The Allometry of Prey Preferences

The distribution of weak and strong non-linear feeding interactions (i.e., functional responses) across the links of complex food webs is critically important for their stability. While empirical advances have unravelled constraints on single-prey functional responses, their validity in the context of complex food webs where most predators have multiple prey remain uncertain. In this study, we present conceptual evidence for the invalidity of strictly density-dependent consumption as the null model in multi-prey experiments. Instead, we employ two-prey functional responses parameterised with allometric scaling relationships of the functional response parameters that were derived from a previous single-prey functional response study as novel null models. Our experiments included predators of different sizes from two taxonomical groups (wolf spiders and ground beetles) simultaneously preying on one small and one large prey species. We define compliance with the null model predictions (based on two independent single-prey functional responses) as passive preferences or passive switching, and deviations from the null model as active preferences or active switching. Our results indicate active and passive preferences for the larger prey by predators that are at least twice the size of the larger prey. Moreover, our approach revealed that active preferences increased significantly with the predator-prey body-mass ratio. Together with prior allometric scaling relationships of functional response parameters, this preference allometry may allow estimating the distribution of functional response parameters across the myriads of interactions in natural ecosystems

Functional Response of Terrestrial Predators

In chapter 2.1. we addressed the question if metabolic or foraging models predict more accurate the energy fluxes between population levels. We calculated from our experimental results, the field encounter rates and energy fluxes between predator and prey and compared the predictive power of both metabolic and foraging model. Our results show that despite clear power law scaling of metabolic and per capita consumption rates with body mass (according to the MTE), the per link predation rates for individual prey followed hump-shaped relationships with predator-prey body-mass ratios (according to OFT). Thus, in contrast to predictions of the metabolic models, our findings suggest that for any prey species per link and total energy fluxes are highest to its predators of intermediate body size than to its largest predators. In chapter 2.2. we extended the approach of chapter 2.1., to test if our previous results are of broad generality. We studied the functional responses in dependence on allometric scaling. These scaling relationships suggest that non-linear interaction strengths can be predicted by the knowledge of predator and prey body masses and integrating these relationships into population models will allow predicting energy fluxes, food web structures and the distribution of interaction-strengths across food web links based on the knowledge of the body masses of interacting species. In chapter 2.3. we addressed the question how increased temperatures affect ingestion and metabolic rates of terrestrial arthropod predators, and how warming affects the interaction strengths and consequently the stability of the system. We could show that warming does not only increase the metabolic requirements of the predators, but also that the temperature effects were weaker on ingestion than on metabolism. From the experimental short term per capita interaction strengths we calculated long term interaction strengths, and these predicted long term per capita interaction strength decreased with temperature. Our results indicate that on the one hand warming could increase intrinsic population stability while on the other hand decreasing ingestion efficiencies increase the extinction risk of the predators. To summarize, warming is expected to have complex and in some cases drastic effects on predator-prey interactions and food web stability. Our approach of chapter 2.3 presents a simplistic and mechanistic null model of warming effects on predator prey interactions in which thermal adaptation effects need to be included in future studies. In chapter 2.4. we extended the approach of chapter 2.3 to varying prey densities including the prey trait “movement pattern” into our experiments. Here we present strong evidence that warming imposes energetic restrictions on arthropod predators by decreasing their ingestion efficiency. Consequently, warming should increase stability of the populations. Our results also confirm the suggestion that warming increases the risk of predator starvation due to decreased ingestion efficiencies. The mechanistic functional response framework of chapter 2.4. may allow making detailed predictions about consequences of increasing temperature on predator-prey interaction strengths depending on metabolic and behavioural constrains. In chapter 2.5. we investigated the influence of changes in habitat structure on the functional response and in additional experiments the prey behaviour. We show that adding habitat structure alters the functional response type II to type IV (roller-coaster). Additional experiments on the prey behaviour suggest that the decreased consumption rates at high prey densities can be explained by aggregative defence behaviour. Analysing the net energy gain of the predators in both treatments showed that with habitat structure the predators’ energy net gain was limited at intermediate prey densities where prey aggregation reduced the consumption rate. Our results stress the importance of both, habitat structure and prey behaviour in shaping the functional response in soil-litter predator-prey interactions

Allometric functional response model: body masses constrain interaction strengths

1. Functional responses quantify the per capita consumption rates of predators depending on prey density. The parameters of these nonlinear interaction strength models were recently used as successful proxies for predicting population dynamics, food-web topology and stability. 2. This study addressed systematic effects of predator and prey body masses on the functional response parameters handling time, instantaneous search coefficient (attack coefficient) and a scaling exponent converting type II into type III functional responses. To fully explore the possible combinations of predator and prey body masses, we studied the functional responses of 13 predator species (ground beetles and wolf spiders) on one small and one large prey resulting in 26 functional responses. 3. We found (i) a power-law decrease of handling time with predator mass with an exponent of -0 center dot 94; (ii) an increase of handling time with prey mass (power-law with an exponent of 0 center dot 83, but only three prey sizes were included); (iii) a hump-shaped relationship between instantaneous search coefficients and predator-prey body-mass ratios; and (iv) low scaling exponents for low predator-prey body mass ratios in contrast to high scaling exponents for high predator-prey body-mass ratios. 4. These scaling relationships suggest that nonlinear interaction strengths can be predicted by knowledge of predator and prey body masses. Our results imply that predators of intermediate size impose stronger per capita top-down interaction strengths on a prey than smaller or larger predators. Moreover, the stability of population and food-web dynamics should increase with increasing body-mass ratios in consequence of increases in the scaling exponents. 5. Integrating these scaling relationships into population models will allow predicting energy fluxes, food-web structures and the distribution of interaction strengths across food web links based on knowledge of the species' body masses

Kalinkat et al. 2011 data

Data on a series of laboratory feeding experiments with ground beetles and cursorial spiders of different sizes as predators. Each trial contained one predator individual and two prey species of different body sizes. <br

Conceptual graphic showing allometric relationships in the single-prey functional response parameters capture rate, handling time and the scaling exponent <i>q</i> as revealed by the previous study of Vucic-Pestic and colleagues [<b>18</b>].

<p>Conceptual graphic showing allometric relationships in the single-prey functional response parameters capture rate, handling time and the scaling exponent <i>q</i> as revealed by the previous study of Vucic-Pestic and colleagues <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0025937#pone.0025937-VucicPestic1" target="_blank">[<b>18</b>]</a>.</p

Figure 1

<p>Conceptual illustrations of (a) type II and type III (single-prey) functional responses and the implications of variance in the scaling exponent <i>q</i> as well as consequences for <i>absolute</i> prey consumption and (b–e) preferences and switching in two-prey (here: <i>j</i> and <i>k</i>) experiments: b) “Traditional” preference plot with <i>relative</i> consumption depending on relative density of prey <i>j</i>: Consumption is strictly density-dependent (the diagonal solid line), or exhibits preferences for prey <i>j</i> (upper, long-dashed line) or switching behaviour (sigmoid, dotted line). c–e) Novel null model based on two-prey functional responses (Equation 3) with varying capture rate ratios (<i>b_ij</i>/<i>b_ik</i> with 0.01<<i>b_ij</i><10 and <i>b_ik</i> = 1) for the two prey in c) type II (<i>q_ij</i> = <i>q_ik</i> = 0) and d) type III functional responses (<i>q_ij</i> = <i>q_ik</i> = 1). e) Gradual conversion of type II to type III functional responses when both prey are consumed with the same capture rate (<i>b_ij</i> = <i>b_ik</i> = 1). Constant handling time is used in figures c–e (<i>T_hij</i> = <i>T_hik</i> = 0.1). Note that the diagonal of strictly density-dependent consumption as the traditional null model (panel b) only emerges if both prey are consumed with exactly the same type II functional response (solid black lines in figures c and e).</p

Active preferences (partial residuals) for the larger prey of (a, c) spiders and (b, d) beetles depending on the body-mass ratio between the predator and the larger prey (a, b) and the square of relative initial densities (c, d).

<p>Parameters: a) slope = 5.674, (s.e. ±2.594) intercept = 7.699 (s.e. ±4.734); b) slope = −0.002 (s.e. ±0.0004) intercept = 7.699 (s.e. ±4.734); c) slope = 46.575 (s.e. ±8.644), intercept = 5.227 (s.e. ±4.402); d) slope = 0.005 (s.e. ±0.0008) intercept = 5.227 (s.e. ±4.402).</p

Single prey functional responses as a function of predator-prey body mass ratios from previous study[<b>18</b>] for the following predator-prey combinations: a) wolf spiders – <i>Drosophila</i>, b) ground beetles – <i>Alphitobius</i>, c) wolf – spiders – <i>Heteromurus</i> and, d) ground beetles – <i>Drosophila</i>.

<p>Parameters applied for these models are given in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0025937#pone-0025937-t001" target="_blank">Table 1</a>. Combining of the single-prey functional responses for one large and one small prey allowed calculating predictions of the allometric functional response models for the two-prey preference experiment with e) spiders (body-mass range from 1 to 200 mg) with <i>Drosophila</i> as large prey and <i>Heteromurus</i> as small prey, and f) beetles (body-mass range from 1 to 600 mg) with <i>Drosophila</i> as small and <i>Alphitobius</i> larvae as large prey. The coloured lines indicate the six species (i.e., body size classes) that were tested empirically in this study (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0025937#pone-0025937-g004" target="_blank">Fig. 4</a>). Note the difference between <i>absolute</i> consumption in plots a–d while 3 e and f show <i>relative</i> consumption on the x- and z-axes. Note that for the two-prey plots (3 e and f) the predator-prey body-mass ratio (<i>R</i>) on the y-axes relates to the ratio between the predator and its larger prey.</p

Foraging theory predicts predator-prey energy fluxes

1. In natural communities, populations are linked by feeding interactions that make up complex food webs. The stability of these complex networks is critically dependent on the distribution of energy fluxes across these feeding links. 2. In laboratory experiments with predatory beetles and spiders, we studied the allometric scaling (body-mass dependence) of metabolism and per capita consumption at the level of predator individuals and per link energy fluxes at the level of feeding links. 3. Despite clear power-law scaling of the metabolic and per capita consumption rates with predator body mass, the per link predation rates on individual prey followed hump-shaped relationships with the predator-prey body mass ratios. These results contrast with the current metabolic paradigm, and find better support in foraging theory. 4. This suggests that per link energy fluxes from prey populations to predator individuals peak at intermediate body mass ratios, and total energy fluxes from prey to predator populations decrease monotonically with predator and prey mass. Surprisingly, contrary to predictions of metabolic models, this suggests that for any prey species, the per link and total energy fluxes to its largest predators are smaller than those to predators of intermediate body size. 5. An integration of metabolic and foraging theory may enable a quantitative and predictive understanding of energy flux distributions in natural food webs

Parameters of the allometric two-prey functional response model as the null model for the preference experiment (Figs. 3 and 4): N = number of replicates; <i>M_P</i> = average predator mass [mg]; <i>R</i> = average predator-prey body-mass ratio; <i>q</i> = scaling exponent; * parameters taken from ref [18].

<p>Parameters of the allometric two-prey functional response model as the null model for the preference experiment (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0025937#pone-0025937-g003" target="_blank">Figs. 3</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0025937#pone-0025937-g004" target="_blank">4</a>): N = number of replicates; <i>M_P</i> = average predator mass [mg]; <i>R</i> = average predator-prey body-mass ratio; <i>q</i> = scaling exponent; * parameters taken from ref <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0025937#pone.0025937-VucicPestic1" target="_blank">[18]</a>.</p