Elizabeth King, Department of Ecology & Evolution, University of California, Irvine, CA 92697-2525, USA. Tel.: (949) 824 5994; fax: (949) 824 2181; e-mail: firstname.lastname@example.org
Many models of life history evolution assume trade-offs between major life history traits; however, these trade-offs are often not found. The Y model predicts that variation in acquisition can mask underlying allocation trade-offs and is a major hypothesis explaining why negative relationships are not always found between traits that are predicted to trade-off with one another. Despite this model’s influence on the field of life history evolution, it has rarely been properly tested. We use a model system, the wing dimorphic cricket, Gryllus firmus as a case study to test the assumptions and predictions of the Y model. By experimentally altering the acquisition regime and by estimating energy acquisition and energy allocation directly in this species, we are able to explicitly test this important model. Overall, we find strong support for the predictions of the Y model.
The Y model was most clearly articulated by van Noordwijk & de Jong (1986). Their model consists of two traits (x1 and x2) drawing from a common resource pool and includes variation in both acquisition (the size of the total resource pool = T) and proportional allocation (proportion of resources allocated to x1 = P) of resources. For a fixed acquisition value, variation in allocation leads to a negative covariance between traits. However, if some individuals in a population are able to acquire more resources than others, they will have a larger resource pool and can allocate more resources to both traits involved in a trade-off. This variation in acquisition can lead to a positive correlation between these traits when measured across individuals in a population even while there is a functional trade-off within individuals. The Y model makes the important assumption that variances in acquisition and in allocation are independent. Specifically, this model predicts that the strength and sign of the covariance between the two traits depends on relative variation in acquisition and relative variation in allocation and can be predicted from the following equation (van Noordwijk & de Jong, 1986):
where is the covariance between x1 and x2, is the variance in acquisition, is the variance in allocation, μT is the mean of acquisition and μP is the mean of allocation. From this equation, it can been seen that if the variance of acquisition () is zero, the covariance will be negative (). If the reverse is true and variance of allocation () is zero, the covariance will be positive (). We do not generally expect populations to show zero variance in either acquisition or allocation, therefore, two more informative predictions are as following:
1 For a constant , , and increasing variance in acquisition () makes the correlation between x1 and x2 more positive.
2 For a constant , , , and increasing variance in allocation () makes the correlation between x1 and x2 more negative.
For most life history trade-offs, it is assumed that energy is the major limiting resource, and in this case, total acquisition will be the total energy acquired by an organism and allocation will be the proportion of that energy allocated to various traits. Estimating energy acquisition can be challenging. Energy acquisition is a complex trait that is potentially influenced by many factors, including food availability, time spent foraging, the rate of digestion and absorption of nutrients, and the efficiency of digestion and absorption of nutrients (for reviews see Ricklefs, 1991; Weiner, 1992; Hammond & Diamond, 1997). In the past, energy acquisition has been estimated by a number of different methods, including total mass (Christians, 2000; Brown, 2003; Uller & Olsson, 2005), size at a given age (Biere, 1995; Dudycha & Lynch, 2005), growth rate (Tessier & Woodruff, 2002), absorption efficiency of macronutrients (Zera & Brink, 2000) and feeding rate (Ernande et al., 2004). Estimating allocation includes similar challenges. Studies of differential resource allocation typically do not measure allocation in units of energy. For example, a study of the trade-off between reproduction and survival might use egg number and/or egg size as an estimate for reproductive output and lifespan as a measure of survival. These types of measures are assumed to be correlated with the amount of energy allocated to different functions. However, life history traits are complex and will often involve many factors not accounted for by these simple measures. Any test of the Y model requires a more complete estimate of acquisition and allocation in units of energy.
This task is difficult enough in a single population let alone for many different populations or species. Therefore, researchers aiming to test this model typically must make assumptions regarding acquisition and/or allocation. For example, Glazier (1999) attempted to test the Y model by comparing laboratory and field studies. He made the assumption that variation in acquisition will be minimized in the less variable conditions of the laboratory, and therefore, negative correlations will be found more often in laboratory studies. This hypothesis was consistent with what he found in a review of the literature, and he concluded the Y model was supported. However, the opposite claim has also been made. Variation in acquisition may be minimized in low resource environments (Messina & Fry, 2003; Ernande et al., 2004), and negative correlations may be found more often in harsher, more resource-stressed conditions, such as those in the field (Tuomi et al., 1983; Bell & Koufopanou, 1986; Reznick, 1985). Additionally, because the Y model predicts that the trade-off function will depend on the mean and variance of allocation as well, Glazier (1999) also assumes that the mean and variance of allocation are not also changing under laboratory conditions. Without explicitly measuring acquisition and allocation, we can only make hypotheses regarding the causes of changes in observed trade-off patterns.
In this study, we take the approach of utilizing the well-studied trade-off between flight capability and reproduction in the sand cricket, Gryllus firmus as a case study to test the Y model. We first estimate energy acquisition and allocation for a set of G. firmus individuals and use these data to formulate a model to predict these quantities from organ masses alone. Subsequently, we experimentally alter variation in acquisition by rearing individuals on three different food levels and utilize our predictive model to estimate acquisition and allocation to directly test the assumptions and predictions of the Y model.
Most studies of this trade-off in wing dimorphic insects utilize ovary mass as a proxy for allocation to reproduction and DLM mass as a proxy for allocation to flight capability. The masses of these organs are likely correlated with allocation to reproduction and flight capability. However, because allocation is measured as a proportion, it is important that an estimate of allocation accurately reflects the relative amounts allocated to flight capability and reproduction. In G. firmus, ovaries are an order of magnitude larger than DLMs, but this difference does not accurately reflect the relative allocation to reproduction and flight capability.
The energy allocated to ovaries encompasses a majority of the allocation to reproduction in females of this species. Gryllus firmus females retain their eggs when kept as virgins, and the mass of ovaries at 7 days of age past the final ecdysis is known to correlate very highly (r >0.99) to total fecundity (Roff, 1994), allowing ovary mass to serve as a reliable index of fecundity. Energy devoted to producing eggs is a good estimate of allocation to reproduction in this species. Gryllus firmus, like most insects, do not care for their offspring and incur few energy costs beyond those required to produce eggs (Gillott, 1995). Therefore, an estimate of the energy allocated to ovaries is a good proxy for allocation to reproduction.
Allocation to flight capability is a complex trait and is not encompassed by the energy allocated to DLMs alone. Previous studies have shown that LW females have higher levels of biosynthesis of lipids and higher levels of triglycerides than SW females (Zera & Larsen, 2001; Stirling et al., 2001; Zera, 2005). The increased accumulation of triglycerides in the LW morph prepares it for flight, because triglycerides are the main flight fuel in orthopterans (Gillott, 1995). Macropterous (LW) females also allocate more protein and lipid to the soma, whereas SW females allocate more protein and lipid to ovaries (Zera & Zhao, 2006). In addition to these differences in the allocation of nutrients, previous studies have suggested that large DLMs may have a high maintenance cost. Female macropters (LW) with functional DLMs were found to have a significantly higher whole-organism metabolic rate than SWs (Crnokrak & Roff, 2002; Nespolo et al., 2008), and functional DLMs have a higher metabolic rate than histolyzed or underdeveloped DLMs (Zera et al., 1997). However, none of the aforementioned studies have determined the specific relationship between the mass of the DLMs and increased allocation of nutrients to the soma and/or an increased maintenance cost. An accurate proxy for allocation to flight capability must include the higher allocation to the soma and the possible higher maintenance cost of functional DLMs.
Each cricket was dissected, and the DLMs, ovaries and remaining body tissue were dried (at 50 °C for 24 h) and weighed to the nearest 0.0001 g. The state of muscle histolysis was also scored for each dissected cricket using a three-level scale as earlier (2 = no evidence of histolysis 1 = partially histolyzed, 0 = totally histolyzed or absent). For the purpose of testing the Y model, we are interested in the direct relationship between ovary mass and DLM mass, and we therefore restrict our analysis to only individuals in categories 1 and 2. Individuals in category 0 completely lack DLMs, and therefore there is no among-individual variance in DLM mass whereas among-individual variance in ovary mass remains. Although these individuals are informative when examining differences between the groups of individuals with and without muscles, this was not the focus of this study. Our focus was instead the covariance between DLM mass and ovary mass. Including individuals that completely lack muscles but still vary in ovary mass could obscure the direct relationship between ovary mass and DLM mass.
Estimating energy acquisition and allocation
We converted tissue masses into units of energy to more directly estimate acquisition, allocation to reproduction and allocation to flight capability. Using detailed physiological assays, we developed a predictive model to estimate energy acquisition and energy allocation to reproduction and flight capability from organ masses alone. Details regarding the physiological assays and development of this model can be found in the Supporting Information (Appendix S1). Using the energy content, synthesis costs and maintenance costs of each tissue, the model allows us to predict the amount of energy allocated to reproduction from ovary mass and the amount of energy allocated to flight capability from DLM mass. Because only two functions are considered (flight capability and reproduction), the proportion allocated to one function (P) is one minus the proportion allocated to the other function. Thus, we only require one measure of allocation, P. The choice between allocation to flight capability or to reproduction is arbitrary and herein we use allocation to flight capability.
We estimated acquisition (T) as the total energy allocated to reproduction plus the total energy allocated to flight capability. The Y model only considers two traits, and therefore, the appropriate measure of acquisition to test this simple model should only include the total resource pool available to these two traits. There are more complex models that consider trade-offs involving multiple traits (e.g. de Laguerie et al., 1991; de Jong, 1993; Worley et al., 2003) where acquisition is defined as the total resource pool acquired by the individual; however, those models are not the focus of this study.
Predictions 1 and 2
1 For a constant , and , increasing variance in acquisition () makes the correlation between x1 and x2 more positive.
2 For a constant , and , increasing variance in allocation () makes the correlation between x1 and x2 more negative.
In our study, we experimentally alter variation in acquisition by rearing individuals on three different food levels. We can test prediction 1 by comparing the correlation measured across food levels with the correlations within food levels. Specifically, we predict that correlations across food levels will be more positive because variance in acquisition will be high. In contrast, within each food level, we predict more negative correlations because variance in acquisition will be lower. Prediction 2 can be tested by restricting variation in allocation. This restriction is easily achieved in this system as a result of our measurement of the state of muscle histolysis. By including only individuals with fully developed, nonhistolyzed muscles (i.e. DLM category 2) in the analysis, we effectively constrain variation in allocation. We can then compare the correlations from the data set including only individuals with fully developed DLMs with the correlations from the full data set (i.e. DLM categories 1 and 2), predicting a higher (more positive) correlation in the former.
To confirm these changes in the relative variation in acquisition and allocation, we used the coefficient of variation to correct for correlations between the means and variances (Zar, 2010). However, the coefficient of variation is not expected to perform well when the mean is near zero. In this case, small changes in the mean have large effects on the coefficient of variation. Because we measure allocation as a proportion, this is a potential problem. We used a simulation to show that the coefficient of variation for a proportion will be most influenced by changes in the mean when the mean is below 0.2 (data not shown). Our mean values are all above 0.5 and therefore will not be strongly influenced by changes in the mean. We used a Bonferroni procedure to estimate simultaneous confidence intervals described by Miller & Feltz (1997) as a multiple comparisons test for differences between our estimated coefficients of variation. We also tested for differences in the raw sample variance using the multiple comparisons procedure outlined in Zar (2010). We can then compare the observed correlations to changes in the coefficients of variation in acquisition and allocation.
We computed Pearson’s correlation coefficients between DLM mass and ovary mass for the following data sets (Fig. 1): (i) the full data set including all individuals across all food levels, (ii) all individuals in the low food treatment, (iii) all individuals in the 50% food treatment, (iv) all individuals in the ad libitum treatment, (v) individuals with nonhistolyzed muscles across all food levels, (vi) individuals with nonhistolyzed muscles in the low food treatment, (vii) individuals with nonhistolyzed muscles in the 50% food treatment and (viii) individuals with nonhistolyzed muscles in the ad libitum food treatment. We test for differences between these estimated correlation coefficients using Fisher’s z transformation followed by Tukey’s multiple comparisons (Zar, 2010).
The correlations between ovary mass and DLM mass within food treatments did not differ significantly from one another for the full data set or for the data set restricted to nonhistolyzed DLMs and most are significantly negative (Table 1). As predicted, the coefficient of variation in acquisition is significantly higher across food treatments than within food treatments for both data sets (Table 1). For both data sets, the correlation across food treatments was also significantly more positive than the correlations within food treatments as would be expected by the Y model (Table 1).
Table 1. Sample sizes (N), variances and coefficients of variation for acquisition (T) and allocation (P). are correlations between dorso-longitudinal muscle (DLM) mass (x1) and ovary mass (x2). Different superscripts indicate significant differences for comparisons between the eight different data sets. P values indicate significant differences from zero for the correlation coefficients ().
Full data set
All food levels
Nonhistolyzed DLMs only
All food levels
The coefficients of variation in allocation for the data set including only individuals with nonhistolyzed DLMs are all significantly lower than those for the full data set, and the raw variances follow the same pattern (Table 1). As predicted, this decrease in variability in allocation corresponded to significantly less negative correlations within food treatments for the data set restricted to individuals with nonhistolyzed DLMs compared to those for the full data set (Table 1). In addition, the correlation across food treatments from the restricted data set is significantly more positive than the correlation across food treatments for the full data set (Table 1). The correlation for the data set in which variation in allocation is restricted (only nonhistolyzed DLMs) but variation in acquisition is inflated (across food levels) is of particular interest because it is significantly positive (Table 1) and completely obscures the trade-off, as predicted by the Y model.
Does equation 1 accurately predict the covariance between dorso-longitudinal muscle mass and ovary mass?
The aforementioned tests took advantage of marked changes in the variance of acquisition and allocation. However, we know that more subtle changes in both the mean and the variance of acquisition and allocation will influence the observed covariance. We can test the performance of the predicted relationship between acquisition and allocation and the covariance by comparing predicted covariances from eqn 1 using our values of P and T (in units of energy) with our observed covariances between DLM mass and ovary mass for all the examined data sets. Equation (1) performs very well: the predicted values explain 94% of the variance in the observed covariances as measured by linear regression (R2 = 0.94, d.f. = 6, P <0.001; Fig. 2). When the full data set is examined separately from the data set with only individuals with nonhistolyzed muscles, eqn 1 performs well for the full data set (R2 = 0.91, d.f. = 3, P =0.05) but not for the data set with only individuals with nonhistolyzed muscles (R2 = 0.004, d.f. = 3, P =0.94). This result indicates that the fit is driven by differences within the full data set and the difference between the set of points from the restricted data set (lower variance in allocation) and the full data set. It is possible that the low variability in the restricted data set is contributing to the poor fit within that data set.
Are acquisition and allocation independent as assumed by the Y model?
A major assumption of the Y model is that acquisition and allocation of resources are independent. We tested this assumption by testing whether acquisition and allocation were significantly correlated within and across food levels. The null expectation of a correlation of zero was first confirmed with a simulation model (data not shown). The proportion of resources allocated to flight capability was significantly correlated with total acquisition in all examined data sets (all food levels: r4146 = −0.46, P <0.001, Low food: r1390 = 0.07, P =0.009, 50% food: r1375 = −0.26, P <0.001, ad libitum food: r1377 =−0.56, P <0.001). The relationship between acquisition and allocation was weaker within the lower food levels and while still significant, was near zero in the low food treatment. In all cases except the latter, higher acquisition was associated with lower proportional allocation to flight capability and higher proportional allocation to reproduction.
We found strong support for the predictions of the Y model in this system. As predicted, the correlation between DLM mass and ovary mass was less negative in the data set where we experimentally inflated variability in acquisition by rearing individuals on different food levels. In addition, when we restricted variability in allocation by considering only individuals with nonhistolyzed muscles, the correlation also became less negative. Despite these changes, most correlations remained negative, indicating that variability in allocation was still the dominant influence. However, when we inflated variability in acquisition by looking across food levels and reduced variability in allocation by including only individuals with nonhistolyzed DLMS, the correlation between DLM and ovary mass did become significantly positive, as predicted, completely obliterating the trade-off. Previous tests have also found support for the predictions of the Y model, but they have had to make various assumptions regarding acquisition and/or allocation because of the difficulty associated with estimating these values (Glazier, 1999; Christians, 2000; Brown, 2003). Ours is the first test in which both acquisition and allocation have been explicitly estimated in units of energy and directly compared to the predictions of the Y model.
We also tested an assumption of the Y model that acquisition and allocation are independent of one another. We found that acquisition and allocation were significantly correlated in all of our examined data sets, with the highest correlations across food levels and at the high food treatment. The correlation across food levels indicates that G. firmus shows phenotypic plasticity in allocation in response to changes in resource availability. Individuals with access to higher food levels allocate proportionally more to reproduction. This relationship was maintained within ad libitum and 50% food levels where individuals that were able to acquire more resources tended to allocate proportionally more to reproduction. The trade-off between DLM mass and ovary mass is evident in all food levels as shown by significant negative correlations; however, the correlation between acquisition and allocation indicates that the amount allocated to different functions changes depending on the amount of resources an individual acquires. The Y model still performed well when predicting the covariance between DLM mass and ovary mass, despite the violation of the assumption of independence. Christians (2000) also found that acquisition and allocation were correlated in his test of the Y model in waterfowl. However, he was also still able to find support for the predictions of the Y model. Thus, the Y model seems to be robust to the assumption of independence at least for moderate correlations between acquisition and allocation. However, the degree to which the predictions of the Y model are expected to change if the assumption of independence is relaxed has yet to be explored and could be the subject of future theoretical work.
The Y model is commonly suggested as an explanation when the relationships between life history traits deviate from expectations (e.g. Spitze et al., 1991; Genoud & Perrin, 1994; Yampolsky & Ebert, 1994; Reznick et al., 2000; Jordan & Snell, 2002; Messina & Fry, 2003; Ernande et al., 2004; Vorburger, 2005). In addition, acquisition is often also defined as ‘condition’ or ‘quality’ in the literature, especially in regards to male condition and sexual selection (e.g. Rowe & Houle, 1996; Hunt et al., 2004). Variation in condition (or acquisition) has been used to explain the maintenance of genetic variation in sexually selected traits as well as other condition-dependent traits (Rowe & Houle, 1996). It is therefore critical to evaluate the performance of this fundamental model. Previous studies attempting to test the Y model have been challenged by the difficulties associated with quantifying acquisition and allocation (Glazier, 1999; Christians, 2000; Brown, 2003). Our study is the first to use physiological methods to explicitly estimate energy acquisition and energy allocation to test this influential model. Using this approach, we were able to show robust support for the predictions of the model, validating the use of this model as a potential explanation for variability in trade-off patterns in natural populations.
This work was supported by National Science Foundation grant DEB-0807657, a SICB Grant-in-Aid-of-Research and the University of California, Riverside. We thank Christopher Caridi for countless hours of data acquisition and laboratory assistance. Dr. Mark A. Chappell provided invaluable assistance with our metabolic equipment and helpful advice regarding our physiological measurements. Two anonymous reviewers provided comments that greatly improved this paper.