Some related species give rise to interspecies hybrids with hemiclonal inheritance. The gametes of such hybrids transfer the set of hereditary information of one of the parental species. The water frog, Pelophylax esculentus, is an example of such hybrids. The hemiclonal hybrids together with their parental species form a biosystem for which the suggested name is Hemiclonal Population System (HPS). The phenomenon of interspecific hemiclonal reproduction of water frogs has been intensively explored for several decades, but insufficient study has been devoted to the mechanisms of the composition constancy and ecological stability of their population systems. In this paper we focus on sustainability and possible results of transformations (in terms of different genetic forms and of population dynamics of each of these forms) of HPSs that consist of diploid representatives. By means of a simulation model we evaluated the long-term consequences of parameters that were derived from empirical research on a natural HPS at a particular brief time-period. This research was carried out in the region of eastern Ukraine, the so-called Siverskyi Donets center of diversity of the Pelophylax esculentus complex. Our study describes the development of a dynamic typology of the HPS by principal component analysis of data generated by the simulations. We investigate the space of the possible states of the HPS. The simulations helped to split this state-space into six areas of stability, each of which corresponds to a different type of stability. Before conducting the simulation study we assumed there were only four truly stable states. Two new states were identified as a result of using this model.
The processes of transformation of natural biological systems (populations, ecosystems etc.) are an important challenge for modern science. In many cases these processes are not readily available for direct study (e.g. because of their long duration). In such cases we have to reconstruct their transformation models based on (1) the observed diversity of their natural states, (2) our hypothesis of what controls the change of such states, and (3) available empirical data. A simulation model plays a key role in such studies. Thanks to it, we can determine the possible directions of transformation of the target systems and build their typology. One of the insufficiently studied types of biological systems are those that create species capable of interspecies hybridization and their hemiclonal hybrids. Reproduction of hemiclonal hybrids occurs in biological systems which have been described as Hemiclonal Population Systems (HPSs) [15]. Water frogs are a typical model organism for studying such systems.
This paper describes a computer simulation study of Hemiclonal Population Systems
(HPS) of water frogs. First we introduce the peculiar characteristics of these
biosystems. In the next section we indicate the advantages of computer simulation as a
modelling tool together with the specific characteristics of the model presented here.
Computer simulation has been described as the collaboration between experimenting and
modelling [
Most life forms which arise from sexual reproduction exhibit the typical biosystem hierarchy in which organisms exist as part of populations that form species. In these populations, genetically unique individuals produce sex cells (gametes), which bear a unique genome (holistic unitary complex of hereditary information) resulting from recombination of two parental genomes (Fig.1 A). The consequence of this is the existence of a population gene pool (common pool of genes). Populations of organisms with clonal reproduction, on the other hand, consist of clones, i.e. sets of genetically identical organisms (with accuracy limited by the error rate of copying during reproduction). These populations are presented as a set of relatively isolated lines consisting of genetically identical maternal and child individuals.
This work is dedicated to a relatively rare type of population reproduction which
differs from the two mentioned options. It is characteristic of hybridogenic complexes
of species. This complex consists of two parental frog species [
The differences between the genomes of the parental species lead to the fact that production of normal gametes through recombination becomes impossible. Breeding hybrids is made possible by specific changes in their life cycle (Fig. 1B). One parent genome of such hybrids is eliminated from the germline cells (i.e. those cells which subsequently form the sex cells, gametes). Thereafter, the second parental genome undergoes endoreduplication (i.e. doubles without cell division). This gives rise to cells with two genomes that are identical (with accuracy limited by the errors of copying). They form genetically identical gametes.
Hemiclonal hybrids differ both from usual organisms with recombinant reproduction and from clonal organisms. A HPS, where hemiclonal hybrids are reproduced, differs from normal recombinant and from clonal populations. The features of a HPS are as follows [15]: — Cooperative reproduction of individuals that differ in species composition of their genomes (i.e. representatives of parental species and hybrids of various genome compositions); — Vertical transmission of the clonal genome lines, which can combine with other recombinant or clonal genomes; — In the HPS, which includes individuals of the parental species, these individuals support the existence of a pool of recombining genes (gene pool), which corresponds to the gene pool of conventional monospecific populations; — Cases of limited interspecies recombination are observed (i.e. transferring of fragments of genetic information from the genome of one parental species into the gene pool of another parental species).
The most common typology of a HPS is associated with an indication of the parental species and diploid hybrids and/or triploid hybrids, which are included in their composition. The presence of P. esculentus is indicated by the letter E, letter L stands for P. lessonae, and letter R for P. ridibundus. The presence of polyploid P. esculentus is denoted by the letter p. Thus, L-E-HPS consists of P. lessonae and diploid P. esculentus, and R-E-HPS consists of P. ridibundus and diploid P. esculentus. Clonality of a genome is designated by putting its symbol in brackets. The water frogs' sex determination system is similar to that in humans. The structure of the female genome includes the sex chromosome X. Individuals that have two female genomes are female (♀). The structure of the male genome includes the sex chromosome Y. Individuals with one female and one male genome are male (♂).
Consider the simplest example of a L-E-HPS (Fig. 2), which includes a parent species (P. lessonae) as well as hybrids which clonally transmit the female P. ridibundus genome (XR). Hybrids are reproduced when crossed with the parental species individuals: ♀XL(XR)×♂XLYL → ♀XL(XR) : ♂YL(XR); ♀XLXL×♂YL(XR) → ♀XL(XR).
Different regions of the P. esculentus complex distribution are characterized by HPSs
of various compositions [
By crossing hybrids, which transmit genomes of the same parental species, there may occur representatives of these species. Typically, these individuals die before sexual maturity: ♀XL(XR)×♂YL(XR) → ♀XRXR → †.
Different forms of frogs in a HPS differ in their vitality and fertility. The composition
of zygotes, tadpoles and frogs of the different ages in the same HPS may vary
significantly. Another feature of the hybridogenic complex of water frogs (not considered in
this study) is that in some regions there are not only diploid hybrids (i.e., having two
genomes), but hybrids with three (LLR or LRR) and even four (e.g. LLRR) genomes
[
Hemiclonal hybridization, the consequence of which is the occurrence of a HPS, is
observed not only for the water frogs, but also for some other species groups [
HPSs of hybridogenic species complexes are a little-known category of biosystems. Their study, part of which is a simulation of their transformations, should lead to important results. For example, the particular genome-selective elimination in interspecific hybrids may open new opportunities in biotechnology and genetic medicine. This allows, if necessary, the removal of unwanted fragments of the genome. Hemiclonal inheritance supports all offspring from crossing of two individuals (each of which transmits a clonal genome) to be genetically identical, i.e. clonal. The resulting organisms, which inherit clonal genomes of two different parent species, may be useful for biotechnology and agriculture. Study of the reason of the hemiclonal hybridization occurrence and the effects of this phenomenon on the evolution of hybridizing species are of considerable theoretical interest. Although study of HPS transformations per se cannot solve these problems, it allows one to better understand mechanisms of appearance and maintenance of the stability of a biological system in which such amazing genetic phenomena are possible.
For further study, it is necessary to describe the variety of possible states of HPSs, their dynamics, regularities and the conditions under which they are stable.
Direct study of HPSs faces significant challenges. Determination of their composition and reproduction mechanisms is associated with a significant amount of fieldwork. HPSs are relatively unusual and differ from well known biosystems such as biocenoses and sexually or clonally reproducing populations. Processes of change in HPS are quite extended temporally and may take decades. There is a high degree of variability in the composition of different HPSs and some are unique objects whose occurrence is highly unlikely. The study of only one unique HPS may not be enough for understanding the regularities of their dynamics. Additionally, HPSs are complex systems containing many stochastically interacting components.
Some authors have used analytical modelling to describe the dynamics of a population system of water frogs [14, etc.]. Analytical models are suitable for the study of separate aspects of the HPS dynamics, however their usage faces significant challenges due to fact that a HPS is governed by an interrelated set of stochastic processes. We therefore consider simulation to be a more useful tool to study the general properties of HPSs.
Christiansen [
Differences of our simulation from others are as follows. At the same time, we consider typical for most populations demographic factors (non-competitive and competitive mortality, differences in the reproduction probability, changes in viability with age) and the unique features of HPS. Our work considers the entire space of possible states of a certain category of HPS. Finally, we use population parameters, the estimates of which were obtained during field studies of this category of HPS. 1.3
Several authors of this work have previously built a deterministic discrete-time
simulation model [
The research was conducted in two stages. In the first stage a number of simulation experiments were performed for various initial compositions of the model HPS. The aim of this stage was to get insight into the possible end states for the HPSs. The second stage analyzed and classified these end states. The dynamic typology of the system was constructed based on the various initial compositions of the HPSs, the observed final states, and the observed transitions from initial to final states.
Dynamic typology is based not only on analysis of the observed object states, but,
above all, on a forecast of their future dynamics [
Hybrid frogs are reproduced differently in different regions [
We plan to describe the total variety of HPSs from the Siverskyi Donets center of diversity of the Pelophylax esculentus complex. As the first step, we consider a variety of HPSs located in the Mzha and the Uda river basins which consist of diploid representatives.
αnga βnga γnga δnga ωnga P(ffa,mma')
A simulation model, as opposed to an analytical model, describes the process of the state transformations during time, not the dependence of the future states of the system on the current one. Therefore, for model development it is sufficient to describe the algorithm of changes in the HPS sizes with time. In this model, time is divided into discrete steps through which the model cycles. The cycle of the model corresponds to the calendar year. It sets the sequence of transformations: αnga → βnga → γnga → δnga → ωnga. Here αnga, βnga, γnga, δnga and ωnga is a sequence of transformations of the individual's groups of the genotype (g) and of the age (a) which correspond to the different stages of the annual cycle (Table 1).
Of k genotypes, x is female and y is male one. At a certain stage, the females of genotype fa and males of genotypes ma form a pair then descendants appear. The other symbols are explained in the description of the input parameters of the model. The numbers of individuals in Algorithm of the groups after joining immigrants Competitive reduction calculation ωtnga based on Thegmrnoouurmtpasbliearteryfstsedooruufcericontemodsiplvaeictdiktuioavlfes in Cpirniaenrandetuniivomtaindbluoeparfaliotsrhfse δbtacnanagsdlaecdA,eduelcmlsgoagcaotnar'i,rio(ωbiditnntehgdfiPmaas,(badfolenfeffladaso,,tcmwVhωreinm)b(miaet'da)i's separately below) ωtng0
The number of offspring (a=0)
ωtng0=Σ(P(ffa,mma')× og(ff,mm)×bfa×wma')
Viability parameters. sga∈[
сga∈[
dga, (dga>=0) — demand. This is the number of resources required for individual of a certain group. It’s magnitude is given for one cycle of the model.
lfa∈[
Similarly, ema∈[
bfa∈N — breed. This is the female fertility. That is specified by the number of eggs produced by the females.
wma∈[
og(ff,mm)∈[
Conditions for experiment. The following global settings should be set to run an experiment or series of experiments.
0nga∈N— number, which is the initial number of all groups.
tiga∈N — inbound, which is number of individual-immigrants at a certain cycle (t) provided by the experiment script.
V — volume — availability of resources that is amount of resources provided by habitat. It is measured in the number of resource units. 2.3
A cycle of the model work is described in the Table 1. The table describes variations in the numbers of individual groups. However, in the model, calculations are made for each individual and then summarized for the groups of individuals. For example, for a non-competitive reduction of quantities γtnga≈ βtnga × sga. This process is implemented stochastically, and that explains usage of sign ≈, and not =. The pseudo-random number generator defines the fate of each individual of the every genotype and every age. An individual survives with probability sga, and dies with probability 1-sga. Algorithm of the competitive mortality rate. Denote the δD = Σ(δtnga × dga), εtnga = δtnga × cga and εD = Σ(εtnga × dga ).
If δD≤V, then ωtnga=δtnga.
If δD>V and εD=V, then ωtnga ≈ εtnga.
The fate of each individual of each genotype and each age is determined by the pseudo-random number generator. They survive with probability ωtnga / δtnga and die with probability 1 – ωtnga / δtnga.
Such a reduction in the quantities satisfies the following conditions: 1) Quantity before reduction is reduced up to the value that corresponds to resource availability.
2) Quantity of each group before the competitive reduction, δtnga, is reduced to a quantity after competitive reduction, ωtnga, in such a way that percent of individuals of each group, which passed through the competitive reduction, is proportional to the competitiveness of this group’s representative: ωtnga / δtnga ~ cga.
male’s mma' pairs is determined in the following way:
P(ffa,mma') ≈ ωnfa × (ωnfa×lfa / Σ(ωnfa×lfa)) × (ωnma'×ema' / Σ(ωnma')×ema')).
The total number of females from the group ffa is multiplied by the probability for the females of the group to be selected by any male. This allows you to set the number of the females in the group, who should find a partner in this iteration. The resulting number is multiplied by the probability for the male of the group mma' to be chosen by any female. In this way one can identify the females from group ffa, which form a pair with the male from group mma'.
The probability for the females from the group ffa to find a partner is determined by the ratio of the product of quantity of this group ωnfa and the success factor of this group of representatives in finding a partner lfa, to the sum of such products for all groups of females.
The probability for the males from the group mma' to find a female is determined by the ratio of the product of quantity of this group ωnma' and the success factor of this group of representatives in finding a partner ema' to the sum of such products for all groups of males.
The fate of each particular female and male is determined by the random number generator in accordance with the probabilities, given the expected number of pairs of P(ffa,mma').
The adequacy of the model was tested on the processes observed in the all-diploid HPS from the Siverskyi Donets center of diversity of the Pelophylax esculentus complex. In total, eight different genomes can be transmitted in HPS of these water frogs (Table 2).
In the Siverskyi Donets center of diversity of the Pelophylax esculentus complex there are no mature P. lessonae, and therefore are no genomes of XL and YL. In this paper, we have considered only diploid frogs. Therefore, in the simulation described only eight genotypes were considered as shown in Table 3.
The set of genomes is defined as G=[
The set of HPS systems HPS=ФN+M⊂R13(N+M)consists of N + M frogs, where N is the size of the spawning HPS, and M stands for the number of immature individuals.
The following data input is used in the model: — A description of the initial composition of the model HPS, and the scenario of migrants entering into it; — A description of the parameters of the viabilities for all considered groups of individuals that differ by age and by genomic composition; — A description of the results of all possible crossings in the model (distribution of the probability of occurrence of offspring with a specific genomic composition from a crossing of different parents).
Genotypes ♀♀ XRXR XR(XL) (XL)(XR) 4 4.1
A detailed justification of the chosen default settings is beyond the scope of this
work. It is done on the basis of study of the natural HPS, including above all the
determination of the lifespan and the frog's growth rates using skeletochronology data, and
results from the estimation of the population size and composition of the natural HPS
by the mark-and-recapture method. Assumptions about the results of crossings (Table
4) were made based on the results of a study of the nature of gametogenesis of hybrid
frogs from the Siverskyi Donets center of diversity of the Pelophylax esculentus
complex [
A preliminary research was carried out to determine the age structure of the model HPS in which we determined the equilibrium age structure of the HPS P. ridibundus. In further experiments, the age distribution of the initial composition of HPS corresponds to that age structure. In those cases when we added the new specimens into HPS at a certain step, they were considered as 4 years old.
To determine the set of possible end states of the water frogs' HPS, consisting of diploid representatives, we chose a set of initial states, evenly distributed in the space of possible states. For 8-examined genotypes, the part of each (p♀XRXR, p♂XRYR etc.) varied in increments of 1/8 from 0 to 7/8. Total 8! = 16,777,216 such combinations are possible. Of this amount, the combinations that satisfy the following conditions were selected:
p♀XRXR + p♂ XRYR + p♀ XR(XL) + p♂ XR(YL) + p♂ YR(XL) + p♀( XL)(XR) + p♂(XL)(YR) + p♂(YL)(XR) = 1; p♀XRXR + p♀XR(XL) + p♀(XL)(XR) > 0; p♂XRYR + p♂XR(YL) + p♂YR(XL) + p♂(XL)(YR) + p♂(YL)(XR) > 0.
Naturally, it does not make sense to consider the combinations in which the total proportion of genotypes involving into the HPS is not equal to unity, as well as those in which there are no male or female. The total number of genotypes that satisfy the above conditions equals 5895. Ten simulations of 500 steps were conducted for the 5895 starting points. The collection of all observed outcomes of the simulation was divided into types, depending on what kind of genotypes presented in the model HPS over 500 steps. For 4778 initial states, all 10 iterations led to any one outcome. In 1117 cases, outcomes were variable. For these 1117 initial states, 10 more runs were carried out; thus, the total number of simulations was 70,120.
To determine the states, which the model HPS can move to, we examined the intervals between step 100 and 200, step 200 and 300, 300 and 400 as well as 400 and 500. The total number of intervals were 162,580; its number is less than possible one due to the model HPS, which dies at any stage of the simulation.
To divide the obtained set of 70,120 final states of individual simulations into groups, we used the analysis of this aggregation by the method of principal components. The first and the second major components make it possible to divide the HPS into 6 groups (Fig. 3. A): — Extinction — 37,946 runs ended in HPS extinction; — R-E-HPS — 22,204 runs ended in different HPSs R-E-types; — E-HPS-type I — 5884 results; such HPS include ♀(XL)(XR) and ♂(XL)(YR); — E-HPS-type II — 3892 results corresponding to another possible type of the E-HPS, which include ♀(XL)(XR) and ♂(YL)(XR); — Extincting — 124 results located nearby of the point Extinction. They continue to end up in extinction. The structure of these finals can be further divided into 13 types; — R-population — 70 results, consisting only of the population P. ridibundus.
The R-E-HPS group, which corresponds to 22,204 results by its composition, can be divided into three parts. Their relative positions can be seen in the plane of the first and the third main component (Fig. 3. B): — Stable R-E-HPS-type I — 18,852; — Stable R-E-HPS-type II — 2,847 results; — Indifferent R-E-HPS — 505 results in which P. ridibundus is present as well as P. esculentus, which transmits both genome P. lessonae and female genome P. ridibundus.
Fig. 3. Ordination of the results of 70,120 simulations. A. Ordination of the results on the plane of the first two principal components. B. Ordination of the results on the plane of the first and third principal components.
To determine the types of stability for the dynamic types of the allocated HPS, the 162 580 pairs of initial state and its outcome were analyzed. The observed stated were classified by the types of stability as shown in Fig. 4.
The observed states are divided into three groups (Equilibrium states, Transient states and Attractive states) as shown in Fig.6, though this division is rather subjective. The Indifferent equilibrium (II) can be considered as a transient state as well. Two versions of the transient states are associated with the directed transitions to other states. Extincting state (IV) is associated with the transition to the extinction state (VI), and transforming stage (III) with the transition to other states. Six basins of sustainability exist in the space of possible states of HPS that consists of diploid individuals, and this corresponds to specific features of the Siverskyi Donets center of diversity of the Pelophylax esculentus complex by their character of the genome transmission. One of them complies with the population of parental species. Two are E-HPS, i.e. spawning population of HPS consisting exclusively of P. esculentus. When crossing P. esculentus with the hybrid amphispermy, the offspring of parental species appearing in such systems dies before the age of maturity.
E-HPS-type I: ♀(XL)(XR)×♂(XL)(YR)→XLXL:(XL)(XR):(XL)(YR):XRYR→♀(XL)(XR) : ♂(XL)(YR); E-HPS-type II: ♀(XL)(XR)×♂(YL)(XR)→XLYL:(XL)(XR):(YL)(XR):XRXR→♀(XL)(XR) : ♂(YL)(XR).
There are two more basins of stability corresponding to the R-E-HPS containing P. ridibundus and P. esculentus, and the last basin is associated with extinction of the HPS. 5
When assessing the results, one must be aware that the result of the simulation is not proof of a hypothesis. At the same time, using simulation models as an exploratory tool has a significant advantage over unformulated conceptual models. We do not have the sufficient empirical data to describe precisely the processes occurring in the natural HPS. The lack of empirical data is offset by a set of presumptions [13] and hypotheses. Simulation allows us to derive consequences arising from the set of initial assumptions.
These sets of consequences may or may not contradict the observable empirical picture. An observed contradiction is the basis for rejecting a set of initial assumptions or adjustments. Agreement is not an evidence for the initial assumptions, but can be seen as an argument in their favor, in other words as corroboration, not as proof (Fig. 5).
Fig 5 shows how the simulation results can be used to select between different versions of the assumptions in the absence of empirical data. Model predictions regarding the expected diversity of HPS conditions, depends on assumptions, on which the variant part of the model was constructed. The predicted (modeled) expected diversity of HPS states can be compared to empirically observed diversity of HPS states. The results of this comparison can be seen as the arguments in favor of such initial assumptions that yielded close to the empirical distribution of states HPS.
Simulation results, among other things, stimulate the collection of the empirical data.
Comparison of predictions, obtained by modelling, and the available fragmented data
about the composition of the natural HPS and character of P. esculentus gametogenesis
shows that currently there is an absence of E-type HPS in the studied region, although
that there are grounds for thinking that such a system probably existed in 1995 [
The authors believe that this research is only a starting step in design of the dynamic typology of the water frogs’ HPS. The usefulness of the simulation is not limited to fact that two stable states, previously not known to the authors, can theoretically be found: R-E-HPS-type II and E-HPS-type II. Results of simulations allow developing a program for further research. The simulation results define the data collection program for testing the adequacy of the results. The currently available data do not contradict the model findings. Future work will include the study of unstable states of HPS that are observed in the natural environment [16], as well as the extension of the model by incorporating hybrids with three genomes, which are specific for the Siverskyi Donets center of diversity of the Pelophylax esculentus complex. 6
We study the unusual category of biosystems, Hemiclonal Population Systems (HPS), through the example of the hybridogenic complex of water frogs, the Pelophylax esculentus complex. The unusual method of reproduction of interspecific hybrids within HPS results in their unusual features, which need more investigation. An important method for studying such systems is computer simulation.
A simulation model of the water frogs’ HPS has been presented. The model inputs are the parameters describing the comparative vitality of various genetic forms of frogs, the results of their probable crossings, as well as the experimental conditions such as the capacity of the environment, the initial composition of the model HPS, and a scenario for the introduction of migrated frogs into the model HPS. Evaluation of the comparative vitality and the crossing results are defined in accordance with the results of population-environmental research in the Siverskyi Donets center of diversity of the Pelophylax esculentus complex. Since direct empirical data was lacking, the values of the parameters used have been estimations that authors put forward on the basis of a study of this region.
Repeated runs of the model yield a probability distribution of outcomes of various HPS transformations according to their initial states and experimenter-determined parameters. We analyzed the processes in all-diploid HPS from the Siverskyi Donets center of diversity of the Pelophylax esculentus complex, which is characteristic for the Mzha and the Uda river basins. When sampling evenly among the starting point of runs in the space of possible states of such systems, a set of outcomes has been established. Only six stable states have been found for such systems, one of which corresponds to the population of the parental species, two coincide with the HPS consisting of representatives of the parental species and hybrids, two correspond to the HPS consisting solely of hybrid individuals, and one state corresponds to the extinction of frogs in the simulated habitat. 12. Quilodran, C.S., Montoya-Burgos, J.I., Currat, M.: Modelling interspecific hybridization with genome exclusion to identify conservation actions: the case of native and invasive Pelophylax waterfrogs. Evolutionary Applications, 8 199–210 (2015). 13. Rasnitzyn, A.P.: Theoretical Foundations of Evolutionary Biology. In: Introduction to palaeoentomology. Moscow: KMK (in Russian) (2008). 14. Reyer, H.-U., Wälti, M.-O., Bättig, I., Altwegg, R., Hellriegel, B.: Low proportions of reproducing hemiclonal females increase the stability of a sexual parasite–host system (Rana esculenta, R. lessonae). Journal of Animal Ecology, 73, 1089–1101 (2004). 15. Shabanov, D.A.: Evolutionary ecology of population hybridogenic complex of water frogs (Pelophylax esculentus complex) Left-Bank Ukraine steppe: Thesis for the Degree of Doctor of biological sciences, spec. 03.00.16 ecology. Dnipropetrovsk (in Ukrainian) (2015). 16. Shabanov, D., Usova, O., Kravchenko, M., Biriuk, O., Leonov, A., Korshunov, O., Mair, Q., Meleshko, O., Newman, J., Vladymyrova, M., Zholtkevych, G.: Sustainable coexistence of the parental species and hemiclonal interspecific hybrids is provided by the variety of ontogenetic strategies. Herpetological Facts Journal, 2, 35–43 (2015).