Viability of Natural Populations of Hypancistrus zebra (Siluriformes, Loricariidae), Xingu, Brazil

Hypancistrus zebra is an endemic �sh species from the Middle Xingu River and recently included in the Critically Endangered (CR) category in the Red Book List of Endangered Brazilian Fauna that follows IUCN criteria. Given these impacts and the lack of information about the species, it is di�cult to assume the viability of natural populations. Thus, this work aims to evaluate the effect of the variation of intrinsic parameters on the population viability of H. zebra. For this, an Individual Based Model (MBI) was created of the type Agent Based Modeling (MBA). To create the model, we considered “individuals” as an entity and the following variables of interest: longevity, age of sexual maturity, annual reproduction number, instant birth rate (b0), instant mortality rate (d0), interference of each individual in population growth (b1), interference of each individual in population mortality (d1), time (t), radius, richness (S), tolerance (tol) and population size (N). The model showed that natural populations today, even not taking human impacts in account, are at the limit of viability. However, any factor that causes a reduction in resource availability, even if not evident, can lead to a steep population decline, affecting the viability of the populations.


Introduction
The construction of Hydroelectric Power Plants (HPP) has become one of the main threats to the maintenance of the global ichthyofauna [1][2][3] .The dam causes the blocking of migratory sh activities (e.g.reproductive migration of Salmo salar), physical changes (e.g.change from lotic to lentic environment and retention in sediment transport), chemical changes (e.g.physicochemical water characteristics) and affects community (e.g.causes the process of biotic past, present or projected population, based on habitat quality and/or reduction of the occupied area (AOO) and extent of occurrence (EOO) 44 .Hypancistrus zebra is a species of sh in the subfamily Hypostominae (Loricaridae, Siluriforme) known for having a black and white oblique stripe pattern on the body and ns, and a snout with an "E"-shaped "striped" pattern [45][46][47] .These characteristics allow it to be highly valued in the ornamental sh market, and the high value of acquiring the specimen has generated great demand in the clandestine market 56,48 .However, the impact caused by the Belo Monte HPP is the main concern regarding the viability of its populations 44 .Furthermore, there are no data, or even predictions, about the current situation of natural populations of H. zebra.Therefore, we seek to understand how the variation in the intrinsic parameters of the species H. zebra can affect its population viability.Additionally, we intend to answer the following questions: (I) What are the combinations between the values of birth and death rates necessary to keep the population viable?(II)   What are the combinations between the level of in uence of habitat specialization and intraspeci c competition in the persistence of this species?(III) Based on the generated scenarios, what is the viability condition of natural populations?

Results
The algorithm that describes the effect of birth and mortality rates on the population viability of H. zebra (MetaZebra 01) presented 137 (31%) scenarios with 100% persistence of the populations (Table 1).The remaining scenarios, 304 (69%), had some chance of extinction, ranging from 0.020 to 1,000, with 201 (45%) of the scenarios having a probability greater than 50% of extinction and 162 (36.7%) of the scenarios had 100% chances of extinction (Table 1).Based on our results, the combinations between the values of birth and death rates necessary to keep the population viable must have a birth rate greater than 0.55 and a mortality rate lower than 0.25.Otherwise, the population starts to decline, however it does not inhibit the chances of the population re-establishing itself.
However, if a b is less than 0.55 and d greater than 0.6, the population goes into extinction.

Mortality rade (d)
As for the algorithm used to describe the in uence of the level of habitat specialization and intraspeci c competition on the species' persistence (MetaZebra 02), we had 219 (49.6%) scenarios with 100% persistence (Table 2).There were 345 (78.2%) scenarios with a greater than 50% of persistence.Our results showed that the combinations between the values of the rates of tolerance level and radius of competition necessary to maintain the persistence of the population owe the level of tolerance with a rate greater than 0.5 and a radius of competition with a rate less than 0.4.No scenario presented a 100% chance of extinction of the population (Table 2).As for the level of in uence of habitat specialization and competition, the results showed that tolerance has a greater in uence on population persistence than the effect generated by intraspeci c competition.The competition starts to act more conspicuously on the population from radius greater than 0.4.The tolerance level is more likely to keep populations viable with tolerance rates higher than 0.5, below these rates the population starts to in uence population decline.Based on the scenarios generated by the MetaZebra 01 algorithm (Table 1) and considering the birth rate of 0.6 and the intrinsic mortality rate of 0.3, natural populations have 100% probability of survival in nature.Considering this, the three natural populations would be viable, but sensitive changes in birth and mortality rates, as well as environmental changes.

Discussion
The 441 scenarios generated by the model showed that the relationship between the intrinsic birth rate above 0.6 with the intrinsic death rate below 0.5 allows populations to remain viable for a long time (Table 1).The model also showed that the number of scenarios with some extinction risk was higher (69% of the scenarios) than the number of scenarios with a 100% chance of persistence.This may be an indication of the vulnerability of H. zebra populations to events that may change the demographic stochastic process.
Stochastic birth-and-death process is probably the simplest modeling approach to predicting extinction 33,56 .In simple models they are independent rates, but they can show high correlation through the years in real populations, since the temporal variation can provide years with high or low resource availability, affecting the reproduction and survival of individuals 68 .However, not always that the value of R is negative (the birth rate lower the death rate) is a guarantee of short-term population persistence, just as a high birth rate and low mortality do not guarantee long-term persistence of time 68 .The high number of scenarios expands the view of stochastic variation and can make it easier to predict the actual population fate.The persistence of a population depends on stochastic or variation 69 .
Generally, the persistence of a population is ensured by large, connected, suitable and close to each other habitats, high population reproductive rate and environmental conditions with variation in balanced carrying capacity 70 .Hypancistru zebra is an endemic species, restricted to about 170 km from the middle Xingu river 44 , possibly its populations are closed and currently the environmental conditions and available resources are not favorable due to the dam.
The variation in habitat quality in the landscape (spatial variation) also affects population persistence 68 , therefore, the feasibility presented by the model does not guarantee the real maintenance of H. zebra populations.Generally, stochastic events are of concern especially for viability of small populations 33,71,72 , as they present greater chances of extinction due to their demographic uctuation, whether due to demographic stochasticity (internal mechanisms) or environmental stochasticity (external mechanisms) 30,72,73 .These events are linked to birth and death rates 74 .We consider that the three natural populations of H. zebra are represented by high population size, which could have a different result in viability if their populations go into decline, either by mortality or the removal of individuals with over shing.
In the model, it was observed that tolerance has a greater in uence on population persistence than the effect generated by intraspeci c competition (competition radius; Table 2).Since the radius is less than 0.5, the tolerance force is greater.However, in scenarios with a radius greater than 0.55, competition starts to have a greater effect on populations, regardless of the high tolerance rate.Therefore, even in scenarios with a high tolerance rate, the probability of population extinction will be greater when the competition radius reaches high values in the rate.However, if both rates are low, it is possible that the population will be maintained.This indicates that intraspeci c competition is an interaction that acts more visibly in the population from a radius greater than 0.4.On the other hand, the tolerance level is more likely to maintain viable populations with tolerance rates greater than 0.5, below these rates the population starts to present a greater risk of extinction.
We did not include effects of anthropogenic actions in the study.We emphasize that models that address the variation between individuals is essential to develop and study population dynamics and associate it with different life history tactics 75 .The development of modeling with intrinsic parameters allows testing uncertain impacts on the life history, evaluating the demography of species 76 , in addition to making it possible to identify predominant parameters in the system when well delimited 77 .
Data from the life history or population growth rate are used for the functioning of the PVA, this information serve as parameters in the model projecting the population dynamics 78 .As these rates vary, they in uence intrinsic processes (e.g.stochasticity, genetic drift, demographic, social structure) 79 , and given the uctuation in population size and over time, random (stochastic) variation occurs.The greater the amount of information about the population, the more detailed is an MBI 30 , which bene ts better results, but requires a more advanced computer system 80,81 .MBI is widely used to assess population dynamics through intrinsic rates 82 .Individual variation is the evolutionary basis existing in all populations and organisms and this individual heterogeneity occurs in practically all characteristics, including reproduction, physical conditioning and survival 75,[83][84][85] .
Our results show a 100% probability of population viability for the three natural populations of H. zebra, given the combination of values of birth rate (b = 0.6) and intrinsic mortality (d = 0.3).However, the models that generated the scenarios did not include shing pressure and habitat change caused by the Belo Monte HPP, which covers the entire area of occurrence of the species 56,57 .Due to the fact that these impacts already exist in the area of occurrence of the species and already promote changes in conditions and resources, we can suggest that populations are threatened.Since a decrease in the birth rate or an increase in mortality would cause species to move from the area green (100% probability) for areas with a lower probability of viability.
The model that investigates the relationship between birth and mortality rates showed that birth rates below 0.55 and mortality rates above 0.25 can lead to extinctions.Our model populations showed little difference in these thresholds, 0.6 for birth and 0.3 for mortality, reinforcing the idea that natural populations nowadays would not be in conditions of 100% viability.Females of Hypancistrus zebra guarantees breed in plots and have low fertility 43 .This can demonstrate that the natural behavior of the species prioritizes spending more energy for individual maintenance than for reproduction, such as spending looking for mates and investing in offspring.In the absence of a good amount of available resources, individuals tend to choose to spend more energy with reproduction (increasing the birth rate of newborns and reducing adult individuals) or avoid the risk of mortality (lower mortality of mature individuals, but low rate of newborns) 86 , in uencing a dynamic in population birth and mortality rates.Poor reproduction and high mortality (positive and/or negative covariance) also result in resource availability in the face of temporal variation.
Loricariidae show low tolerance in sections of reservoir formation 59 and species with characteristics adaptable to fast-owing water habitats are more vulnerable to dams 2 .In addition, the model showed that natural populations of H. zebra are viable, but it is possible to observe that it is an intrinsically sensitive species and may be vulnerable to human disturbances.So it is also with regard to the level of specialization of the habitat.In Table 2, no scenario showed 100% extinction, however, it is possible to observe that tolerance has a greater in uence on the intraspeci c competition radius, demonstrating the high specialization of the species.Although these is not small populations, it is an endemic species, with high removal of specimens from nature for illegal sale 48,49 and its habitat is practically all affected by the implementation of a hydroelectric plant 44 .In addition, paucity of data is likely a major limitation in assessing population viability 87 .
The reduction in the birth rate can be a process of response to increased mortality, fewer individuals to reproduce, or the removal of individuals from the population, either through migration or shing, in the case of sh.Another worrying factor in population decline is overexploitation of the species.Such a decline had already been reported due to the consequent history of exploitation and habitat loss caused by mining activities 88 and even after the shing prohibition, their specimens are still being collected due to their high value and di cult inspection 89 .In this way, it will promote a reduction in the population's birth rate, but the change in habitat does not only affect recruitment.Considering the paucity of studies on the niche and reproductive biology of H. zebra, possibly it is a kind of k-strategist due to its low fertility that takes time to reach sexual maturity, takes care of parents, is sedentary and has a long life cycle 55- 57 .Given the parameters that fed the algorithms, the tolerance level is greater than the concurrency radius effect.
Our study presents a theoretical ecological intrinsic modeling for predicting how the populations of H. zebra will behave with variation of the parameters, showing that a high rate of withdrawal of individuals or impacts caused by the alteration of the water ow in the natural environment can cause a reduction of population viability that will generate extinction of its populations.In addition, some authors claim that H. zebra is sensitive to changes in water quality 88 and climate changes 90 .In addition to these factors, the species is considered endemic 42,47 which corroborates that it is a more specialized niche species.Their narrow tolerance range indicates that their populations are below the median tolerance level in Table 2, which should not be a concern if the current ecological condition is to contribute to greater competition between individuals for resources.In natural conditions without human alterations and capture pressure, natural populations of H. zebra are viable in a delicate balance, however, according to the model, small disturbances can promote a decline in population growth, generating great probabilities of the species' extinction.Impacts such as the change in the hydrological cycle caused by the Belo Monte HPP dam, as well as the high rate of specimen withdrawal by illegal shing, will synergistically cause irreversible damage to the population viability of this species.

Material And Methods
In this research, was used the IBM type Agent Based Modeling (ABM).The algorithms used (Supplementary Material I, II and III) were developed within the platform Matlab® version R2015a 50 .The model description is structured according to the protocol ODD (Overview, Design concepts, Details) updated suggested by Grimm et al. (2010).

Purpose
The purpose of the models is to assess the effect of varying intrinsic parameters on the population viability of an endemic sh species.Although endemism and species unity are not a limiting feature for replicating models.Thus, the developed algorithms indicate how (i) the ratio between the birth and mortality rates (Supplementary II -MetaZebra01) and (ii) the level of specialization and competition (Supplementary III -MetaZebra02) of the specimens affect population viability.

Entities and state variables
The model has only one entity, specimens.The specimens are representatives of a single species of sh distributed in three populations of different sizes.Each specimen was characterized by a set of speci c parameters based on information from literature and breeders of the species.Basically, we used characteristics that in uence population dynamics, including the following state variables: longevity, age of sexual maturity, annual reproduction number, instant birth rate (b0), instant mortality rate (d0), interference of each individual in population growth (b1), interference of each individual in population mortality (d1), time (t), radius, richness (S), tolerance (tol) and population size (N).We consider the following assumptions for determining the values of our variables: Longevity.Species of the same family (e.g.Ancistrus ssp.) can reach more than 15 years of age [51][52][53] .According to aquarists, longevity in captivity is at least 15 years for the species under study.However, probably in a natural environment, specimens have a shorter life span when compared to individuals in good health in captivity 54 .Therefore, in the model, we estimate that specimens can reach 12 years of life in nature.
Age of sexual maturity.According to breeders who produce the species in captivity, individuals reach sexual maturity at the age of three.
Annual reproduction rate.To determine b0, we need to know the number of individuals who enter the cohort each year by birth.Because the male copulates with more than one female 55 , we only consider females in the calculation.We used 50% of the specimens of each hypothetical population, since the parameter is more related to the fertility of females, as the number of individuals depends more on that sex, so the sex ratio considered was 1:1.Each female spawns an average of 14 eggs per spawn 48,55 .In captivity, multiple spawning are observed throughout the year.In a natural environment, reproduction can occur at any time of the year, but two reproductive peaks were observed annually 56,57 .We estimate that 95% of the females in each cohort are able to reproduce.Most females spawn twice a year, possibly larger females with better nutritional performance, are more apt for a greater number of annual reproduction 58 .We consider the following rates: 35% of females reproduce only once / year, 45% reproduce twice/ year and only 15% of females reproduce three times / year.
Mortality rate.Regarding mortality, we arbitrarily de ne that in a natural environment despite parental care, the mortality of individuals under one year of age (juvenile and egg) is high, around 50%, due to predation and competition for hide.Additionally, adult females are assigned a 25% mortality rate, while adult males have 20%.We consider that the behavior of the male to stay hidden and protecting it's crevice (Ramon, 2011; Gonçalves, 2011) provides less vulnerability to males and consequently a lower mortality rate than females in the population.
Intrinsic birth rate (b0).According to the assumptions of the hypothetical natural population size and annual reproduction rate, we obtained the result of b0= 0,6.We used only the females of each population (50% of the individuals) and the rate value was obtained through a difference equation presented in more detail in section 2.6 (sub-models).
Intrinsic mortality rate (d0).Following the assumptions of the hypothetical natural population size and annual mortality rate it was estimated as d0= 0,3.We used only the females of each population (50% of the individuals) and the rate value was obtained through a difference equation presented in more detail in section 2.6 (sub-models).
Interference of each individual in the growth (b1) and mortality (d1) of the population.We did not consider the effect of b1 (interference of each individual on population growth) and d1 (interference of each individual on population mortality) in the models.Time (t).Time was measured in years in models with t = 0 as a starting point, ending in 1,000 years.
Radius.The radius rate varies from 0 to 1, being 0 when there is no competition and 1 when everyone is competing with each other.There are no studies that say how competitive the species is.So, we determine an average value (0.5).
Richness (S).As the study deals with the population of just one species, we considered S = 1.

Tolerance (tol)
. There is also no information on the species tolerance, therefore, we determined an average value (0.5).
Initial population size (N).In both modules of model execution, we considered n the initial size of the population with 100,000 individuals.

Process overview and scheduling
The processes of the models promote the simulation of the dynamics of individuals within the population in an environment without anthropic effects and interspeci c interaction (Figure 1; Supplementary I -PopZebra).The process begins with the entry of a cohort with an initial number of individuals (n = 10.000) in the population.Gradually, individuals are assigned to the Optimal level range (OLR) randomly determined, or to the Maximum or Minimum tolerance level range (LRMaxMin) ranging from zero to one, according to the model.Specimens included in the OLR are aged, go through the update of age and later young individuals go through the process of sexual maturity until they reach the age of sexual maturity (adult individuals), the individuals enter the reproduction process, causing the origin of a new cohort by birth.
As for the individuals that enter FNMaxMin, they are destined to the competition processes for resources (territorialism and / or food).Randomly, some individuals are classi ed as survivors and enter the aging process and the consecutive ones mentioned above, while the rest are removed from the model by the mortality process.Individuals who reach the age of longevity are also removed by the model through the process of natural mortality (by age).
This dynamic is generated through the PopZebra program (supplementary material I).However, to meet our objectives, two metaprograms were developed.
MetaZebra 01 (supplementary material II) for objective one and MetaZebra 02 (supplementary material III) for objective two.The values of the variables used in the algorithms (shown in Table 3) are based in knowledge gathered in specialized hobbyists' magazines, hobbyists and shermen personal communications, as well as experiments carried out in captive breeding program in the laboratory.The MetaZebra 01 algorithm was built to create combinations of birth and mortality, thus varying b0 and d0 from zero to one in 0.05 intervals.Considering H. zebra as r or k strategist (depending on the mortality rate).This procedure will build an interface of values where the x-axis will be the entire variation of the mortality rate while the y-axis will be the entire variation of the birth rate and the 441 cells (21 birth values multiplied by 21 mortality values) will represent all possible combinations between these two rates.
Thus, indicating the effect of the ratio between birth and mortality rates on population viability.As for the MetaZebra 02 algorithm, it was created to vary the tolerance and the radius of competition, thereafter the tol and the radius vary from zero to one in 0.05 intervals.Considering the species as generalist or specialist (depending on the tolerance rate) and little or very competitive (depending on the competition radius rate) in the face of changes.This procedure will generate an interface of values, where the x axis will be the entire variation of the competition radius rate and the y axis will be the entire variation of the tolerance rate and, the 441 cells (21 tolerance values multiplied by 21 radius values competition) will represent all possible combinations between these two rates.This way, it is possible to compare the effect of the species' level of specialization (tolerance) and relate it to the in uence of intraspeci c competition on the persistence of H. zebra.Each algorithm generated 441 combinations of values (scenarios) that represent the population's probability of survival over an interval of 1,000 years.This probability was calculated from ve replicates of each combination.

Design concepts
Basic principles.Population dynamics are maintained with the constant in uence of several factors.Growth is determined by the number of entities (individuals) that enter (birth and migration) and leave (mortality and emigration) the population 59 .The population grows exponentially until it is controlled by the amount of resources available in the environment, called support capacity 60 .In addition, ecological factors within the habitat will in uence the interaction between individuals (intraspeci c interaction) and with the environment (Law of Tolerance), which depending on the level of specialization of the species will determine the growth and survival of this set of organisms [61][62][63] .We assumed, in the model under study, the population as being a closed one (entry of individuals by birth and exit by mortality), since it is an endemic species with no migratory characteristics, restricted to about 170 km of the river section.
Emergency.Population dynamics included an emerging result of behavior and interactions between individuals and their habitat.Processes that promote the dynamics of specimens in the model over an interval of 1,000 years.

Figures
Figures

Table 1
Values of population survival probability in different combinations in the birth rate (b) and in the mortality rate (d) estimated by the model.Values closer to gre persistence of the population, values in yellow and next to the red are scenarios between mid to low chances of persistence.While values in red represent 100% of the population remaining over a long period of time.

Table 2
Values of probability of population persistence in different combinations in the tolerance rate and in the radius of intraspeci c competition rate estimated by t with greater chances of persistence of the population, values in yellow and close to red are scenarios between mid to low chances of persistence.While value probability of 100% of the population remaining over a long period of time

Table 3
Condition variables used in the algorithms to generate the models.Randomized values were determined by "Minimum Value: Interval: Maximum value".