Density-dependent Mortality Research Articles

The Eurasian badger-generated seed rain drives the natural (re)colonization of vacant human-altered areas by a keystone pioneer palm

Seed dispersal is an essential ecological process for plant (re)colonization, especially in intensively human-altered habitats such as old-fields (i.e. abandoned farmlands) where seed arrival is often limited. Assessment of spatial patterns of mammal-generated seed rain and their matching with the spatial distribution of adult plants provides essential information on the patterns and pace of the (re)colonization processes. For instance, increased seedling survival far from adult plants could indicate density-dependent mortality (Janzen-Connell) effects whereas increased survival close to adult plants could suggest facilitative effects. Here, we characterized during two dispersal seasons the spatial distribution of feces from four frugivorous mammals and quantified its spatial association with the distribution of adult plants of the pioneer Mediterranean dwarf palm (Chamaerops humilis) in two old-fields in southwestern Spain. We also estimated the dispersal kernels of both emerged and surviving seedlings and assessed potential evidence for Janzen-Connell and/or facilitative effects. Using a spatially explicit approach, we revealed strong differences between study sites in the strength and scale of spatial associations between mammal feces with C. humilis seeds and adult dwarf palms, being strongly positive at small scales in one site and slightly positive at larger scales in the other one. Further, we found some evidence of both Janzen-Connell and facilitative effects depending on the study site. Altogether, our results emphasize the central role as seed disperser of the Eurasian badger (Meles meles) in the natural (re)colonization of Mediterranean old-fields and the spatial variations of the underlying mechanisms and demographic consequences for plant populations.

Data for: Modelling the impact of wood density dependent tree mortality on the spatial distribution of Amazonian vegetation carbon

Data for: Modelling the impact of wood density dependent tree mortality on the spatial distribution of Amazonian vegetation carbon

Targeting river operations to the critical thermal window of fish incubation: Model and case study on Sacramento River winter‐run Chinook salmon

AbstractAllocating reservoir flows to meet societal and ecosystem needs under increasing water demands and climatic variability presents challenges to resource managers. Often, rivers have been regulated to meet flow and temperature compliance points or mimic historical patterns. Because it is difficult to assess if this approach is efficient, process‐based models are being used to design river operations. This paper describes a model for fish incubation survival based on the premise that mortality from thermal stress occurs over a critical window (CW) of embryo development. A model for the embryo CW based on metabolic studies of development is combined with density‐dependent and background mortalities to describe salmonid survival from egg fertilization to fry detection downstream. The model is calibrated with a two‐decade dataset of Sacramento River winter‐run Chinook salmon egg‐to‐fry survival. The effects of temperature exposure over a range of CWs were explored. Based on statistical and biological support, two alternative CWs were identified for temperature control: the entire incubation period and a short duration window prior to hatching. Survival under different CW assumptions and temperature control operations were simulated with an internet‐accessible form of the model. The analysis indicated that under years of limited cold‐water resources, targeting water releases to the CW prior to hatching would yield the highest incubation survival.

Optimal harvest strategy based on a discrete age-structured model with monthly fishing effort for chub mackerel, Scomber japonicus, in South Korea

Currently, the catch of fishery resources in South Korea has fallen more than 40%, from 1.73 million tons in 1986 to 1.01 million tons in 2018. In particular, the amount of chub mackerel, one of the most favored fish species by South Koreans, caught in 2017 was 103,870 tons, which was only 25% of the total catch, compared with 415,003 tons in 1996. The total allowable catch system and the closed season are currently in place as a countermeasure to the continued decline in fishery resources; however, their effectiveness is questionable. Our study aims to maximize fishing profits by controlling the monthly fishing effort while maintaining the amount of chub mackerel. Discrete age-structured mathematical model was established with an optimal harvest control system. Density-dependent mortality was applied at the juvenile stage to reflect fish mortality because it is highly dependent on population density in the underage phase. The conditions of the parameters guaranteeing the existence of optimal harvest strategies were demonstrated and obtained using Pontryagin's maximum principle. We compared an optimal harvest strategies and the actual harvest strategies of fishing effort from July 2010 to June 2020. In addition, we compared the profit and biomass of the optimal harvest strategies when designating one month in a year as closed season. We also conducted sensitivity analysis by varying the price of chub mackerel and cost of fishing effort. As a result, the optimal harvest strategies are to have the highest amount of fishing effort from August to September and gradually reduce the amount of effort. The optimal harvest strategies could improve the maximum economic yield and the maximum sustainable yield by 11.9% and 10.9%, respectively, over the observed strategy. To the best of our knowledge, forecasting analysis of the maximum economic yield and closed season conducted based on optimal harvest control system for Chub mackerel in South Korea. The appropriate allocation of monthly fishing effort can increase sustainable catch and profit. In addition, it is better to implement a closed season in July to maximize the profit of fishing and in June to the resource recovery.

Deriving tree growth models from stand models based on the self-thinning rule of Chinese fir plantations

Self-thinning due to density-dependent mortality usually occurs during the forest development. To improve predictions of such processes during forest successions under climate change, reliable stand-level models are needed. In this study, we developed an integrated system of tree- and stand-level models by deriving tree diameter and survival models from stand growth and survival models based on climate-sensitive self-thinning rule of Chinese fir plantations in subtropical China. The resulting integrated system, having a unified mathematical structure, should provide consistent estimates at both tree and stand levels. Predictions were reasonable at both stand and tree levels. Because stand-level values aggregated from the tree model outputs are different from those predicted directly from the stand models, the disaggregation approach was applied to provide numerical consistency between models of different resolutions. Compared to the unadjusted approach, predictions from the disaggregation approach were slightly worse for tree survival but slightly better for tree diameter. Because the stand models were developed under the climate-sensitive self-thinning trajectory, the integrated system could offer reasonable predictions that could aid in managing Chinese fir plantations under climate change.

Detecting population regulation of winter flounder from noisy data

Year-class size of marine fish is thought to be determined during the first year of life, with density-dependent mortality occuring during the larval or juvenile stages. However, investigations of such dynamics are often limited by data availability. To test this paradigm for winter flounder (Pseudopleuronectes americanus) in Narragansett Bay, Rhode Island, the abundances of 29 year classes moving through seven life stages were analyzed with a novel extension of key-factor analysis. Evidence of density dependence was identified between the egg and July young-of-the-year stages and high process-error variance was detected throughout the life cycle, suggesting year-class size is not fully determined until age-2. However, the first summer appeared to be a critical life stage for winter flounder, during which high temperatures, hypoxia, and predator abundance contributed to increased mortality rates behind a long-term population decline. Due to its general data requirements, the key-factor analysis method developed here may be applied to other aquatic populations to identify the impacts of external stressors at particular life stages and the degree to which they are compensated by density-dependent processes.

Effects of fertilization on the growth dominance of Inland Northwest forests of the United States

Large trees have disproportionally large competitive advantage in access to light, which has been proposed to increase growth dominance of large trees (e.g., a larger proportion of volume growth than standing volume is in large trees in a stand). Tree growth may also be limited by the availability of other resources besides light. Nutrient deficiency, especially of nitrogen, is considered common among temperate forests including mixed-conifer forests of the Inland Northwest of the United States. Data from a long-term forest nutrition study across four Inland Northwest states were analyzed to evaluate nitrogen ​× ​potassium fertilization's effects on growth dominance over an eight-year period following treatment. Our results show that growth dominance varied substantially across plots in each vegetation series and fertilization treatment, and its mean values generally were at minuscule magnitudes, negative, and not significantly different from 0. We propose that this lack of a clear pattern in growth dominance was the result of the mixed-species composition where shade-tolerant species remained in lower crown positions, yet their relative growth kept pace with large trees. Limited moisture availability at dry sites may have hampered the development of growth dominance. Growth dominance also was lowered by mortality observed among relatively large trees. The largely negative growth dominance across fertilization treatments indicated that small trees seem to have maintained higher relative growth rates than large trees, even if absolute growth was higher among large trees. In the case fertilization does improve stand growth, a significant part of this improved growth will be lost in density-dependent mortality over time if not captured through thinning/harvesting.

Mathematical modeling and analysis of Phytoplankton–Zooplankton–Nanoparticle dynamics

In this paper, we investigate the population dynamics of phytoplankton–zooplankton–nanoparticle model with diffusion and density dependent death rate of predator. The functional response of predator in this model is considered as Beddington–DeAngelis type. The stability analysis of the equilibrium points is observed by applying the Routh–Hurwitz criterion. Numerical simulations are given to illustrate the theoretical results.

Tree spatial pattern and mortality prediction in burned patches of Dahurian larch (

Background Fire-caused tree mortality and spatial pattern are crucial for evaluating forest dynamics and developing management prescriptions. Aims We investigated direct fire effects on spatial distribution and mortality of Dahurian larch (Larix gmelinii Rupr.) and assessed the Ryan and Amman (R–A) model performance and the importance of immediate mortality predictors. Methods We analysed spatial patterns of fire-killed and surviving trees of three size classes in plots that burned at low- to high-severity using pair-correlation functions and tree mortality with the R–A model and generalised linear mixed models. Key results The mixed-severity fire caused strong density-dependent mortality and more aggregated surviving tree patterns at short distances. The R–A model generally performed acceptably, and crown scorch and bole char height were critical predictors determining post-fire tree mortality. Conclusions Fire-caused tree mortality and spatial patterns are controlled primarily by spatial variation in tree size and biological and structural characteristics. The prediction biases of the R–A model arose primarily from the intrinsic traits of Dahurian larch and the imbalanced dataset. Fine-scale neighbourhood density might be a fundamental priority for fire management and restoration. Implications This study could possibly improve mechanistic understanding of spatial pattern development and tree mortality in similar fire-prone conifer forests.

Global stability of an age-structured population model on several temporally variable patches

We consider an age-structured density-dependent population model on several temporally variable patches. There are two key assumptions on which we base model setup and analysis. First, intraspecific competition is limited to competition between individuals of the same age (pure intra-cohort competition) and it affects density-dependent mortality. Second, dispersal between patches ensures that each patch can be reached from every other patch, directly or through several intermediary patches, within individual reproductive age. Using strong monotonicity we prove existence and uniqueness of solution and analyze its large-time behavior in cases of constant, periodically variable and irregularly variable environment. In analogy to the next generation operator, we introduce the net reproductive operator and the basic reproduction number R_0 for time-independent and periodical models and establish the permanence dichotomy: if R_0le 1, extinction on all patches is imminent, and if R_0>1, permanence on all patches is guaranteed. We show that a solution for the general time-dependent problem can be bounded by above and below by solutions to the associated periodic problems. Using two-side estimates, we establish uniform boundedness and uniform persistence of a solution for the general time-dependent problem and describe its asymptotic behaviour.

Does the legacy of historical thinning treatments foster resilience to bark beetle outbreaks in subalpine forests?

Promoting ecological resilience to increasing disturbance activity is a key management priority under warming climate. Across the Northern Hemisphere, tree mortality from widespread bark beetle outbreaks raises concerns for how forest management can foster resilience to future outbreaks. Density reduction (i.e., thinning) treatments can increase vigor of remaining trees, but the longevity of treatment efficacy for reducing susceptibility to future disturbance remains a key knowledge gap. Using one of the longest-running replicated experiments in old-growth subalpine forests, we measured stand structure following a recent (early 2000s) severe mountain pine beetle (MPB; Dendroctonus ponderosae) outbreak to examine the legacy of historical (1940s) thinning treatments on two components of resilience. We asked: 'How did historical thinning intensity affect (1) tree-scale survival probability and stand-scale survival proportion (collectively "resistance" to outbreak) for susceptible trees (lodgepole pine [Pinus contorta] ≥ 12 cm diameter) and (2) post-outbreak stand successional trajectories?' Overall outbreak severity was high (MPB killed 59% of susceptible individuals and 78% of susceptible basal area), and historical thinning had little effect on tree-scale and stand-scale resistance. Tree-scale survival probability decreased sharply with increasing tree diameter and did not differ from the control (uncut stands) in the historical thinning treatments. Stand-scale proportion of surviving susceptible trees and basal area did not differ from the control in historically thinned stands, except for treatments that removed nearly all susceptible trees, in which survival proportion approximately doubled. Despite limited effects on resistance to MPB outbreak, the legacy of historical treatments shifted dominance from large-diameter to small-diameter lodgepole pine by the time of outbreak, resulting in historically thinned stands with ~2× greater post-outbreak live basal area than control stands. MPB-driven mortality of large-diameter lodgepole pine in control stands and density-dependent mortality of small-diameter trees in historically thinned stands led to convergence in post-outbreak live tree stand structure. One exception was the heaviest historical thinning treatments (59-77% basal area removed), for which sapling dominance of shade-tolerant, unsusceptible conifers was lower than control stands. After six decades, thinning treatments have had minimal effect on resistance to bark beetle outbreaks, but leave persistent legacies in shaping post-outbreak successional trajectories.

Predation by Euseius scutalis (Acari: Phytoseiidae) on Tetranychus urticae and Eutetranychus orientalis (Acari: Tetranychidae): effect of prey density and developmental stage

Predation ability is a key component determining the suppression of agricultural pests by natural enemies. The aim of this study is to evaluate the effect of prey density and developmental stage on the predation of Euseius scutalis (Acari: Phytoseiidae) on the two-spotted spider mite, Tetranychus urticae (Acari: Tetranychidae) and the oriental red mite, Eutetranychus orientalis (Acari: Tetranychidae). For this purpose, laboratory functional response experiments were conducted using female adults of E. scutalis. Results indicated that the predator causes an inverse density dependent mortality to larvae, nymphs and adults of the two-spotted spider mite, as well as the oriental red mite. The random predator equation was used to fit the data. E. scutalis handling time increased significantly with T. urticae and E. orientalis developmental stage. The maximum number of T. urticae prey consumed was 48.3 larvae, 28.5 nymphs and 11.0 adults, where the corresponding values for E. orientalis were 48.8, 32.2 and 18.2 larvae, nymphs and adults, respectively. Estimated handling times and attack rates of E. scutalis on larvae, nymphs and adults of T. urticae were 0.4970 h and 0.1058 h-1, 0.8435 h and 0.1395 h-1, and 2.1834 h and 0.0835 h-1, respectively. The corresponding values on larvae, nymphs and adults of E. orientalis were 0.4920 h and 0.1166 h-1, 0.7452 h and 0.1361 h-1, and 1.3186 h and 0.0597 h-1, respectively. The results of this study may be indicative of the predation ability of adults of E. scutalis on these notorious pests, providing a basis for determining release rates appropriate for various pest densities.

Leave or Stay: Simulating Motility and Fitness of Microorganisms in Dynamic Aquatic Ecosystems.

Simple SummaryMotile bacteria are widespread in various water ecosystems along with nonmotile species, which posits the question: what makes motility an advantage in such habitats, and under what conditions? This simulation study addresses these problems using a computer model of competition of two microbial species: Nomad of a motile population and Settler of a sedentary one. We simulated their competition under various environmental conditions such as the nutrient availability and frequency of changes in the location of the nutrient source as well as depending on some population parameters determining how much energy it takes for a bacterium to migrate and what the effect of density-dependent mortality is on the outcome of Settler vs. Nomad competition. We showed that dynamic and nutrient-scarce environments favour motile populations, whereas nutrient-rich and stagnant environments promote sedentary microorganisms. Moreover, the energetic costs of migration determine whether or not the motile population outcompetes the sedentary one, though it also depends on such conditions as nutrient availability. There is also another way for Settler to succeed even without penalties for migration—by grasping an opportunity to occupy the nutrient source, bringing about a biotic desert around it, which cannot be overcome by Nomad constantly searching for locally optimal conditions.Motility is a key adaptation factor in scarce marine environments inhabited by bacteria. The question of how a capacity for adaptive migrations influences the success of a microbial population in various conditions is a challenge addressed in this study. We employed the agent-based model of competition of motile and sedentary microbial populations in a confined aquatic environment supplied with a periodic batch nutrient source to assess the fitness of both. Such factors as nutrient concentration in a batch, batch period, mortality type and energetic costs of migration were considered to determine the conditions favouring different strategies: Nomad of a motile population and Settler of a sedentary one. The modelling results demonstrate that dynamic and nutrient-scarce environments favour motile populations, whereas nutrient-rich and stagnant environments promote sedentary microorganisms. Energetic costs of migration determine whether or not the Nomad strategy of the motile population is successful, though it also depends on such conditions as nutrient availability. Even without penalties for migration, under certain conditions, the sedentary Settler population dominates in the ecosystem. It is achieved by decreasing the local nutrient availability near the nutrient source, as motile populations relying on a local optimizing strategy tend to follow benign conditions and fail, enduring stress associated with crossing the valleys of suboptimal nutrient availability.

The competitive mechanism between post-abandonment Chinese fir plantations and rehabilitated natural secondary forest species under an in situ conservation policy

During the past 30 years, the global forest area has been subject to a continuous increase in planted forests and a decline in natural forests, raising significant concerns about biodiversity protection. Once these plantations are abandoned due to changes in conservation or forest management policies, can they recover to the same state as natural forests during secondary succession? The key ecological processes supporting the stable coexistence or competitive elimination mechanisms between post-abandonment plantations and natural secondary forest tree species are still poorly understood and may be the decisive ecological processes driving secondary forest restoration. A 12-ha long-term forest plot was established in an abandoned Chinese fir plantation that has been protected under an in situ protection policy for 40 years. In total, 66,317 individual trees were stem mapped and identified at the species level, and the spatial survival strategies and species coexistence mechanisms between Chinese fir and natural secondary forest tree species were investigated. The results showed that the spatial survival strategy of Chinese fir could effectively trade off a high conspecific density-dependent mortality rate of individuals during the early stage of secondary succession for the long-term survival of the whole population, which promoted its dominance during later stages of succession. By contrast, although the higher survival rate and larger intraspecific aggregation scale of natural secondary forest individuals favored their survival during initial colonization, this spatial survival strategy might occur at the cost of neglecting suitable habitats and the loss of competitive advantages at the later stage of succession. Regarding interspecific competition, the asymmetric competition process further ensured the advantages of Chinese fir in individual size growth and increased the competitive advantage of Chinese fir over natural secondary forest tree species by exclusion through interspecific competition during the later secondary succession stage. Our results suggest that implementing a forest recovery program or an in situ protection policy based on post-abandonment monoculture plantations may involve great uncertainty about whether the goal can be achieved. Specifically, although this strategy could quickly increase forest coverage and restore the forest landscape, it may also create difficulties in restoring the forest to its original state.

Density-Dependent Cannibalism in Dragonfly Nymphs (Odonata: Anisoptera) Overwintering in Temperate Freshwater Ponds.

Density-dependent mortality by predation and cannibalism has been observed in aquatic insects such as dragonflies in response to shrinking habitat caused by summer drought. Winter conditions might also reduce the amount of livable habitat in temperate ponds and could augment rates of cannibalism. We hypothesized that cannibalism in dragonfly nymphs would increase in winter due to a seasonal decrease in available habitat caused by stratified lower oxygen levels leading to increased nymph density around pond edges. To determine whether cannibalism in nymphs is density-dependent and size-dependent (i.e., with smaller nymphs consumed) we experimentally manipulated nymph density in aquaria. To evaluate whether these patterns are observed in nature during the winter, we conducted field surveys for nymphs in two ponds across the fall and winter seasons. When nymphs were housed at different densities for 24 h, cannibalism was density-dependent, and only smaller nymphs were preyed upon. Our field surveys found that fewer nymphs were caught in the late winter sampling period (mixed-effects model, P < 0.001), and that these were larger than nymphs caught in the fall, although both patterns were restricted to the deeper pond (P < 0.05). Our results were consistent with the process we hypothesized, and the observed reduction in dissolved oxygen at the bottom of the deeper pond. The lack of significant changes to the relative abundance and size of nymphs in the shallower pond reveals that differences in pond characteristics can influence the degree to which winter conditions induce density-dependent cannibalism among dragonfly nymphs.

Mathematical modeling and projections of a vector-borne disease with optimal control strategies: A case study of the Chikungunya in Chad

In this work, we extend existing models of vector-borne diseases by including density-dependent rates and some existing control mechanisms to decrease the disease burden in the human population. We begin by analyzing the vector model dynamics and by determining the offspring reproductive number denoted by N as well as the trivial and nontrivial equilibria. Using theory of cooperative systems and the general theory of Lyapunov, we prove that, although there is a possibility that the trivial equilibrium coexists with a positive equilibrium, it remains globally asymptotically stable whenever N ≤ 1 . The fact that the non-trivial equilibrium is globally asymptotically stable permits us to reduce the study of the full model to the study of a reduced model whenever N > 1 . Thus, we analyze the reduced model by computing the basic reproduction number R 0 , equilibrium points as well as asymptotic stability of each equilibrium point. We also explore the nature of the bifurcation for the disease-free equilibrium from R 0 = 1 . By the application of the centre manifold theory, we prove that the backward bifurcation phenomenon can occur in our model, which means that the necessary condition R 0 < 1 is not sufficient to guarantee the final extinction of the disease in human populations. To calibrate our model, we estimate model parameters on clinical data from the last Chikungunya epidemic which occurred in Chad, using the non-linear least-square method. We find out that R 0 = 1.8519 , which means that we are in an endemic state since R 0 > 1 . To determine model parameters that are responsible for disease spread in the human community, we perform sensitivity analysis (SA) using a global method. It follows that the density-dependent death rate of mosquitoes and the average number of mosquito bites are key parameters in the disease dynamics. Following this, we thus formulate an optimal control model by including in the autonomous model, four time-dependent control functions to fight the disease spread. Pontryagin’s maximum principle is used to characterize our optimal controls. Numerical simulations, using parameter values of Chikungunya transmission dynamics, and efficiency analysis, are conducted to determine the better control strategy which guaranteed the final extinction of the disease in human populations.

Quantifying the nature and strength of intraspecific density dependence in Arctic mosquitoes.

Processes that change with density are inherent in all populations, yet quantifying density dependence with empirical data remains a challenge. This is especially true for animals recruiting in patchy landscapes because heterogeneity in habitat quality in combination with habitat choice can obscure patterns expected from density dependence. Mosquitoes (Diptera: Culicidae) typically experience strong density dependence when larvae compete for food, however, effects vary across species and contexts. If populations experience intense intraspecific density-dependent mortality then overcompensation can occur, where the number of survivors declines at high densities producing complex endogenous dynamics. To seek generalizations about density dependence in a widespread species of Arctic mosquito, Aedes nigripes, we combined a laboratory experiment, field observations, and modeling approaches. We evaluated alternative formulations of discrete population models and compared best-performing models from our lab study to larval densities from ponds in western Greenland. Survivorship curves from the lab were the best fit by a Hassell model with compensating density dependence (equivalent to a Beverton-Holt model) where peak recruitment ranged from 8 to 80 mosquitoes per liter depending on resource supply. In contrast, our field data did not show a signal of strong density dependence, suggesting that other processes such as predation may lower realized densities in nature, and that expected patterns may be obscured because larval abundance covaries with resources (cryptic density dependence). Our study emphasizes the importance of covariation between the environment, habitat choice, and density dependence in understanding population dynamics across landscapes, and demonstrates the value of pairing lab and field studies.

On periodic solutions of a discrete Nicholson\u2019s dual system with density-dependent mortality and harvesting terms

In this study, we discuss the existence of positive periodic solutions of a class of discrete density-dependent mortal Nicholson’s dual system with harvesting terms. By means of the continuation coincidence degree theorem, a set of sufficient conditions, which ensure that there exists at least one positive periodic solution, are established. A numerical example with graphical simulation of the model is provided to examine the validity of the main results.

Existence and Stability of Periodic Solutions of Nicholson-Type System with Nonlinear Density-Dependent Mortality

Existence and Stability of Periodic Solutions of Nicholson-Type System with Nonlinear Density-Dependent Mortality

The cecal appendix is correlated with greater maximal longevity in mammals.

The cecal appendix had been considered as a useless vestige since Darwin's work, but recent research questioned this idea demonstrating that the cecal appendix appeared among the mammals at least 80 million years ago and has made multiple and independent appearances without any obvious correlation with diet, social life, ecology, or size of the cecum. However, functions and probable selective advantage conferred by this anatomical structure still remain enigmatic. We found, through analyses of data on 258 mammalian species, that cecal appendix presence is correlated with increased maximal observed longevity. This is the first demonstration of a correlation between cecal appendix presence and life history. Interestingly, the classical evolutionary theory of aging that predicts an increased longevity when the extrinsic mortality is reduced has been questioned several times, but recent comparative studies asserted its validity in the taxa, which experience age‐dependent and density‐dependent mortality, as in mammals. Thus, the cecal appendix may contribute to the increase in longevity through a reduction of extrinsic mortality. A lower risk of fatal infectious diarrhea is one of the most plausible hypotheses that could explain it. However, several hypotheses coexist about the possible functions of the cecal appendix, and our results provide new insights about this much‐disputed question. In addition, we show that the cecal appendix arose at least 16 times and was lost only once during the evolutionary history of the considered mammals, an asymmetry that supports the existence of a positive selective of this structure.