growth rate 2.27 d⁻¹, the half saturation Constant of growth 1.2 μg PO₄-P I⁻¹ and the minimal cell quota 1.74 nig P g dry weight⁻¹. The dry weight of cells showed a minimum, the chlorophyll-a/biomass ratio a maximum as a function of growth rate. Above the quota of 3.4 fg P Cell⁻¹ significant amounts of non-reactive dissolved Phosphorous were released.     

Growth and biomass productivity of Scenedesmus vacuolatus on a twin layer system and a comparison with other types of cultivations

Scenedesmus is a genus of microalgae employed for several industrial uses. Industrial cultivations are performed in open ponds or in closed photobioreactors (PBRs). In the last years, a novel type of PBR based on immobilized microalgae has been developed termed porous substrate photobioreactors (PSBR) to achieve significant higher biomass density during cultivation in comparison to classical PBRs. This work presents a study of the growth of Scenedesmus vacuolatus in a Twin Layer System PSBR at different light intensities (600 μmol photons m⁻² s⁻¹ or 1000 μmol photons m⁻² s⁻¹), different types and concentrations of the nitrogen sources (nitrate or urea), and at two CO₂ levels in the gas phase (2% or 0.04% v/v). The microalgal growth was followed by monitoring the attached biomass density as dry weight, the specific growth rate and pigment accumulation. The highest productivity (29 g m⁻² d⁻¹) was observed at a light intensity of 600 μmol photons m⁻² s⁻¹ and 2% CO₂. The types and concentrations of nitrogen sources did not influence the biomass productivity. Instead, the higher light intensity of 1000 μmol photons m⁻² s⁻¹ and an ambient CO₂ concentration (0.04%) resulted in a significant decrease of productivity to 18 and 10–12 g m⁻² d⁻¹, respectively. When compared to the performance of similar cultivation systems (15–30 g m⁻² d⁻¹), these results indicate that the Twin Layer cultivation System is a competitive technique for intensified microalgal cultivation in terms of productivity and, at the same time, biomass density.

     

First estimates of productivity in Lessonia trabeculata and Lessonia nigrescens (Phaeophyceae, Laminariales) from the southeast Pacific

Lessonia is the main Laminariales found along the southeast Pacific coast. Lessonia nigrescens Bory de Saint‐Vincent in the intertidal and Lessonia trabeculata Villouta et Santelices in the subtidal, are the most important habitat constructors in rocky coastal communities in northern and central Chile. In both species, the seasonal production and erosion of distal tissue were estimated in biomass units using the Area of Constant Biomass Model that combined the individual blade elongation, obtained with the traditional hole‐punching method, with the blade length and biomass distribution along the blade. In austral late spring (December 96) and autumn (May 97), blade production and erosion were transformed to the level of population from standing stock measurements (number and biomass of blades and plants per substrate area), considering that previous blade weight analysis showed the highest and lowest values at these times, as well as the population parameter extremes that were expected to occur. Both species displayed a seasonal pattern, with a production increase in later winter and spring and decrease towards the end of summer that coincided with higher distal tissue erosion. At the level of individual blades, Lessonia trabeculata showed higher mean production (0.026 g dw d⁻¹) and erosion (0.01 g dw d⁻¹) than L. nigrescens (production 0.01 g dw d⁻¹ and loss 0.002 g dw d⁻¹). The standing stocks, with respect to density and biomass, were similar in spring and autumn for both populations. Nevertheless, the net productivity (production minus erosion) of the intertidal L. nigrescens showed greater values due to the greater density of blades (2112 ± 1360 (SE) blades m⁻²) compared with the subtidal L. trabeculata (527 ± 151 (SE) blades m⁻²). Spring net productivities of 42 g dw m⁻²d⁻¹ (254 g ww m⁻²d⁻¹; 11.46 gC m⁻²d⁻¹) for L. nigrescens and 11 g dw m⁻² d⁻¹ (64 g ww m⁻² d⁻¹; 2.46 gC m⁻²d⁻¹) for L. trabeculata were estimated. A preliminary model of production and biomass fate for Lessonia populations is proposed.