Introduction

The ability of organisms to increase their populations is crucial to their establishment in a new habitat especially for the invasive species. Local foundress population density and size are two important socio-environmental factors that regulate reproduction and population growth (Kunin 1997a; Danko et al. 2018). The former represents a function of spacing between neighbouring individuals in a finite area and the latter is the number of individuals in a local population (Kunin 1997a). In nature, resources are unevenly partitioned among individuals, and this inequality increases when resources become scarce with increasing population density and size (Krebs 1971; Łomnicki 1978; Rodenhouse et al. 1997; Leips & Travis 1999; Creighton 2005; Goubault et al. 2007). Therefore, it is fundamentally important to understand the nature and extent of population regulation by density- and size-dependent processes in population ecology (Levins 1979; Newton 1994, 1998; Ferrer & Donazar 1996; Rodenhouse et al. 1997; Penteriani et al. 2003).

It is widely reported that population growth is a decreasing function of population density (Harrison & Cappuccino 1995; Turchin 1995; Sibly et al. 2005), inducing a negative density-dependent reproduction associated with present and/or past population densities (Adler & Levins 1994; Sinervo et al. 2000; Rotem & Agrawal 2003; Meylan et al. 2007; Allen et al. 2008; Creighton 2005; Leips et al. 2009). The negative density-dependent reproduction could arise either through decreasing territory quality and resource scarcity which limit the individuals to low provisioning rates at high population densities (Andrewartha & Birch 1954; Pulliam & Danielson 1991; Dhondt et al. 1992; Ferrer & Donazar 1996; Rodenhouse et al. 1997; Both 1998; Kruger & Lindstrom 2001; Danko et al. 2018), or by adjusting the reproductive behaviours of individuals as a response to the varying density within the same habitat (Lack 1954; Both 1998; Fernandez et al. 1998). In a similar fashion the size of a population may also affect its dynamics, especially when conspecifics compete for resources (Krebs 1971; Rodenhouse et al. 1997; Leips & Travis 1999; Creighton 2005; Goubault et al. 2007) and when there is direct interference among individuals (Post et al. 1997). However, most studies on density-dependent reproduction are based on the relationship between the mean reproduction and population density (see Sinclair 1989), without knowing whether density is the only cause of such a relationship or the extent to which individuals respond to the varying density (Kempenaers & Dhondt 1992; Both 1998). It is necessary to understand the role of population size in reproduction (Harris 1984; Saunders et al. 1991) or whether and how population size could mediate density-dependent reproduction.

Nevertheless, the effect of varying population size on population growth has received less attention. This may be because the different notions of population density and size are often highly intercorrelated in most natural populations (Gaston 1994; Saether et al. 2002; Sibly et al. 2005) and are hard to be differentiated (Kunin 1997a). In practice, population density is sometimes used in place of population size when population size is low (Saether et al. 2002; Sibly et al. 2005) and the negative effects of population size are often considered as the results of the density-dependent regulatory process mediated by negative reactions between population density and growth (Murdoch 1994; Turchin 1999). However, local population density and size may have different effects on population dynamics (reviewed in Kareiva 1983; Kunin 1997b). Therefore, ignoring the role of local population size in population regulation may magnify the impact of local population density. Few studies have quantitatively examined how reproduction or population growth is related to the variations of animal population density and size (Saether et al. 2002, 2016), probably because the spacing between individuals constantly shifts as individuals are mobile (Kunin 1997a). To date, little is known about whether population density and size interact and regulate population dynamics in the same way and whether individuals will adjust their reproductive strategies in response to variations of these two factors.

In this study, we used Tetranychus ludeni Zacher (Acari: Tetranychidae) as the model species to investigate how foundress population density and size affected the reproductive performance and population growth by altering the population size of a given population density and vice versa. T. ludeni is an invasive haplodiploid spider mite native to Europe and now globally distributed (Bolland et al. 1998). It attacks many vegetable crops in the world (Bolland et al. 1998; Zhang 2003; Adango et al. 2006; Gotoh et al. 2015). The mite has a short life cycle (10 days at 27–28°C) (Moros & Aponte 1994; Da Silva 2002; Adango et al. 2006), long longevity (up to 28 days) and high reproductive potential (up to 112 eggs) (Adango et al. 2006). Tetranychid females usually mate at emergence and then disperse to establish new colonies with a female-biased sex ratio (Carey & Bradley 1982; Macke et al. 2011). These life history characteristics may encourage the outbreaks of mite populations in the fields or greenhouses.

Based on the knowledge outlined above, we designed a factorial experiment by altering the population density for each test population size and vice versa, and tested two hypotheses: (1) ovipositing females make earlier reproductive effort at high population densities and sizes, and (2) ovipositing females have higher reproductive output and population growth at low population densities and sizes. We recorded daily oviposition patterns and lifetime fecundity and daughter production at various population densities and sizes and computed life table parameters. Information generated in this study will contribute to knowledge on population dynamics in response to foundress population density and size in general and T. ludeni population forecast and management in particular.

Materials and Methods

Statistical analysis

All data were analysed using SAS software (SAS 9.4, SAS Institute Inc., Cary, NC). Rejection level of H₀ was set at P < 0.05. For each treatment, an asymptotic exponential model (Archontoulis & Miguez 2015) was applied to fit the daily cumulative number of eggs and daughters produced (y) (Figures 2 and 3):

where a is the maximum y value, x₀ is the inflection point at which the instantaneous growth rate is maximized, b is the constant growth rate of the curve. We developed a nonlinear regression model to fit data of daily number of eggs and daughters produced (y) (Figures 2 and 3):

where a is the maximum y at age x₀, b is a constant rate controlling the width of the peak. For each model, the estimated parameters were compared between treatments according to the 95% confidence limits (CL), i.e., if the 95% CL overlapped, then there was no significant difference between treatments (Tables S2 and S3). NLIN Procedure was used for modelling.

FIGURE 1.

A diagram of factorial experimental design showing the population densities and sizes.

The life table parameters (y) were analysed by a generalized linear mixed model (GLIMMIX Procedure), with foundress population density and size and their interaction as fixed factors and replicate as a random factor (Figure 4):

where a is the intercept, and b, c and d are the estimated constants of population density (PD) and size (PS) and their interaction (PD×PS), respectively. To minimise the potential effect of decreasing population density and size with the progress of experiment, data recorded within 15 days of foundress lifespan were used for analyses in this study because > 85% of lifetime eggs were laid during this period.

Results

We detected a negative density-dependent production of eggs and daughters (a in eq. 1) at higher foundress population sizes of 5 and 10 but not at the low population size of one foundress (Figures 2 and 3, Table S2). However, the number of eggs and daughters accumulated significantly faster at high population sizes of 5 and 10 than at the population size of only one foundress (b in eq. 1), except at the highest population density and size (Figures 2 and 3, Table S2). The daily number of eggs and daughters produced peaked significantly earlier (< 6 days) at high population sizes of 5 and 10 than that (7.4–8.5 days) at the population size of only one foundress regardless of local population densities (x₀ in eq. 2), with a greater (a in eq. 2) and sharper peak (b in eq. 2) except at the highest population density and size (Figures 2 and 3, Table S3).

FIGURE 2.

Cumulative and daily number of eggs laid by a foundress at different population densities (0.7, 1 and 2 ♀/cm²) and sizes (1, 5 and 10 ♀). Cumulative number of eggs: y = a/{1+exp[-b(x-x₀)]}; daily number of eggs: y = a/{1+[(x-x₀)/b]²}. The arrows indicate the timing of peaks of eggs laid. The estimated parameters of models are listed in Tables S2 and S3.

FIGURE 3.

Cumulative and daily number of daughters produced by a foundress at different population densities (0.7, 1 and 2 ♀/cm²) and sizes (1, 5 and 10 ♀). Cumulative number of daughters: y = a/{1+exp[-b(x-x₀)]}; daily number of daughters: y = a/{1+[(x-x₀)/b]²}. The arrows indicate the timing of peaks of daughters produced. The estimated parameters of models are listed in Tables S2 and S3.

FIGURE 4.

Effects of foundress population density (number of foundresses/cm²) and population size (number of foundresses per leaf square) on life table parameters: (a) net reproductive rate (R₀), (b) intrinsic rate of increase (r_m), (c) generation time (T), and (d) doubling time (Dt). The estimated parameters of models are listed in Table S4.

Population density and size had no significant independent effect on the net reproductive rate (R₀) but their significant negative interaction resulted in a decrease of R₀ when both population density and size increased (Figure 4a, Table S4). Increase in population density caused a significant decrease of intrinsic rate of increase (r_m) whereas increasing population size incurred a significant increase of r_m (Figure 4b, Table S4). In contrast, increasing population density significantly prolonged the mean generation time (T) and doubling time (Dt) whereas increasing population size shortened these two parameters (Figure 4c–d, Table S4).

Discussion

In the present study, T. ludeni exhibited negative impacts of foundress population density and size on reproduction; however, the negative density-dependent reproduction was detected at higher population sizes of 5 and 10 foundresses but not at the low population size of one foundress, and foundresses at higher population sizes maximised their reproduction significantly faster and earlier during their lifespan, regardless of their local densities (Figures 2, 3 and 4a, Tables S2 and S3). The results have three implications. First, spider mites feed upon plant leaves by piercing cells and sucking cell contents, which will induce white or yellow spots or ‘stipplings’ and reduce the photosynthetic surface (Dhooria 2016). The overexploitation associated with quick cumulative excrement on host plants at high population densities may reduce the food availability and quality and thus offspring fitness. Furthermore, spider mites show scramble resource competition with a fast resource depletion when population density or size is high (Krips et al. 1998). Therefore, a decrease of reproduction under the elevated resource competition conditions can be considered as an adaptive strategy of ovipositing foundresses (De Roissart et al. 2016) to reduce the food resource competition of offspring with their mothers or among the offspring (Bonduriansky & Head 2007).

Second, the life history theory assumes that natural selection on organisms enables them to evolve optimal strategies, including the timing of reproduction and number of offspring produced, to maximize or optimize the reproductive fitness by allocating resources to a range of different demands throughout the lifespan (Stearns 1992; Roff 2002). A previous study reports that virgin females adjusted their resource allocations to yield larger sons that could produce more daughters at a higher rate, suggesting that T. ludeni has evolved the resource allocation strategy to compensate the loss of producing daughters for females at virgin stage through their sons' production of more daughters in the next generation (Zhou et al. 2018). Our results provide further evidence that foundresses maximising fecundity and producing more daughters during the early lifespan at higher population densities and sizes (Figures 2 and 3, Tables S2 and S3) could be a fitness advantage, as production of more daughters early enables more dispersing individuals to complete development, reducing future food competition intensity and elevating population growth (Osakabe et al. 2008; Yano 2008; Le Goff et al. 2010; Azandémè-Hounmalon et al. 2014).

Third, population density and size are usually intercorrelated in a population (Gaston 1994; Saether et al. 2002; Sibly et al. 2005) but are hard to be differentiated (Kunin 1997a). Previous studies have demonstrated the individual adjustment of reproductive behaviours in response to the varying density within a habitat (Lack 1954; Both 1998; Fernandez et al. 1998) rather than to the varying population size. In the present study, we differentiated the functions of population density and size and revealed that foundress population density and size interacted and affected the population dynamics in the same way (Figure 4a, Table S4); however, the negative density-dependent reproduction and early onset of reproductive peak occurred only when the population size was high. The results suggest that: (1) the individual adjustment of reproductive behaviours results from the increasing intensity of conspecific competition for resources (Krebs 1971; Rodenhouse et al. 1997; Leips & Travis 1999; Creighton 2005; Goubault et al. 2007) and direct interference among individuals (Post et al. 1997) at higher population sizes, and (2) the population size regulates population-density dependency and individual adjustment. Therefore, population size may have overweighed population density as a major socio-environmental factor regulating future population dynamics in T. ludeni.

The life table of a species summarises the life history characteristics such as survival, development, time of reproduction, and fecundity or female offspring production of individuals in a population (Jervis et al. 2005), reflecting the potential or capacity of population growth. Previous studies reveal that population density is a decreasing function of per capita growth (Harrison & Cappuccino 1995; Turchin 1995; Rotem & Agrawal 2003). We found that the simultaneous increase of population density and size reduced the net reproductive rate (R₀) (Figure 4a). According to the mathematical equations for life table parameter calculation (Jervis et al. 2005), decreasing net reproductive rate (R₀) will result in a smaller intrinsic rate of natural increase (r_m) and longer doubling time (Dt). However, our results only partially agreed with the notion because r_m was higher and Dt was shorter at lower population densities and higher population sizes (Figure 4b and d). These may be attributed to the faster rates of cumulative egg and daughter production and early onset of reproductive peak at higher population sizes (Figures 2 and 3, Tables S2 and S3). The higher r_m reduced the Dt, and higher r_m with relatively small R₀ shortened the mean generation time (T) (Figure 3c; Jervis et al. 2005).

In conclusion, results of this study demonstrate that: (1) both negative population density- and size-dependence may limit T. ludeni reproduction but the effect of population size overweighed that of population density, and (2) ovipositing females are capable to accelerate population growth at higher population sizes through producing more daughters early during their lifespan. Our findings that the population grows faster at low population densities and high population sizes could be used to forecast the future population size and decide the timing of pest control.