Experimental and Applied Acarology 26: 43–70, 2002. © 2002 Kluwer Academic Publishers. Printed in the Netherlands.
Interactions in a tritrophic acarine predator-prey metapopulation system IV: effects of host plant condition on Tetranychus urticae (Acari: Tetranychidae) GÖSTA NACHMAN 1,* and ROSTISLAV ZEMEK 2 1 Department of Population Ecology, Zoological Institute, University of Copenhagen, Universitetsparken 15, DK-2100, Copenhagen Ø, Denmark; 2Institute of Entomology, Branišovská 31, CZ-370 05, C { eské Budeˇjovice, Czech Republic; *Author for correspondence (e-mail:
[email protected]; phone: +45 35 32 12 60; fax: + 45 35 32 12 50)
Received 23 January 2001; accepted in revised form 11 July 2001
Key words: Beans, Density-dependence, Dispersal, Plant condition, Population growth, Tetranychus urticae, Two-spotted spider mites Abstract. Feeding by spider mites can cause severe injury to a host plant and lead to a decreasing per capita growth rate and an increasing per capita emigration rate. Such density-dependent responses to local conditions are important in a metapopulation context because they allow the herbivores to colonize new host plants and thereby prolong the time until regional (metapopulation) extinction. In order to include density-dependent responses of the two-spotted spider mite (Tetranychus urticae) in a realistic metapopulation model, a series of greenhouse experiments was conducted with the purpose to quantify how the condition of bean plants (Phaseolus vulgaris) influences the demographic parameters of T. urticae. Plant age per se reduced the growth rate of the spider mites only slightly, whereas the growth rate declined significantly as the plants were injured by the mites. The relationships between plant condition (expressed by the plant injury index D) and the birth and loss (death + emigration) rates of the mites were quantified so as to predict population growth as a function of D. Maximum per capita growth rate (r) was estimated to be c. 0.21 day −1. The growth rate is expected to be negative when D exceeds 0.8. When mites were allowed to emigrate to neighbouring plants via bridges, the per capita emigration rate increased almost exponentially with D. The proportion of eggs in the population decreased with D while the numerical ratio between immatures to adults and the sex ratio did not change with D. Overall, immatures and adults constituted 74% and 26%, respectively, of the active mites and c. 46% of the adults were males. The bridges that connected a donor plant with the surrounding recipient plants were responsible for the majority of the emigrations from donor plants. Most mites stopped after having crossed a single bridge, but a few crossed two bridges while none crossed three bridges within 24 h. The significance of the results for biological control is discussed.
Introduction Spider mites are among the most serious crop pests in the world (Tomczyk and Kropczynska 1985; Helle and Sabelis 1985). They inflict injury to plants by means of their needle-shaped mouthparts that are injected into leaf tissue and used to suck out cell fluids (Liesering 1960; Tomczyk and Kropczynska 1985). In large num-
44 bers, spider mites are able to cause substantial leaf necrosis, which may affect the growth and yield of the infested plants (Tulisalo 1970; Tomczyk and Kropczynska 1985; English-Loeb 1990; Skovgård et al. 1993a; Wilson 1993). However, as a plant deteriorates, its quality as food for the spider mites also declines, which may counteract their population growth (Wrensch and Young 1974; Krainacker and Carey 1990; Skovgård et al. 1993b; Wilson 1994). If the negative feed-back between plant condition and the growth of a spider mite population is strong enough it may prevent the pest from overexploiting and killing the host plants. This seems to be the case for the cassava green mite (Mononychellus tanajoa (Bondar)) attacking cassava (Skovgård et al. 1993b), but not for the two-spotted spider mite (Tetranchus urticae Koch) attacking e.g. cucumbers and beans (Hussey and Parr 1963a; Pallini et al. 1997). If a host plant is very vulnerable to spider mites (or other pest species), it shortens the time in which control of the pest can take place. Especially in case of biological control, the timing between a herbivore pest and its natural enemies can be decisive for whether the pest surmounts the plant or not and for the extent to which the pest reduces the crop yield. For instance, at 25 °C T. urticae has an intrinsic rate of natural increase (r m) of about 0.25 per day (Sabelis 1985), which means that a single individual has the potential to produce about 40 million offspring in less than 10 weeks. Even though this number will not be reached in practice, it is far above what is needed to overexploit and kill the host plant. Therefore, an effective natural enemy should be able not only to reproduce at a high rate, but also to localize and destroy local populations of prey before they manage to cause severe injury to the host plant. Experiments have shown that the phytoseiid predator Phytoseiulus persimilis (Athias-Henriot) possesses this capacity (Nachman 1981) provided the predators can move easily among the plants (Nachman 1999). However, if the predators become too efficient they may risk to overexploit their prey at both the local and the regional scale (e.g in a greenhouse) unless prey individuals can escape adverse local conditions (low food quality and/or high predator density) by moving to better host plants. A prerequisite for long-term coexistence of prey and predators is that colonization rates on average balance extinction rates of both species. This type of non-equilibrium dynamics (called “hide-andseek”) has been modelled by means of a spatially explicit stochastic simulation model (Nachman (1987a, 1987b); Walde and Nachman 1999). In order to parameterise this model for T. urticae and P. persimilis inhabiting a multi-plant bean system, empirical data on local and regional dynamics are needed. This article concentrates on investigating how host plant condition affects local population growth and emigration of T. urticae in the absence of predators. The effect of spider mites on host plants (Phaseolus vulgaris L.) was studied in Nachman and Zemek (2001), while the dispersal of P. persimilis in response to density of spider mites was described in Zemek and Nachman (1998, 1999). The combined effect of plant condition and P. persimilis on the density of T. urticae will be the topic of a following paper (Nachman and Zemek, in prep). Several studies have shown that plant condition affects both the growth rate and the dispersal rate of spider mites (Wrensch and Young 1974; Bernstein 1984; Smitley and Kennedy 1985; Krainacker and Carey 1990; Li and Margolies 1993), but
45 none of these studies provide quantitative relationships between the degree of plant injury and these demographic parameters.
Materials and methods General description of the experiments In all experiments beans, Phaseolus vulgaris L. Bon-Bon from L. Dæhnfeldt Ltd, were used as host plant for the two-spotted spider mite, Tetranychus urticae Koch. The plants were grown in greenhouses under the same conditions as described in Nachman and Zemek (2001). Most statistical analyses were done by means of SAS™ for Windows version 6.12 (SAS Inst. 1994). However, circular data were analysed by means of a randomisation programme developed by Zemek and Nachman (1999). Effect of plant age on spider mite population growth rate The purpose of this experiment was to test whether plant age has an effect on the population growth rate of T. urticae. Five groups of five pots with bean plants were used for the experiments. The groups differed with respect to plant age, since the plants were sown with intervals of two weeks. On the same day, when the plants were 3, 5, 7, 9 and 11 weeks old, respectively, they were inoculated with 10 adult female spider mites per pot. Two weeks later all leaves were detached and the spider mites (eggs, immatures, adults) occurring on the underside of the leaves were counted under a dissecting microscope. The area and leaf damage index (LDI) of each individual leaf were also recorded (see (Nachman and Zemek 2001)). The average per capita growth rate of the spider mites, r, measured from the day of inoculation (t = 0) to day t, when the experiment stopped, was estimated as (see e.g. Odum (1971))
冉冊
Xt 1 rˆ ⫽ ln t X0
(1)
where X t denotes the number of mites on the plant at day t and X 0 is the initial number (10 individuals). Note that since rˆ also includes losses due to emigration, it may underestimate the growth rate compared with a completely isolated population. Effect of host plant condition on population growth of spider mites Data from the previous experiment were used to estimate the rate at which a spider mite individual extracts chlorophyll from leaves of the host plant. The rate (expressed as the amount of chlorophyll extracted per mite and time unit) is denoted
46
. It is estimated from the relationship (Appendix 1) L t ⫽ M t
(2)
where L t is the amount of chlorophyll the plant has lost after having been exposed to M t mite-days. Mite-days is defined as the cumulated number of mites occupying a given spatial unit (which in the present case is a plant) from day 0 to day t (cf. Hoyt et al. (1979)). The empirical value of was found from Equation (2) as the slope of the straight line passing through the origin when fitted by linear regression to empirical values of L t and M t. For a given plant, L t was estimated as n
Lˆ t ⫽ c max 兺 A i ⫺ i⫽1
n
兺cA
i⫽1
i
(3)
where A i is the leaf area of the i’th leaf, c i its chlorophyll concentration (g/cm 2), and c max the maximum chlorophyll concentration, that is, if no feeding had taken place. c i was not measured directly but estimated from the leaf damage index (LDI) as ˆ
b ˆ cˆ ⫽ cˆ maxe ⫺ a共LDI兲
(4)
where cˆ max ⫽ 22.945g/cm 2, aˆ ⫽ 0.059 and bˆ ⫽ 1.453 (see Nachman and Zemek (2001)). Mite-days (M t) for the same plant were calculated as (Appendix 1) Mt ⫽
Xt ⫺ X0 rˆ
⫽
共X t ⫺ X 0兲t ln共X t/X 0兲
(5)
Equation (5) applies only as long as the spider mite population increases exponentially, but not when the per capita growth rate begins to decrease due to the injury inflicted to the host plant. To incorporate the feedback between plant condition and spider mites, a more sophisticated model was developed (Appendix 2). It is based on the assumption that the per capita birth rate decreases while the per capita loss rate increases with an increase in the plant injury index D defined as D⫽
c max ⫺ c¯ c max ⫺ c min
(6)
where c¯ ⫽
n
n
i⫽1
i⫽1
兺 cˆ iA i/ 兺 A i
and c min is the value of c¯ if all leaves have LDI = 5 (Nachman and Zemek 2001).
47 The model fitted to data predicts the density of spider mites (x) on a plant with injury index D as x⫽
冋
共1 ⫺ 共1 ⫺ D兲 兲 ⫹ 共1 ⫺ 共1 ⫺ D兲 ⫺ ␥兲  ␥
1 b s0
册
共x ⭓ 0兲
(7)
where b and denote the per capita birth and loss rates, respectively, when D = 0 and  and ␥ are positive constants expressing the density dependent effects of D on the growth rate. s 0 is the maximum amount of leaf area a spider mite destroys per day. It is estimated as sˆ 0 ⫽
ˆ cˆ max ⫺ cˆ min
(Appendix 2). The remaining parameters of Equation (7) were estimated by fitting it to data using PROC NLIN in SAS. Data consisted of the associated values of x and D obtained from the 45 donor plants used in the dispersal experiments (see below). Since none of these plants had very high levels of injury, six heavily infested plants were later added to the data to obtain more values of x for D > 0.8 in order to show experimentally that the relationship between D and x is not monotonously increasing. Dynamics of spider mites on exploited host plants The purpose of this experiment was to follow the population growth of spider mites as the host plants gradually deteriorated due to exploitation. In total, 50 plants were used for this experiment. Each plant was inoculated with five adult female T. urticae. At two-week intervals, ten plants were sampled and all the leaves were detached, their leaf damage index (LDI) was assessed, mite eggs, immatures, adult males and females were counted and the leaf area measured. Consequently, data consist of five groups of ten plants that had been infested with mites for 2, 4, 6, 8 and 10 weeks. Effect of host plant condition on dispersal of spider mites The purpose of this experiment was to investigate the influence of host plant condition on the tendency of T. urticae to move from one plant to another. The experimental set-up corresponded to the way plants were connected with each other in the multi-plant experiments described in Nachman (1999). The pots with bean plants were placed on a table as shown in Figure 1. The distance between two pots in the main cardinal directions (measured from centre to centre) was 25 cm. Only the central (donor) plant was infested by spider mites. The donor plant was connected to either eight (variant A, Figure 1) or four recipient plants (variant C, Figure 1). One variant consisted of eight recipient plants of which half were connected
48
Figure 1. Experimental set-up used for estimating emigration rates, with the donor plant (filled circle) in the centre connected by bridges (lines) to the eight recipient plants (open circles) in the periphery. A: Variant with 8 recipient plants and 8 bridges; B: Variant with 8 recipient plants and 4 bridges; C: Variant with 4 recipient plants and 4 bridges.
(variant B, Figure 1). Connections were established by means of metal/plastic “bridges” (see Zemek and Nachman (1998) for details). Bridges were either 13 cm or 24 cm long. The latter type was used to connect plants in the diagonal. Since the table was covered by a water-saturated blanket, mites could not easily move from one pot to another unless they used a bridge. At the end of an experiment, the mites on the donor plant and the recipient plants were counted. The leaf area and the LDI of all the leaves on the donor plant were also recorded. Immatures, adult males and females were counted separately in 19 experiments, whereas the two sexes were pooled in the remaining 26 experiments to make counting faster. By a mistake, immatures on the recipient plants were not recorded in six of the experiments with eight bridges. Since the initial number of mites present on the donor plant has to be estimated at the end of an experiment (see later), it is an advantage to make the duration of an experiment as short as possible. Otherwise, natural mortality and egg hatching (which occurs c. three days after an egg is laid) could bias the estimates. On the other hand, if the duration of an experiment is too short, no or very few dispersal episodes will be recorded, especially when the donor plant is lightly infested. To balance these two considerations, experiments lasted two or three days when lightly infested donor plants were used, but only one day if the plant was heavily infested. A total of 45 dispersal experiments was conducted. 30 were of variant A, 6 of variant B, and 9 of variant C. The unconnected pots in variant B served as a check of the assumption that the bridges were the main mediator of mite dispersal between plants. The 30 experiments of variant A served also as a check of whether there was any effect of bridge length on the dispersal rate. Within each experiment, the numbers of dispersing mites (immatures and adults) found on the four recipient plants connected by short bridges (N, W, E, S) and on the four plants connected by long bridges (NW, NE, SW, SE) were summed and the difference between the two sums calculated. To test for a possible effect of bridge length, matched pairs tests
49 were applied (sign test and Wilcoxon signed ranks test (Siegel and Castellan 1988)). Both tests control for the between-experiment variation and do not require normally distributed data. Besides, the tests are not sensitive to the fact that the bridges may differ with respect to how accessible they are for the mites (i.e. dispersal events are not independent) as long as this property is randomly distributed among short or long bridges, which seems to be a reasonable assumption. The sign test compares the number of times where more mites had crossed the short bridges than the long bridges with the number of times the opposite occurred, whereas Wilcoxon’s test uses the ranks of the numerical differences between the numbers of mites found on the two groups of recipient plants. The latter test has the highest power. Data from the experiments with eight bridges were also used for testing whether dispersing mites had a preferred direction of movement. The statistical analysis was performed by means of randomisation of the numbers of individuals recovered from the eight directions (see Zemek and Nachman (1999) for details). Dispersal propensities of immatures and adults, and of adult males and females were compared using matched pairs tests (sign test and Wilcoxon signed ranks test (Siegel and Castellan 1988)). The rate of dispersal was estimated from the data by means of a model based on the following assumptions: 1. Individuals emigrate independently of each other. 2. During an experiment, the mite population inhabiting the donor plant grows with a constant per capita rate r. 3. All dispersal takes place via bridges. 4. The instantaneous rate of emigration is proportional with the number of bridges (B) 5. Immigrants on the recipient plants do not die or leave again during an experiment. As shown in Appendix 3, the model implies that the per capita rate of dispersal per bridge () of the individuals present on the donor plant can be estimated as
ˆ ⫽
rˆR t ˆ
BX t共1 ⫺ e ⫺ rt兲
ˆ ⫽
Rt BX tt
共rˆ ⫽ 0兲
共rˆ ⫽ 0兲
(8)
(9)
where R t is the number of individuals of a given stage and sex present on the B recipient plants at the end of an experiment lasting t time units and X t is the total number of individuals on the donor plant at time t. r estimated as rˆ ⫽ b共1 ⫺ D兲  ⫺
共1 ⫺ D兲 ␥
50 (see Equation (18)), where the parameters have been found from Equation (7). The parameters 0 and 1, which are used to model the propensity of individuals to emigrate (Equation 28), were estimated from data by fitting the expression (see Appendix 3) E共R t兲 ⫽
共1 ⫺ 共1 ⫹ e 0 ⫹ 1D兲 ⫺ B兲X t共1 ⫺ e ⫺ rt兲 r共1 ⫺ D兲 ␥
(10)
to observed values of R t. Finally, the expected per capita rate of emigration per bridge is found from E共兲 ⫽
ˆ
ˆ
ˆ
共1 ⫺ 共1 ⫹ e 0 ⫹ 1D兲 ⫺ B兲 B共1 ⫺ D兲 ␥
(11)
which can be compared with the values of estimated directly by means of Equation (8). Effect of host plant condition on the stage distribution and sex ratio The data from the dispersal experiments were also used to analyse whether plant condition affects the stage composition and sex ratio of T. urticae. Three different stages were considered: eggs, immatures and adults. The proportions of each stage relative to all individuals are denoted p E, p J and p A, respectively. The proportion of eggs on the donor plant (p E) was found by dividing the number of eggs with the total number of individuals on the donor plant plus all the motiles (immatures + adults) on the surrounding recipient plants, since these individuals originated from the donor plant. The relationship between D and p E was analysed by means of logistic regression (PROC GENMOD in SAS). If data showed overdispersion, the tests were adjusted by means of a scaling parameter (see McCullagh and Nelder (1989)). The model fitted to data was pE ⫽
e  0 ⫹  1D ⫹  1D
2
1 ⫹ e  0 ⫹  1D ⫹  1D
2
(12)
where  0,  1 and  2 are parameters. The model was reduced until all included parameters were significant at the 5% level. The next step was to analyse whether the proportion of immatures (or adults) of the total number of motile mites on the donor and recipient plants changed with D, using the same approach as with the eggs. Since the proportions of immatures and adults can be considered as conditional probabilities, i.e. provided an individual is known to be a motile, it is an immature with probability p J⬘ and an adult with probability p A⬘ so that p J⬘+p A⬘ = 1. The unconditional probabilities are finally obtained as p J = p J⬘ (1-p E) and p A = p A⬘ (1-p E). The relationship between the propor-
51
Figure 2. Experimental set-up used for estimating dispersal distances. The donor plant (filled circle) is surrounded by eighteen recipient plants (open circles) of which half are connected by bridges (lines). The numbers assigned to the recipient plants denote the minimum number of bridges required to establish connection to the donor plant.
tion of males (p M = males/(males + females)) and D was also analysed by means of logistic regression. Dispersal distances of spider mites The purpose of this series was to find the distance moved by spider mites after leaving an infested plant. 18 pots with bean plants without spider mites were placed on the water-saturated blanket in a set-up as shown in Figure 2. The distances between plants corresponded to those in the previous dispersal experiments. A bean plant, heavily infested with spider mites, was placed in the centre. Half of the surrounding pots (the recipient plants) were connected with the central (donor) plant through five short (13 cm) and four long (24 cm) bridges. The unconnected plants served the same purpose as before. An experiment lasted 24 h, whereupon all mites occurring on the plants were counted under a dissecting microscope. The area and LDI of the donor plant’s leaves were also recorded. Four experiments were conducted. They differed with respect to the position of the connected plants in order to account for a possible effect of light/shadow on the direction of movement.
52
Figure 3. Per capita growth rate (r) of T. urticae as a function of plant age defined as the mid-point of two-week intervals. The growth rate shows no time trend (r 2 = 0.065; t 22 = 1.237; P = 0.23).
Results Effect of plant age on spider mite population growth rate Figure 3 shows the per capita net growth rate (r) against the pivotal age (mid point of an age interval) of the plants during the experiment. On one of the five 8-weeks old plants no spider mites were found at all. Since the most likely explanation for this is that the plant by a mistake was never inoculated, it was omitted from the analysis. The scatter of r within each plant group was considerable, which blurred the slight decreasing trend in r with plant age. Hence, a straight line fitted to the individual observations of r was far from being significant (r 2 = 0.065; t = 1.237; df = 22; P = 0.229). Overall, the 24 values of r ranged from 0.053 day −1 to 0.259 day −1 (average r = 0.184 day −1; SD = 0.058 day −1; SE = 0.012 day −1). There was no clear trend between treatments with respect to the stage distribution of the spider mites when the mites were counted at the end of an experiment (Figure 4). Overall, eggs constituted 56.1%, immatures 17.8%, and adults 26.1% of all individuals. Figure 5 shows the loss of chlorophyll as a function of mite-days. The straight line represents the fit of Equation (2) to the untransformed data. The model ex-
53
Figure 4. Relative distributions of eggs, immatures and adults of T. urticae on plants of different age. Mites were sampled fourteen days after a plant had been inoculated with ten adult females.
plained 83.9% of the variation in the observed values of L t (t 23 = 11.24; P < 0.0001). was estimated to be 0.1453 (SE = 0.0129) g chlorophyll mite −1 day −1. Effect of host plant condition on the growth rate of spider mites The maximum leaf area destroyed per spider mite individual per day (s 0) was estimated to be sˆ 0 ⫽
0.1453 22.945 ⫺ 12.449
⫽ 0.0138cm 2day ⫺ 1
Figure 6 shows the fit of Equation (7) to data from 51 plants. The parameters were estimated as bˆ ⫽ 0.3157 (SE = 0.1360) day −1, ˆ ⫽ 0.1010 (SE = 0.0310) day −1, ˆ ⫽ 0.1016 (SE = 0.0464), and ␥ˆ ⫽ 0.6001 (SE = 0.0012). All parameters were significantly different from 0. The maximum per capita growth rate (r) is found as rˆ ⫽ bˆ ⫺ ˆ ⫽ 0.215 day −1. Figure 6 also includes data from 250 plants used in dispersal experiments with P. persimilis (Zemek and Nachman (1998, 1999)), but in order to avoid a confounding effect of predators these plants were not used for estimation of the parameters of Equation (7). The fact that the model also fits the plants hosting both prey and predators indicates that the number of predators and/or the time they had been allowed to interact with the spider mites (one day) was not
54
Figure 5. The relationship between the number of mite-days (M t) (cumulative number of mites occupying a plant from day 0 to day t) and the amount of chlorophyll lost per plant (L t). The straight line represents the fit of Equation (2) to data with ˆ ⫽ 0.1453 (SE = 0.0129) g chlorophyll mite −1 day −1.
sufficient to clearly separate these plants from those without predators. Figure 7 shows that the model predicts a slightly decreasing birth rate and a steeply increasing loss rate as D increases. The two rates balance (r = 0) when D is approximately 0.8. Dynamics of spider mites on exploited host plants Figure 8 shows the observed densities of mites (all stages combined) overlaid by the predicted dynamics obtained by solving Equations (17) and (18) numerically using a time step (⌬t) of 0.1 day. Since plant area at the time of inoculation was not measured, it was assumed that plants on average had a leaf area of 125 cm 2 corresponding to an initial density of 0.04 mites/cm 2. The model predicts the maximum density to be reached after about 35 days, but unfortunately the intervals between two successive samplings were too long to provide convincing data on this maximum. Besides, the model overestimates the mite density at day 28, whereas agreement between the predicted and the observed plant injury is acceptable taking the large scatter in the data into consideration. The model correctly predicts that the mites overexploit the plants within 50 to 70 days. It also predicts that D will approach an upper limit of about 0.95, but in reality all plants died after having been so severely damaged, implying that D eventually reached one.
55
Figure 6. The relationship between the plant injury index (D) of a host plant and the concomitant density of spider mites (x). Filled circles: Data obtained from 51 experiments with only spider mites; Open circles: Data obtained from 250 plants inhabited by both spider mites and predatory mites (Zemek and Nachman (1998, 1999)). The line shows the fit of Equation (7) to the data set without predators (R 2 = 0.433; n = 51). The parameter values are: sˆ 0 = 0.0138 cm 2 day −1, bˆ ⫽ 0.3157 day −1, ˆ ⫽ 0.1010 day −1, ˆ ⫽ 0.1016, and ␥ˆ ⫽ 0.6001.
Effect of host plant condition on dispersal rates of spider mites In the six experiments where only half of the recipient plants were connected to the donor plant, 369 immatures and 2155 adults were found on the connected plants, whereas only one immature and 24 adults were found on the unconnected plants. Thus, mites recovered from the unconnected plants constituted only 0.27% (SE = 0.53%) and 1.1% (SE = 0.22%) of the dispersing immatures and adults, respectively. The total numbers of dispersing mites (immatures + adults) found on the recipient plants connected by short and long bridges were 4287 (47.1%) and 4817 (52.9%), respectively. In four of the experiments, no mites were found on any of the recipient plants, while in the remaining 26 experiments, most mites were found on the plants connected by short bridges in 12 cases. This distribution is close the expected assuming that bridge length does not influence dispersal (sign test: P = 0.845; Wilcoxon test: T = 170, P > 0.05; n = 26). The observed mean direction of movement of the 9104 mites (immatures + adults) was 293°, which corresponds to a westerly-north westerly direction (North = 0°). However, the intensity of the mean vector was only 0.065, which is not significantly different from 0 (Randomisation test based on 10,000
56
Figure 7. The predicted effects of plant injury (D) on the per capita birth rate (dotted line), loss rate (dashed line) and growth rate (full line) of T. urticae. The relationships are found from Equation (18) using the parameter values given in Figure 6.
permutations: P = 0.556, SE(P) = 0.005). Thus, the result indicates that movement of T. urticae is undirected. The total numbers of dispersing mites found on the donor and recipient plants at the end of the experiments are presented in Table 1 together with the percentage present on the recipient plants. In order to compare immatures and adults, the six experiments in which immatures on the recipient plants had not been counted were omitted from the data set. In the remaining 39 experiments, 9.8% of the immatures and ca. 54.3% of the adults were found on the recipient plants, indicating that adults are about five times more likely to disperse than immatures. In 36 of the experiments, the proportion of adults found on the recipient plants was higher than the proportion of immatures, while in three cases the proportions were the same (and equal to 0). Both a sign test and a Wilcoxon signed ranks test showed that the difference between immatures and adults is highly significant (P < 0.0001). In the 19 experiments where adults were sexed, 70.8% of the males and 58.8% of the females were found on the recipient plants. In eight of the experiments, a higher proportion of males than females occurred on the recipient plants, while in eight other experiments the opposite applied. In the three remaining experiments, the proportions were the same. When Equation (10) was fitted to data, the model explained 48.3% of the variation in the observed values of R t (number of mites on the recipient plants at the end of an experiment), but since the variance of R t tends to increase proportionally with X t 2, we compared the predicted and observed values of log (R + 1) instead.
57
Figure 8. The observed (dots) and predicted (full line) dynamics of spider mites and the observed (squares) and predicted (broken line) development in plant injury index (D) of host plants initially inoculated with five adult female spider mites. Vertical lines indicate 95% confidence limits about the mean (n = 10). The predicted curves are described by Equations (17) and (18) with parameter values given in Figure 6 and assuming an initial density (x 0) of 0.04 mites cm −2 leaf area. Table 1. Numbers of motile mites on donor and recipient plants and numbers of experiments in each category. Omitting six experiments in which the immatures were not counted gives the values in parentheses
Mites on donor plant Mites on recipient plants Total % of mites on recipient plants Number of experiments
Immatures
Adults
Males
Females
48370 5265 53635 9.8 39
11077 (8438) 12309 (10031) 23386 (18469) 52.6 (54.3) 45 (39)
1296 3146 4442 70.8 19
2169 3099 5268 58.8 19
The model explained 70.6% of the observed variation in log(R + 1). The parameters 0 and 1 of Equation (10) were both significantly different from 0 (ˆ 0 ⫽ ⫺ 4.210 (SE = 1.191) and ˆ 1 ⫽ 3.469 (SE = 1.694)). This result shows that the propensity to emigrate (p s) increases with D (from p s = 0.0146 when D = 0 to p s = 0.323 when D = 1). Figure 9 shows that the per capita emigration rate per bridge (ˆ ) increases by a factor 100 as D of the donor plant increases from 0 to 1. The differences between experimental set-ups with four (variant B + C) and eight (variant A) bridges with respect to the predicted emigration rate are relatively small and cannot be demonstrated statistically. The model (Equation 11) explained 57.4% of the variation in
58
Figure 9. The predicted relationship between the plant injury index (D) of donor plants and the per capita emigration rate per bridge () to the recipient plants. Broken line and open circles: Predicted and observed values of when the donor plant is connected to four recipient plants. Full line and filled circles: Predicted and observed values of when the donor plant is connected to eight recipient plants. The lines are based on Equation (11). Four experiments with eight bridges in which D ranged between ¯ = 0.128; SD = 0.093) are not shown because no individuals were found on the re0.035 and 0.245 (D cipient plants so that ˆ = 0.
log ˆ obtained from experiments with four bridges (n = 13) and 37.7% from experiments with eight bridges (n = 22). Effect of host plant condition on stage and sex distribution When Equation (12) was fitted by means of logistic regression to the observed values of p E, the only explanatory variable that remained in the model was D 2. The parameters of the reduced model are ˆ 0 ⫽ 0.285 (SE = 0.272) and ˆ 2 ⫽ ⫺ 2.669 (SE = 0.718). ˆ 2 was highly significant even after adjustment for overdispersion ( 12 = 13.803; P = 0.0002). The result shows that the proportion of eggs declines with increasing damage to the host plant. It was not possible to find any significant change in the relative composition of motile mites. Overall, immatures constituted c. 74% (95% C.L: 68.0% −79.9%) of the motile mites. Consequently, the proportions of immatures and adults in the total population are both expected to increase with an increase in D (Figure 10). No effect of plant condition on sex ratio was found when using data from the19 dispersal experiments where the adults were sexed, although there was a trend towards relatively fewer males as D increased. Omitting D and D 2 from the model
59
Figure 10. The predicted effect of plant injury (D) on the stage distribution of T. urticae. The proportion of eggs (p E) is predicted from Equation (12) with parameters ˆ 0 ⫽ 0.285, ˆ 1 = 0 and ˆ 2 ⫽ ⫺ 2.669. The proportion of immatures (p J) is predicted from p J = p J⬘ (1-p E) and the proportion of adults (p A) from p A = p A⬘ (1-p E), where p j = 0.744 and p A⬘ = 0.256.
yielded ˆ 0 ⫽ 0.171 (SE = 0.114), which corresponds to an overall sex ratio of 45.8% males (95% C.L: 40.3% −51.3%). Dispersal distances of spider mites As shown in Table 2, five adults were found on unconnected plants, but since these plants constituted half of the recipient plants, the number of adults that managed to move from the donor plant to an adjacent plant without crossing a bridge is assumed to be twice that number. Thus, of the 135 adult mites found on the recipient plants, approximately 10 (7.4%) did so without using a bridge. Apparently no immatures managed to cross without using a bridge. Two immatures and 29 adults managed to cross two bridges. Assuming that these individuals have already crossed one bridge, the conditional probability that an individual will cross an additional bridge is estimated as 11.8% (SE = 8.1%) and 22.3% (SE = 2.2%) for immatures and adults, respectively. The two groups were not significantly different ( 12 = 0.471; P = 0.493). No mites were found on the two most distant plants separated from the donor plant by three bridges. Assuming bridge crossing to be a Markovian process, the expected numbers of mites on these two plants can be calculated as 0.06 immatures and 1.68 adults.
60 Table 2. Distance moved by migrant T. urticae from the donor plant to the recipient plants. Distance is measured as the minimum number of bridges required to establish contact between a donor and a recipient plant, although bridges may not have been present. No distinction is made between short and long bridges. Stage
Distance between donor plant and recipient plants Bridges present
Immatures Adults Total
Bridges absent
1
2
3
1
2
3
15 101 116
2 29 31
0 0 0
0 5 5
0 0 0
0 0 0
Discussion The purpose of the present study was to quantify the effects of spider mites on their host plant and the simultaneous responses of the mites to degradation of their food resource. In order to make the experiments more realistic and comparable with greenhouse data, we used entire host plants instead of excised leaves as substrate for the mites (see e.g. Yaninek et al. (1989) and Wilson (1994)). However, the use of entire plants grown under greenhouse conditions also imposes some disadvantages: (1) Temperature, humidity and light conditions in a greenhouse cannot be controlled so precisely as in a phytotron; (2) Plants are difficult to standardise compared to single leaves; and (3) Population censuses cannot be made without disturbing the mites and were therefore done at the end of an experiment. The first two points increase the experimental noise, but this can to some extent be handled statistically. The third point requires more sophisticated solutions because we have to rely on the adequacy of the mathematical models used to describe the underlying dynamics. If these models are inadequate, the results obtained will be biased too. The validity of the models cannot be tested independently of the data, so the only criteria to judge the models are whether their underlying assumptions seem reasonable and to what extent their predictions agree with the terminal observations. Therefore, we encourage the readers to consider the models critically and regard them merely as our currently best suggestions as how to interpret the data in a consistent way. Effect of plant age on spider mite population growth rate The intrinsic rate of natural increase (r m) for T. urticae at 25 °C has previously been reported to range from 0.218 to 0.290 day −1 (Sabelis 1985), whereas we found a per capita net growth rate (r) of merely 0.184 day −1 when we counted the number of mites on plants that had been inoculated with ten adult female spider mites two weeks earlier. The discrepancy between these estimates of per capita growth rates can be attributed to the fact that we did not base our calculations on controlled
61 life-table studies but obtained r from greenhouse experiments where the temperature on average was below 25 °C. Besides, the populations never reached a stable age distribution, individuals could emigrate from the host plants, and the plants were probably suboptimal for the mites after having been exposed to feeding in 14 days. We did not find any effect of plant age on r, but the experimental noise might have obscured such an effect. Thus, Wilson (1994) found that T. urticae developed fastest on young cotton leaves and slowest on cotyledons and old leaves, whereas Karban and Thaler (1999) found the highest growth rate on the cotyledons, but little difference between young and mature leaves. Watson (1964) showed that the fecundity (and to some extent also longevity) of T. urticae feeding on Lima beans was inversely related to both leaf and plant age. Similarly, Yaninek et al. (1989) found that the growth rate of the cassava green mite (Mononychellus tanajoa (Bondar)) was highest on young leaves on young cassava plants. On the other hand, Kielkiewicz and Van de Vrie (1990) found that young leaves of chrysanthmum were relatively better protected against two-spotted spider mites compared with older leaves. Karban and Thaler (1999) further suggest that the growth rate of T. urticae is positively correlated with the rate of photosynthesis, which may vary with leaf age. Effect of host plant condition on population growth and stage distributions When we used the relationship between the plant injury index (D) and mite density (Equations 18 and 7) to model how a population of spider mites will develop when exposed to declining plant condition (increasing D), we estimated r m to be c. 0.21 day −1, which is in the lower end compared with the values given by Sabelis (1985). The model explicitly separates the effect of D on the per capita birth and loss rates instead of lumping these two rates into one (the per capita growth rate r) as in the model of Pels and Sabelis (1999). There are two reasons for our approach: (1) if the system is going to be modelled by means of a simulation model that explicitly incorporates demographic stochasticity (see e.g. Walde and Nachman (1999)), it is necessary to separate the birth rate and the loss rate since their sum determines the variance of the predicted population changes (see e.g. Pielou (1969)); and (2) it allows us to identify which of the two life-history parameters that is most sensitive to plant condition. Figure 7 indicates that it is mainly the per capita loss rate that increases as the host plant starts to deteriorate, whereas the per capita birth rate is rather unaffected. This result is in conflict with the conclusions by Watson (1964) and Tulisalo (1970), Mitchell (1973), Wrensch and Young (1974), Carey (1983), Wilson (1994) who found that fecundity is the most responsive parameter to overcrowding and nutritional stress as compared with mortality. However, it seems likely that the oviposition rate would have declined more steeply if the mites had been confined to a small arena from which they were unable to escape, because this would had intensified the intraspecific competition compared with an open system. In fact, the data indicate that a considerable part of the losses was due to emigrations and not to mortality. The proportion of diapausing females was not recorded separately, but was negligible. As long as light and temperature conditions
62 are favourable, food quality has a minor influence on diapause induction (Veerman 1985). The observed changes in stage distribution towards relatively fewer eggs in the population as D increases (Figure 10) are in accordance with the changes in birth and death rates (Carey 1983). When D = 0, we found that a population is expected to consist of 58% eggs, 32% immatures and 10% adults. This stage composition is fairly close to the stable age distribution given by Carey (1983) as 65% eggs, 25% immatures and 10% adults. Our analysis shows that birth and loss rates balance when D is approximately 0.8, which sets an upper limit of about 15 spider mites (all stages) per cm 2 to the average mite density a bean plant can sustain (Figure 8). However, local density (e.g. on individual leaves) may sometimes exceed 100 individuals per cm 2 (Nachman, pers. obs). The model provided a reasonable fit to the empirical data when it was validated against an independent data set based on plants that have been infested with spider mites for different periods of time (Figure 8). Unfortunately, the time intervals between samplings (14 days) were too long to reveal the underlying dynamics clearly. In a following paper, focusing on the dynamics of spider mites on plants with and without predators (Nachman and Zemek, in prep.), the model is validated against another data set sampled at 7-days intervals (but with only two replicates per sampling). We estimated the amount of chlorophyll removed by spider mites to be 0.1453 g mite −1 day −1. This value corresponds to 1.38 mm 2 leaf area destroyed per mite and day. In comparison, Candolfi et al. (1991) estimated the area to about 13 mm 2 mite −1 day −1. However, their value was based on an unspecified mixture of nymphs and adults, while ours is a population value, including stages with no (eggs and moulting nymphs) and low (larvae and protonymphs) feeding activity. Since these stages constitute a major part of an increasing population (Carey 1983), it may explain why our estimate is only about one tenth of the value given by Candolfi et al. (1991). Effect of host plant condition on dispersal rates of spider mites We found an accelerating propensity of the mites to leave a host plant as it deteriorated due to overexploitation. Several other studies have demonstrated that high densities of mites and resource degradation lead to increased dispersal tendency (Hussey and Parr 1963b; Suski and Naegele 1963; McEnroe 1969; Bernstein 1984; Smitley and Kennedy 1985; Li and Margolies 1993), but none of these studies has quantified the relationship between host plant condition and dispersal rate. The model shows that the per capita emigration rate increases exponentially with D up to an upper limit of 0.03 day −1 bridge −1. In an experimental set-up with eight bridges, this means that c. 25% of all mites (c. 30% of the active stages) present on a plant will emigrate within one day. In comparison, about 50% of adult female Phytoseiulus persimilis are expected to leave a host plant devoid of prey within five h (Zemek and Nachman 1998). We also found that adults disperse with a higher rate than immatures, which agrees with Brandenburg and Kennedy’s (1982) observation that 86% of airborne mites were adults. We were not able to demonstrate a difference between adult males and females with respect to dispersal tendency, al-
63 though Smitley and Kennedy (1985) found that adult females are the dominant wind dispersers, but their tendency to disperse declines with age (Li and Margolies 1993). In order to identify the mechanisms used by T. urticae to assess the density of conspecifics, Dicke (1986) conducted a series of experiments in which he exposed female spider mites to odours from leaves that were either clean or infested with spider mites, and to clean leaves that had been artificially damaged. He found that the mites respond both to a volatile pheromone that elicits dispersal and to a plant kairomone that elicits attraction. The ratio between the two substances determines whether a spider mite will emigrate or stay. However, since all female mites in Dicke’s experiments were well-fed, it is not possible to compare the relative effect of volatile substances on dispersal behaviour with that exerted directly through the amount and/or quality of food when mites feed on injured plants. Pallini et al. (1997) found that adult female T. urticae placed in an olfactometer had a slight preference for cucumber plants already inhabited by conspecifics compared to clean plants, whereas the mites clearly avoided plants with thrips. Dispersal distances of spider mites The dispersal experiments show that most dispersal events were short-distance, taking place when a mite moved to a nearest neighbour plant. At relatively few occasions individuals crossed two bridges within one day, whereas three crossings were never observed. It is important to note that the recipient plants were of good condition (D ⬇ 0), which probably reduced the dispersal distance. It should also be noted that the number of crossings per dispersal event may be underestimated because a mite that crosses the same bridge twice will not be recorded correctly. Implications for biological control The experiments have shown that the dynamics of T. urticae is highly influenced by the condition of their host plant, but also that the host plant is severely influenced by the presence of mites (Nachman and Zemek 2001). As the plant deteriorates, the mites suffer from a decreased birth rate and an increased loss (death + emigration) rate, which gradually slows down population growth and ultimately puts an upper limit to the mite density. Unfortunately, at least from a economic point of view, this negative feed-back mechanism is unable to prevent the spider mites from overexploiting their host plant within a few weeks after it had been colonized. That is why biological control by means of predatory mites is so rewarding, but also the reason for why it is necessary to find natural enemies that can cope adequately with these extreme growth rates. The fact that the phytoseiid predator P. persimilis is able to control T. urticae in a multiplant system (Nachman (1981, 1999); Gough 1991) makes this predator-prey system an ideal model for understanding the role played by interactions in time and space between organisms at three trophic levels and for assessing various pest management strategies. One way to gain further insight is to incorporate the results of the present study into a realistic simulation model of the system (Nachman, in prep.).
64 Acknowledgements The authors wish to thank Jette Andersen, Trine Søberg Nielsen, Viktor Kiel, and Henning Bang Madsen (Zoological Inst., University of Copenhagen) for their technical assistance during the experiments. Professor David C. Margolies, Kansas State University, and Professor Koos Boomsma, University of Copenhagen, are thanked for their useful comments to the manuscript. The project was supported by grant no. 11-1096-1 from the Danish Natural Science Research Council.
Appendix 1
Estimation of the feeding rate () The rate at which chlorophyll is removed by spider mites is assumed to be proportional to the number of spider mites present at time t (X t), i.e., dL dt
⫽ X t
(13)
where is the extraction rate of chlorophyll per individual spider mite. Let X 0 denote the number of mites released on the plant at time 0, and let it be assumed that growth is exponential with a per capita growth rate r during a time period t. If t is not so long that food becomes limiting it is reasonable to consider both and r as constants, which means that Equation (13) can be solved by integration as
⫽t ⫽t L t ⫽ 兰 X d ⫽ 兰 X 0e rd ⫽ 共X 0e rt ⫺ X 0兲 ⫽ 共X t ⫺ X 0兲 ⫽0 ⫽o r r
(14)
⫽t
兰 X d
⫽0
is called mite-days (cf. Hoyt et al. (1979)) and expresses the cumulated number of mites occupying a spatial unit (in this case an entire plant) from time 0 to t. Mitedays (M) can be computed directly from the initial and terminal number of mites as ⫽t
共X t ⫺ X 0兲t
⫽0
ln共X t/X 0兲
M t ⫽ 兰 X d ⫽
(15)
because r in Equation (14) can be substituted by ln(X t/X 0)/t (cf. Equation (1)).
65 Appendix 2
Estimation of density-dependent birth and death rates According to Equations (3) and (6) D can be written as n
D⫽
c max 兺 A i ⫺ i⫽1
n
兺cA i
i⫽1 n
共c max ⫺ c min兲 兺 A i
i
⫽
L 共c max ⫺ c min兲A
i⫽1
where n
A⫽
兺A
i⫽1
i
Equation (13) can therefore be replaced by dD dt
⫽
dL
1
共c max ⫺ c min兲A dt
⫽
X
共c max ⫺ c min兲A
⫽ sx
(16)
where x = X/A is the density of spider mites and s the per capita rate at which spider mites inflict damage. However, since D cannot exceed 1, it is assumed that s decreases as D approaches unity and becomes 0, when D = 1. This assumption leads to the model dD dt
⫽ s 0共1 ⫺ D兲x
(17)
where s 0 is the value of
c max ⫺ c min when is maximal, i.e. when D is close to 0. The growth rate of the spider mites (r) is also assumed to decrease as D increases. To model this, it is assumed that the per capita birth rate (b) decreases and the per capita loss rate () increases with D. The loss rate combines loss of individuals due to deaths and emigrations. The model chosen to describe the instantaneous growth rate of the spider mite population has the form dx dt
冉
⫽ rx ⫽ b共1 ⫺ D兲  ⫺
共1 ⫺ D兲 ␥
冊
x
(18)
66 where b- is the maximum per capita growth rate (r m) when D = 0.  and ␥ are constants. Equations (17) and (18) cannot be solved explicitly with respect to t, but inserting Equation (17) in Equation (18)yields 1 ⫽ 共b共1 ⫺ D兲  ⫺ 1 ⫺ 共1 ⫺ D兲 ⫺ ␥ ⫺ 1兲 dD s 0 dx
(19)
Integration of Equation (19) yields x⫽
冋
共1 ⫺ 共1 ⫺ D兲 兲 ⫹ 共1 ⫺ 共1 ⫺ D兲 ⫺ ␥兲  ␥
1 b s0
册
(20)
provided that both  and ␥ are positive. x is set equal to 0, if Equation (20) predicts negative values of x (as D → 1).
Appendix 3
Estimation of dispersal rate As a first step, it is assumed that the rate at which individuals move from the donor plant to the bridge-connected recipient plants is assumed to be proportional to the number of individuals on the donor plant (X), the number of bridges (B), and the per capita dispersal rate per bridge () i.e. dR dt
⫽ BX
(21)
The rate of change in the number of individuals on the donor plant is described by Equation (18) as dx dt
冉
⫽ b共1 ⫺ D兲  ⫺
共1 ⫺ D兲 ␥
冊
x ⫽ rx
(22)
where
共1 ⫺ D兲 ␥ is the per capita loss rate, which includes emigration. If r is considered to be constant during an experiment, Equation (22) can, upon integration, be inserted into
67 Equation (21) to yield dR dt
⫽ BX 0e rt
(23)
where R is the number of mites on the recipient plants and X 0 is the number of individuals on the donor plant at the start of an experiment. When the experiment ends at time t, the expected number of individuals on the recipient plants is found as ⫽t
E共R t兲 ⫽ BX 0 兰 e rd ⫽ ⫽0
B BX t共1 ⫺ e ⫺ rt兲 X 0共e rt ⫺ 1兲 ⫽ r r
(24)
where X t is the number of mites counted on the donor plant at the end of an experiment. It means that can be estimated as
ˆ ⫽
rˆR t
共rˆ ⫽ 0兲
ˆ
BX t共1 ⫺ e ⫺ rt兲
ˆ ⫽
Rt BX tt
共rˆ ⫽ 0兲
(25)
(26)
ˆ ˆ r is estimated as rˆ ⫽ bˆ 共1 ⫺ D t兲  ⫺ ˆ 共1 ⫺ D t兲 ⫺ ␥ where D t is the plant injury index of the donor plant at time t. The fraction of individuals that are lost from the donor plant because of emigration to one of the recipient plants is denoted , which means that can be written as = (1 − D) −␥/B. depends on the probability that a mite, “motivated” to emigrate, can find a bridge to cross. If there is a single bridge, the probability is = p s. With B bridges, the likelihood that none of the bridges will be crossed is (1-p s) B, implying that = 1-(1-p s) B. The per capita emigration rate per bridge therefore becomes
⫽
共1 ⫺ 共1 ⫺ p s兲 B兲 B共1 ⫺ D兲 ␥
(27)
A logistic relationship is suggested to model the influence of donor plant condition (D) on the emigration propensity (p s), i.e. ps ⫽
e 0 ⫹ 1D 1 ⫹ e 0 ⫹ 1D
(28)
where 0 and 1 are parameters. Substitution of Equations (27) and (28) in Equa-
68 tion (24) yields E共R t兲 ⫽
共1 ⫺ 共1 ⫹ e 0 ⫹ 1D兲 ⫺ B兲X t共1 ⫺ e ⫺ rt兲. r共1 ⫺ D兲 ␥
(29)
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