DOI: 10.5061/dryad.b8gtht7q4
title: Code and Data for: Importance of environmental productivity and diet quality in intraguild predation

description: In the intricate network of ecological interactions, intraguild predation
 emerges as a fundamental community module incorporating omnivory.
 Classical equilibrium theory predicts the exclusion of the intraguild
 predator and prey at low and high environmental productivity,
 respectively, with the coexistence of both species occurring only at
 intermediate productivity levels. However, empirical studies challenge
 this theoretical prediction, particularly concerning the extinction of
 intraguild prey in highly productive environments. To address this
 enigmatic issue, Diehl (2003) and Abrams and Fung (2010a) explore the
 impact of food quality and propose that low nutritional quality of the
 basal resource stabilizes omnivorous systems. Yet, the influence of
 intermediate consumer quality remains inadequately explored. This study
 employs analytical and numerical bifurcation studies to investigate the
 effects of the quality of two diet types. Various bifurcations, including
 supercritical and subcritical Hopf bifurcations, saddlenode bifurcations
 of periodic solutions, and transcritical bifurcations of periodic
 solutions are observed. These bifurcations are directly linked to the
 destinies of intraguild prey and predators. The results reveal that, in
 highly productive environments, it may not be the intermediate consumer
 but the omnivore that faces extinction. This discovery holds significant
 implications for the conservation and management of omnivorous systems.
description: # Code and Data for: Importance of environmental productivity and diet
 quality in intraguild predation Dataset DOI:
 [10.5061/dryad.b8gtht7q4](10.5061/dryad.b8gtht7q4) ## Description of the
 data and file structure This repository encompasses files corresponding to
 Fig. 1 through Fig. 6, and FigS1 through FigS4, three code scripts in the
 CODE folder, and this README document. The DATA folder contains subfolders
 labeled from Fig1 to Fig6, and FigS1 to FigS4, housing data essential for
 constructing bifurcation diagrams. ### DATA Equilibrium values are
 documented in files named REq.dat, RCEq.dat, RPEq.dat, and RCPEq.dat. Data
 files for insets are prefixed by “Inset,” and data files for a linear
 chain in Fig. 6 are prefixed by “LC_.” Each file for equilibrium values
 begins with four lines specifying the model's parameter values. The
 first line encompasses the intrinsic growth rate, carrying capacity of the
 basal resource, and mortalities of the consumer and predator. The second
 to fourth lines capture information on the attack rate, handling time, and
 conversion efficiency concerning the resource by the consumer, the
 resource by the predator, and the consumer by the predator, respectively.
 The subsequent lines provide information on stability flags (-1 for
 stable, +1 for unstable), followed by the bifurcation parameter and the
 densities of the resource, consumer, and predator at the equilibrium
 point. The bifurcation parameter is the carrying capacity in Fig.1 to
 Fig.6, conversion efficiency *eRP* in Figs. S1 and S2, and conversion
 efficiency *eCP* in Figs. S3 and S4. The files conclude with the
 identifier "-99999." In each DATA folder, files such as
 RCStableLimitCycle, RCUnstableLimitCycle, RPStableLimitCycle,
 RCPStableLimitCycle, and RCPUnstableLimitCycle contain information on
 limit cycles. Data files for insets are prefixed by “Inset,” and data
 files for a linear chain in figure 6 are prefixed by “LC_.” Each of these
 files commences with the first four lines delineating parameter values of
 the model, following the same structure as the files for the equilibrium
 values. The subsequent five lines provide specific details about the limit
 cycle. The fifth line specifies the bifurcation parameter: the carrying
 capacity of the basal resource in Fig.1 to Fig.6, the conversion
 efficiency *eRP* in Figs. S1 and S2, and conversion efficiency *eCP* in
 Figs. S3 and S4. The sixth line contains information on the initial
 densities of the resource, consumer, and predator, along with the period
 of the limit cycle. The successive three lines provide details on the
 bifurcation parameter, and the minimum, mean, and maximum values of the
 resource, consumer, and predator, respectively. These five lines are
 iterated as necessary for a comprehensive description of the bifurcation
 diagram. The files conclude with the identifier “-99999.” ### CODE The
 CODE folder contains three C-language programs. 1.   RCPLimitCycles.c This
 program solves a limit cycle of three species coexistence, using Newton’s
 iteration method. 2.   RCLimitCycles.c This program solves a limit cycle
 of the basal resource and consumer, using Newton’s iteration method. 3.  
 RPLimitCycles.c This program solves a limit cycle of the basal resource
 and predator, using Newton’s iteration method. This folder also includes
 six data files from sampledata3_1.dat to sampledata3_6.dat. The first four
 lines of the files delineate the model's parameter values, similarly
 as in files in folders from Fig1 to Fig6, FigS1 to S4. The fifth line
 describes the number of the candidate’s initial points. The sixth line
 denotes the number of candidate values of the bifurcation parameter (*K*
 in figure 3) and its initial value and increment. From the seventh line,
 candidate initial values are written for the basal resource and consumer
 in sampledata3_1.dat and sampledata3_2, for the consumer in
 sampledata3_3.dat and sampledata3_4, and the predator in sampledata3_5.dat
 and sampledata3_6.dat. To generate Figure 3, for example, numerical
 explorations are conducted using the above programs. For instance,
 RCPLimitCycle.c is executed with sampledata3_1.dat, incorporating four
 candidate initial points, to obtain a coexistence limit cycle for *K*=22.
 Subsequently, substituting the seventh line of sampledata3_2.dat with the
 above result, the program was further executed with sampledata3_2.dat to
 gather information on coexistence limit cycles for *K* values ranging from
 22 to 30. For insights into the limit cycles of the resource and consumer,
 RCLimitCycles.c is utilized with sampledata3_3.dat, and the result is used
 to modify the seventh line of sampledata3_4.dat. Then, RCLimitCycles.c is
 executed with sampledata3_4.dat to find limit cycles covering *K* values
 from 22 to 30. Similarly, information on the limit cycles of the resource
 and predator for the same range of *K* values is obtained by running
 RPLimitCycles.c, first with sampledata3_5.dat, and next with the modified
 sampledata3_6.dat based on the former result. This sequential process is
 iterated for *K* values below 22, ensuring comprehensive coverage for
 Figure 3. The resulting data provide a detailed depiction of the
 bifurcations in the ecological system under investigation. Figs. S1 to S4
 can be created using similar procedures with *eRP* or *eCP* as bifurcation
 parameters instead of *K*. ## Code/software C-language