Isolation,Enumeration and Identification of Amebae from a Nebraska Lake*

A plaque technic was evaluated and used for the isolation and enumeration of small, free-living amebae in lake-bottom samples which were collected each month for one year from a Nebraska lake. Several culture media were evaluated, and a simple glucose-salts medium was chosen. The most frequent ameba in the lake-bottom samples was Acanthamoeba polyhaga which underwent marked increases and decreases in population densities during the collection period. This pattern was not correlated with water temperature, bacterial counts, and nitrate or phosphate levels. Other species of amebae of the genera Hartmannella, Vahlkampfia, Naegleria, Paratetramitus and Echinamoeba were isolated. Most of these were either found infrequently or remained at relatively low, constant densities throughout the year. In addition, 4 species of Acrasieae of the genera Dictyostelium and Polysphondylium were isolated from the lake-bottom samples.     

Sustained biological control of the cassava mealybugPhenacoccus manihoti [Hom.: Pseudococcidae] byEpidinocarsis lopezi [Hym.: Encyrtidae] in Nigeria

Following the successful introduction ofEpidinocarsis lopezi (De Santis) for biological control of the cassava mealybug (CM)Phenacoccus manihoti Mat.-Ferr. in southwestern Nigeria in 1981 and 1982, 11 groups of cassava fields were sampled every 2 weeks up to 1988 for impact assessment. After 1984, CM populations remained mostly below 10 per tip despite the presence of native hyperparasitoids, demonstrating the long-term success of biological control byE. lopezi in the region. Indigenous polyphagous coccinellids were found only during peak host densities, whereas the specificE. lopezi was common throughout the year. During some periods, percentage parasitism indicated delayed density dependence. Since 89% of all sampled cassava tips had no CM at all and the parasitisme is very mobile, parasitization rates were also calculated for individual infested tips (N=4,878). Parasitism increased slightly with host density on tips having between 1 and 10 CM of the 3^rd and 4^th instars, indicating positive density dependence. Such tips comprised 64% of all infested tips. At higher host densities, parasitism rates fell rapidly. The results are discussed in view of different theories on population regulation by biological control agents.      

Density dependence of Anaphes sordidatus (Hymenoptera: Mymaridae) parasitism on eggs of Listronotus oregonensis (Coleoptera: Curculionidae)

Listronotus oregonensis (LeConte) (Coleoptera: Curculionidae) oviposits in carrot leaves and the larvae feed in carrot roots. Its eggs are parasitized by Anaphes sordidatus (Girault) (Hymenoptera: Mymaridae) throughout its oviposition period. This parasitoid is the major biotic mortality factor for L. oregonensis. Parasitism by A. sordidatus was studied for three years in sequentially sown plots of carrots, Daucus carota var. sativa. Over the scason, significantly fewer L. oregonensis eggs were oviposited in later sown carrots than in earlier sown carrots because oviposition started later in late sown plots of carrots. A positive temporal density-dependent relationship was observed each year between parasitism rates and host densities. This positive density dependence occurred in early and mid-summer for earlysown carrots where host density reached 1–2 host eggs per plant but disappeared in late summer when host density decreased while parasitism remained high. Latesown carrots had low host egg density (0.2 host egg per plant) and contributed little to the total number of eggs. In these late sown plots, parasitism increased rapidly to over 80% but no density dependence was observed. Spatially, few statistically significant regressions were found but all indicated a positive spatial density-dependence. Most non-significant regressions occurred because the range of egg density was too small between plots for a given date.     

Functional response to host density by the egg parasiteTrichogramma pretiosum

The effect of host density on parasitism byTrichogramma pretiosum Riley was studied by exposing groups of 150, 300, 600 or 1200 eggs of potato tuber moth to 2, 4 or 8 female parasites per group. The parasite exhibited a type 2 functional response. As host density increasedT. pretiosum parasitised more hosts, but at a decreasing rate. The attack coefficient (a′) decreased as parasite density increased, whereas the handling time (T _h ) remained almost constant. The search rate (a) decreased with increasing host density.T. pretiosum responded to increasing host density by increasing the number of its encounters with hosts and the number of hosts it parasitised only up to host density of 300 when the parasite density was 2 and up to host density of 600 when the parasite densities were greater and then remained almost constant. The observed incidence of parasitism was higher than that expected on the assumption that the parasites behaved the same at higher host densities as at the lowest. When parasite density was raised from 2 to 8 females per group the percentage of female progeny fell from about 73 to about 48%. A 2-fold increase in the number of female progeny was observed when parasite density was reduced from 8 to 2 and also when the host density was raised from 150 to 1200 eggs.     

The functional response of Uscana lariophaga under different egg distributions of its host Callosobruchus maculatus

The functional response of the egg parasitoid Uscana lariophaga Steffan (Hymenoptera: Trichogrammatidae) was tested under three different host distributions (even, clumped and random) within clusters of Callosobruchus maculatus Fab. (Coleoptera: Bruchidae) eggs. A Holling Type II functional response was found for all three distributions. Over low host densities, less than 50% of the host clusters was parasitized. At low host densities, U. lariophaga females parasitized significantly fewer eggs in random egg clusters with many beans than in clusters with fewer beans and an even or clumped egg distribution. At higher egg densities, plateau levels of maximum number of hosts parasitized were the same for all three egg distributions. Uscana lariophaga appears to be adapted to search for even or clustered egg distributions, as can be found in the field and under storage conditions.     

The natural enemy complex of the gypsy moth, Lymantria dispar (Lep., Lymantriidae) in different phases of its population dynamics in eastern Austria and Slovakia – a comparative study

Parasitism and pathogen mortality of Lymantria dispar were compared between host populations of different densities in Slovakia and Austria. Over a period of 4 years, L. dispar eggs, larvae, and pupae were collected in a stage‐specific manner at three mixed oak stands in each country and reared in the laboratory to assess parasitoid and pathogen mortality. At sites with low host densities, L. dispar abundance was artificially augmented by exposing egg masses and young larvae. We ascertained marked differences between the natural enemy complexes of L. dispar populations in Slovakia and Austria. Overall, pathogens caused highest mortality in the former and parasitoids in the latter. Moreover, the species composition differed significantly between both countries. High variation was also observed between years and host populations at different densities. The investigations revealed that egg parasitization was low in Slovak L. dispar populations, and no egg parasitoids were found in Austria. Larval and pupal parasitism was low at sites with outbreak populations, but higher at the Austrian than at the Slovak site. The tachinid Parasetigena silvestris was the dominant species at elevated host densities. Nuclear polyhedrosis virus also caused significant mortality in these cases. An increase in parasitism by several species was noticed after the breakdown of L. dispar populations. The ichneumonid Phobocampe spp. caused high levels of parasitism during the post‐culmination years. At sites where host abundance increased in the first year of the study, significant differences between the Austrian and the Slovak locality could be ascertained. Mortality was low in the population at the latter site, and host abundance increased to outbreak levels the year after. The population at the Austrian site suffered high parasitism by the tachinids P. silvestris and Blepharipa pratensis and this might have contributed to the prevention of a further increase in L. dispar abundance in this locality. Braconids showed a strong reaction to the local, artificial increase in host density at study plots with innocuous L. dispar populations. Particularly high parasitism by Glyptapanteles liparidis was observed at the Austrian site, but G. porthetriae and Cotesia melanoscela also accounted for significant mortality in both low‐density populations. The artificial L. dispar populations were usually eradicated by natural enemies before pupation of the hosts.     

SEED BANK,SURVIVORSHIP, AND SIZE DISTRIBUTION OF A NEBRASKA POPULATION OF IMPATIENS CAPENSIS (BALSAMINACEAE)

The growth and survivorship of a population of Impatiens capensis were followed in eastern Nebraska. Soil cores were taken within the population to estimate the size of the seed bank. The number of seeds in the soil remained relatively constant from April through October, with a mean of 200 seeds/m². The seed bank size corresponded to observed seedling densities in the following years. Twenty permanent plots were established within the population and censused for three years, 1983–1985. Seedling recruitment to the population was similar in 1983 and 1984 but 30% higher in 1985. The seedling densities of plots were uncorrelated from year to year. Survivorship in 1983 followed a Deevey Type I pattern. Almost one-third of the population survived until chasmogamous reproduction. Plant size (stem height) was measured monthly on all individuals during 1983. The frequency distribution of stem height was positively skewed as long as growth was exponential. When the growth rate slowed, the distribution became more normal.     

Epidemiology of damping-off disease (Pythium irregulare) in relation to density of Lepidium sativum seedlings

Controlled experiments on post-emergence damping-off, using small populations of garden cress seedlings (Lepidium sativum) inoculated with Pythium irregulare, demonstrate that planting density of the host population plays an important role in determining the rate of multiplication and the rate of advance of the disease. At high seedling densities the disease is transmitted readily between host plants, but at lower densities the greater distance between adjacent plants reduces the probability of successful transmissions, and this is reflected in the parameters of multiplication and advance. A simple negative relationship was found between the mean distance separating adjacent plants and both rate of advance of disease front and rate of multiplication of disease in a randomly inoculated seedling stand.     

Impact of density and disease on frequency-dependent selection and genetic polymorphism: experiments with stripe rust and wheat

Frequency-dependent disease impacts may contribute to the maintenance of genetic diversity and sexual reproduction in plant populations. In earlier work with experimental wheat (Triticum aestivum) populations at a single density, we found that stripe rust (caused by Puccinia striiformis) created frequency-dependent selection on its host but competitive interactions between host genotypes reduced the potential for disease to maintain genetic polymorphisms in this highly self-pollinated species; the weaker competitor actually exhibited positive disease-mediated frequency-dependent selection. Based on these results we predicted that at low density, where the overall level of competition is lower, disease would have a stronger impact relative to competition and thus be more likely to maintain genetic polymorphisms; at low densities the greatest effect of disease for negative frequency-dependent selection should be seen in the weak competitor. Here we report on results with wheat stripe rust in which we altered both the frequency and density of host genotypes in factorial combinations of two-way mixtures where each host genotype was attacked by its own specialized race of rust. Within each density disease levels increased with genotype frequencies, creating frequency-dependent disease attack at all densities. Similarly, disease created negative frequency-dependent selection on its host at all densities, as a genotype’s fitness was often greater at low than high frequency when disease was present. Disease levels increased with plant density in 1997 but decreased in 1998. While increasing plant density reduced absolute fitness, presumably as a result of increased competition, a genetic polymorphism was not more likely to be maintained at low than high density as we had predicted. Within each density, the impact of disease was insufficient to reverse the slope of the relationship between absolute fitness and planted frequency from positive to negative for the less competitive host genotype, thus preventing the maintenance of a genetic polymorphism.     

Relative host plant species use by the lantana biological control agent Aconophora compressa (Membracidae) across its native and introduced ranges

Aconophora compressa Walker (Hemiptera: Membracidae) was released in 1995 against the weed lantana in Australia, and is now found on multiple host plant species. The intensity and regularity at which A. compressa uses different host species was quantified in its introduced Australian range and also its native Mexican range. In Australia, host plants fell into three statistically defined categories, as indicated by the relative rates and intensities at which they were used in the field. Fiddlewood (Citharexylum spinosum L.: Verbenaceae) was used much more regularly and at higher densities than any other host sampled, and alone made up the first group. The second group, lantana (Lantana camara L.: Verbenaceae; pink variety) and geisha girl (Duranta erecta L.: Verbenaceae), were used less regularly and at much lower densities than fiddlewood. The third group, Sheena’s gold (another variety of D. erecta), jacaranda (Jacaranda mimosifolia D. Don: Bignoniaceae) and myoporum (Myoporum acuminatum R. Br.: Myoporaceae), were used infrequently and at even lower densities. In Mexico, the insect was found at relatively low densities on all hosts relative to those in Australia. Densities were highest on L. urticifolia, D. erecta and Tecoma stans (L.) Juss. ex Kunth (Bignoniaceae), which were used at similar rates to one another. It was found also on a few other verbenaceous and non-verbenaceous host species but at even lower densities. The relative rate at which Citharexylum spp. and L. urticifolia were used could not be assessed in Mexico because A. compressa was found on only one plant of each species in areas where these host species co-occurred. The low rate at which A. compressa occurred on fiddlewood in Mexico is likely to be an artefact of the short-term nature of the surveys or differences in the suites of Citharexylum and Lantana species available there. These results provide further incentive to insist on structured and quantified surveys of non-target host use in the native range of potential biological control agents prior to host testing studies in quarantine.     

Aspects of life-table studies and functional response of Lysiphlebia mirzai

The fecundity, reproductive rate, and survival of Lysiphlebia mirzai parasitising third instar nymphs of the cereal aphid Rhopalosiphum maidis were measured at six different host densities under constant laboratory conditions. The survival rate (l_x) of the female parasitoids was unaffected by host density, with an average adult life-span of 5–6 days at all densities. The age-specific fecundity rate (m_x) was host density-dependent. The value of m_x decreased rapidly from the first day of parasitisation. The number of hosts available determined the maximum possible number of mummies. At 200 hosts available per day, the average fecundity was 184.6 mummies/female; the maximum number of mummies yielded by any female was 200. The relationship between host density and the number of aphids parasitised per female was linear at 50 aphids/cage/day, but at higher host densities (100 aphids/cage/day) a significant curvilinear regression was observed. The intrinsic rate of natural increase (r_m) increased with increasing host density. Maximum value of r_m (0.262) was obtained at a host density of 200. The response of r_m to changes in host density and parasitoid sex ratio is shown. A typical type II functional response was observed for L. mirzai. The curve was described by a logistic curve, N_p=200/[1+exp(5.65–1.60 ln N_o)]. The search rate of the parasitoid was inverse host density-dependent. No significant variation in the sex ratio of F₁ offspring was observed at different initial host densities. Sex ratio values exceeded 0.5 at all host densities. The results evaluated the reproductive potential of L. mirzai as a promising biological control agent.     

Campoletis sonorensis [Hym.: Ichneumonidae] as a parasitoid ofSpodoptera frugiperda [Lep.: Noctuidae]: Host stage preference and functional response

The response of the parasitoidCampoletis sonorensis (Cameron) as a natural control agent of the fall armyworm,Spodoptera frugiperda (J. E. Smith), was evaluated at 6 host densities and 2 temperature regime. A type-II functional response was exhibited by femaleC. sonorensis in response to varying densities of all armyworn larvae at both temperatures. Significantly more larvae were parasitized at 25°C for the host densities of 60 and 75, than for the same densities at 30°C. Third instar fall armyworm larvae were found to be the preferred stage for parasitization byC. sonorensis. This research was supported by funds from HATCH project no. H-368 as allocated to the Georgia Agricultural Experiment Station.     

Inoculum dynamics ofGliocladium virens associated with roots of cotton seedlings

A system was developed to evaluate the effects of root growth of cotton seedlings on the inoculum dynamics ofGliocladium virens in nonsterile soil. In soil infested withG. virens, inoculum densities of the fungus increased when plants remained alive. After 30 days, shoots were excised and the roots allowed to deteriorate. During this portion of the experiment (30–60 days) soil inoculum densities ofG. virens declined. In infested soil without a seedling, inoculum densities remained constant throughout the duration of the experiments. Colonization of roots byG. virens was found to increase throughout the duration of the experiments. At 60 daysG. virens was recovered from approximately 60% of the root pieces (1-cm) sampled. The percentage of primary, secondary, or tertiary roots colonized was different (P = 0.01), but the total colonization of roots at three depths (0–10, 10–20, and 20–30 cm) was not different (P = 0.64). In noninfested soil, colonization of roots by indigenous propagules ofG. virens was never greater than 3%. Offprint requests to: C. M. Kenerley.     

Biological control of oliver scale,Parlatoria oleae (Colvée), in a deciduous fruit Orchard in California

Conclusions Data obtained during the years 1960–1966 show conclusively that the olive scale parasites,Aphytis maculicornis andCoccophagoides utilis, when well-established, are capable of fully effective control of their host on a commerciallty-grown deciduous fruit host.A. maculicornis alone, prior to the establishment ofC. utilis, failed to reduce or maintain control of scale densities. Subsequent to the colonization and establishement ofC. utilis in 1962 and its assumption of a contributing role as an agent of biological control of oliver scale, both species of parasites were able to reduce the host below economic levels within a year. Scale densities have decreased continually since 1963. Continuation of satisfactory biological control is indicated by the low densities of scales now maintained by its parasites. Judicious use of chemical treatments, both in selection and in timing of application, to control other insect and mit problems will ensure the continuing biological control of oliove scale in this deciduous orchard.     

Functional response and mutual interference of Peristenus spretus (Hymenoptera: Braconidae), a parasitoid of Apolygus lucorum (Heteroptera: Miridae)

Peristenus spretus Chen & van Achterberg (Hymenoptera: Braconidae) is a solitary endoparasitoid, which is considered for augmentative biological control of Apolygus lucorum Meyer-Dür (Heteroptera: Miridae) in Chinese cotton fields. Since the association of P. spretus with A. lucorum was only recently discovered, the biology of the parasitoid remains unknown. In order to understand its reproductive biology, the mutual interference and functional response of P. spretus were investigated by altering either the parasitoid or the host density while keeping the other constant. In both experiments, the effects of parasitoid and host densities on parasitism, superparasitism, progeny production and sex ratio were assessed. P. spretus exhibited a Holling type II functional response to changing host densities, indicating that parasitism increases with increasing host density until the parasitoid reaches its maximum reproductive capacity. The model suggested that a single P. spretus female could parasitise a maximum of 88 nymphs per day or four nymphs per hour. Increasing the wasp-nymph ratio from 1:10 to 1:80 significantly increased the offspring production more than fivefold from ±5.8 to ±35.6; further increasing the host densities (above 80 nymphs) did not significantly increase offspring production. Strong mutual interference of foraging P. spretus females occurred only at high parasitoid densities. Parasitoids foraging alone produced an average progeny of 33.4, whereas parasitoids foraging in groups of 16 produced only 2.6. The optimal wasp-nymph ratio for mass-rearing P. spretus is 4:100, given that resources of parasitoids and nymphs are unlimited.     

Bionomics ofTrioxys indicus [Hym.: Aphidiidae], a parasitoid ofAphis craccivora [Hem.: Aphididae]: 31. Effect of host haemolymph on the numerical response of the parasitoid

The influence of kairomones on the numerical response of the parasitoidTrioxys indicus against its hostAphis craccivora at its varying density was studied. The kairomones (applied as aqueous extract of the host) significantly enhanced the rate of parasitisation and multiplication and the area of discovery of the parasitoid and also the K-values of mortality of the host at all parasitoid densities introduced (1, 2, 4, 8, 12 and 16 parasitoids) into troughs having about 200 hosts. The sex-ratio of F₁ offspring decreased at lower parasitoid densities and remained more or less unchanged at higher parasitoid densities after the application of kairomones. The present findings indicate that if kairomones are applied properly, the number of hosts destroyed by a stimulated parasitoid will be about 200, twice the number reported earlier, thus fewer parasitoids will be needed to regulate an estimated population of the hosts.      

Zooplankton,and related phytoplankton cycles,in a eutrophic lake

The seasonal cycles of zooplankton were determined for 18 consecutive months in a sewage-enriched lake in northern Canada and were related to algal availability and utilization, food consumption, temperature and the density of predators. Most of the common species (Daphnia pulex, Daphnia middenorffiana, Keratella cochlearis, Keratella quadrata, Polyarthra vulgaris) increased in abundance in May and June, reached a mid-summer maximum, and declined sharply in the fall. Phytoplankton densities increased sharply in May, peaked early in June and gradually decreased through the summer and fall. Since the quantity of algae in the guts remained constant during this period, algal availability and utilization had no direct impact on the seasonal cycles of any species. Furthermore, the amount of ingested material in D. pulex and D. middendorffiana was similar regardless of time of year, implying that the total quantity of food in the environment did not restrict development. Although temperature was the most important factor influencing variations in the densities of all species, predation by Cyclops spp. probably had little effect on the population dynamics of the fauna.     

Grazing on <Emphasis Type="Italic">Microcystis</Emphasis> (Cyanophyceae) by testate amoebae with special reference to cyanobacterial abundance and physiological state

We examined the growth of testate amoebae preying on Microcystis whose physiological states were different in laboratory experiments and a hypertrophic pond. We prepared three experimental systems using water samples dominated by Microcystis aeruginosa: light incubation (control), dark incubation (dark), and light incubation with addition of nitrogen and phosphorus (+NP). In all the systems, the colony density of M. aeruginosa decreased slightly during incubation. Physiological activity of phytoplankton as determined by chlorophyll fluorescence was high and almost constant in the control and +NP systems, whereas it decreased in the dark system. Cell densities of testate amoebae increased in the control and +NP systems, whereas in the dark system they remained low. Thus, growth of the amoebae was low in the systems where physiological activity of Microcystis was low. In a hypertrophic pond, cell density of testate amoebae increased and remained high when M. aeruginosa predominated. Cell density of testate amoebae increased remarkably, simultaneously with the increases in M. aeruginosa colony density and phytoplankton physiological activity. We also found a significant correlation between densities of M. aeruginosa colonies and testate amoebae. We suggested that the physiological activity of Microcystis is one important factor affecting the growth of testate amoebae grazing on Microcystis.     

Effects of food limitation,notonectid predation,and temperature on the population dynamics of Daphnia carinata

The relative contributions of invertebrate predation (Notonectidae: Anisops spp.), food limitation, and certain abiotic factors in driving the population dynamics of Daphnia carinata were studied for a two year period in a large farm dam in southern Victoria, Australia. Detailed measurements were made on the population densities of Daphnia and Anisops spp., the amount of food available, the nutritional status, and the size-specific fecundity of Daphnia. The density of the Daphnia population at the field site oscillated closely with water temperature. The amplitude of the population fluctuations varied seasonally, being much greater during the warmer months of the year and switching to fluctuations with low peaks when water temperature dropped below approximately 15°C. Anisops spp. densities were greatest in winter and declined during the spring of each year. Nymphs appeared in late spring and early summer and numerically dominated the population. During the warmer periods of the year, the daphnid population went through a series of rapid growth phases leading to over-exploitation of food resources and subsequent population collapses. Daphnia population densities were not correlated with Anisops numbers suggesting that predation was not a major regulatory factor during the warmer periods of the year. When water temperatures fell below ca. 15°C daphnid population densities remained low despite high food levels. During this period the impact of Anisops may have been greater. Two distinct phases were identified: a warm water period when food limitation was the main regulatory factor, and a cool water period when Anisops predation may have been the paramount factor. Low oxygen concentrations were associated with heavy rainfall in the spring and may have had a limiting effect on Daphnia for short periods. Daphnia may have had an important role in sustaining the Anisops population in the pond over each winter.     

Regulatory processes and population cyclicity in laboratory populations ofAnagasta Kühniella (Zeller) (Lepidoptera: Phycitidae). III. The development of population models

1. Life table data for interactions between Anagasta kühniella and its ichneumon parasite Venturia canescens in two room ecosystems (A & B) have been analyzed in an attempt to explain and model each room situation. The life table data have been presented in the form of a graphical key-factor analysis, and have been further analyzed by an investigation of the density relationships between the different mortalities and the Angasta densities upon which the mortalities act.
2. In room A (1.2 gm food per container), the parasites were present throughout the interaction. Egg and early larval mortality (k₁) appeared to be directly density-dependent and was the sole stabilizing influence when introduced into the model for room A. The area of discovery of the parasite was relatively constant and its mean value was used to calculate parasitism (k₃) in the model. All other mortalities were density-independent and treated as being constant at their mean values. The model predicts a series of oscillations of decreasing amplitude which are somewhat similar to those observed in the Anagasta population during the early stages of the interaction. The observed mean densities of host and parasite were very close to those predicted.
3. In room B, the parasites were absent for the first 8 generations (1- 2gm food per container). Model B₁ covers this period and includes a direct density-dependent component describing changes in k₁, the remaining mortalities being constant. The observed mean densities approximate to the calculated densities. The parasites were present from the ninth generation and after the eleventh generation the food per container was increased to 7.2 gm. Model B₂ covers the period in room B from generation 11. The most important component of k₁ after the parasites were established is a delayed density-dependent one which appeared to be due to wounding of very small larvae by the probing activities of the parasites. Since the changes in k₁ could not be suitably predicted, the observed values were used in model B₂. This delayed component was not detected in room A due to the relatively small range of parasite densities in room A compared with the 600-fold change in densities in room B. The calculated area of discovery for the parasite population in each generation was found to vary inversely with searching parasite density, and this ‘interference relationship’ was used in the submodel for parasitism. Again, this relationship was not detected in room A due to the much smaller range of parasite densities there. Model B₂ gives oscillations in host and parasite populations arising from parasitism being a delayed density-dependent mortality. The correspondence with the observed oscillations is partly due to the actual k₁-values being used and partly because the submodel for parasitism adequately describes the observed changes in k₃. The tendency for these oscillations to decrease in amplitude is due to both the damping effect of parasite interference and the direct density-dependent component of k₁.