Demographic Stochasticity Research Articles

Cheater suppression and stochastic clearance through quorum sensing.

The evolutionary consequences of quorum sensing in regulating bacterial cooperation are not fully understood. In this study, we reveal unexpected effects of regulating public good production through quorum sensing on bacterial population dynamics, showing that quorum sensing can be a collectively harmful alternative to unregulated production. We analyze a birth-death model of bacterial population dynamics accounting for public good production and the presence of non-producing cheaters. Our model demonstrates that when demographic noise is a factor, the consequences of controlling public good production according to quorum sensing depend on the cost of public good production and the growth rate of populations in the absence of public goods. When public good production is inexpensive, quorum sensing is a destructive alternative to unconditional production, in terms of the mean population extinction time. When costs are higher, quorum sensing becomes a constructive strategy for the producing strain, both stabilizing cooperation and decreasing the risk of population extinction.

Multi-year evidence of unbiased sex ratios in hatchery and wild-reared age-0 lake sturgeon (Acipenser fulvescens)

Assessment of population sex ratios allows managers to forecast recruitment dynamics and loss of genetic diversity in natural populations and is important when the focal population is in low abundance and subject to demographic stochasticity. If levels of natural or artificial selection differ for males and females and levels of mortality likewise vary, lower levels of population recruitment, loss of genetic diversity, and genetic drift can occur. Lake sturgeon (Acipenser fulvescens) are a species of conservation concern, where restoration efforts increasingly rely on hatchery supplementation. Raising larvae to the juvenile stage can increase survival during important early life stages; however, knowledge is lacking concerning effects of artificial rearing environments on differential sex-specific survival before release. We genetically determined the sex of 1459 age-0 lake sturgeon from three cohorts (2016 through 2018) using PCR assays of the ALLWSex2 acipenserid sexing marker. Sexed individuals represented three groups: (1) wild-captured dispersing larvae that died during hatchery rearing, (2) wild-captured dispersing larvae that survived hatchery rearing to release, and (3) wild-captured, wild-raised age-0 individuals. Sex ratios of wild-captured larvae (dead + live) were nearly 50:50 in all years surveyed. We observed slight, but non-significant, directionality in sex ratios in the live and dead hatchery-reared larvae and in wild-captured age-0 individuals. Genetic sexing methods allow for analyses during prolonged pre-reproductive periods and associated variable environmental and demographic circumstances, in situations where physical determination of sex is not possible.

Stochasticity Leads to Coexistence of Generalists and Specialists in Assembling Mutualistic Communities.

AbstractSpecies interaction networks are subject to natural and anthropogenic disturbances that lead to their disassembly, while natural regeneration or restoration efforts facilitate their reassembly. Previous models for assembling ecological networks did not include stochasticity at the level of population dynamics (e.g., demographic noise, environmental noise) and focused mainly on food webs. Here, we present a model for the assembly of mutualistic bipartite networks, such as plant-pollinator networks, and examine the influence of demographic noise on the trajectory of species and strategy diversity, that is, the range of present strategies from specialism to generalism. We find that assembled communities show at intermediate assembly stages a maximum of species diversity and of average generalization. Our model thus provides a mechanism for nonlinear, hump-shaped diversity trajectories at intermediate succession, consistent with the intermediate disturbance hypothesis. Long-term coexistence of specialists and generalists emerges only in the presence of demographic noise and is due to a persistent species turnover. These findings highlight the importance of stochasticity for maintaining long-term diversity.

A Hybrid Epidemic Model to Explore Stochasticity in COVID-19 Dynamics

The dynamic nature of the COVID-19 pandemic has demanded a public health response that is constantly evolving due to the novelty of the virus. Many jurisdictions in the USA, Canada, and across the world have adopted social distancing and recommended the use of face masks. Considering these measures, it is prudent to understand the contributions of subpopulations—such as “silent spreaders”—to disease transmission dynamics in order to inform public health strategies in a jurisdiction-dependent manner. Additionally, we and others have shown that demographic and environmental stochasticity in transmission rates can play an important role in shaping disease dynamics. Here, we create a model for the COVID-19 pandemic by including two classes of individuals: silent spreaders, who either never experience a symptomatic phase or remain undetected throughout their disease course; and symptomatic spreaders, who experience symptoms and are detected. We fit the model to real-time COVID-19 confirmed cases and deaths to derive the transmission rates, death rates, and other relevant parameters for multiple phases of outbreaks in British Columbia (BC), Canada. We determine the extent to which SilS contributed to BC’s early wave of disease transmission as well as the impact of public health interventions on reducing transmission from both SilS and SymS. To do this, we validate our model against an existing COVID-19 parameterized framework and then fit our model to clinical data to estimate key parameter values for different stages of BC’s disease dynamics. We then use these parameters to construct a hybrid stochastic model that leverages the strengths of both a time-nonhomogeneous discrete process and a stochastic differential equation model. By combining these previously established approaches, we explore the impact of demographic and environmental variability on disease dynamics by simulating various scenarios in which a COVID-19 outbreak is initiated. Our results demonstrate that variability in disease transmission rate impacts the probability and severity of COVID-19 outbreaks differently in high- versus low-transmission scenarios.

Can antioxidant responses be induced by habitat fragmentation process?

Animal populations are increasingly forced to live in small residual natural or semi‐natural areas due to habitat loss and fragmentation. Here, the viability of populations is often compromised by intrinsic threat factors typical of small and isolated populations, such as inbreeding depression, genetic drift and environmental and demographic stochasticity. Under these circumstances, organisms may have low fitness due to inadequate physiological responses needed to face environmental challenges. However, few studies have investigated the relationship between habitat fragmentation and stress defences. In this study, we aimed to test whether an increase in the level of individual inbreeding produced an increase in the antioxidant system response. To this purpose, we genotyped 151 individuals of fire salamander Salamandra salamandra (Amphibia: Urodela) within five sampling populations, located in forest landscapes with different degree of fragmentation in northern Italy. For 113 individuals we also measured the glutathione‐S‐transferase (GST) and catalase (CAT) enzyme activity. Results showed a significant increase in individual GST activity for increasing levels of inbreeding, whereas no relationship was found for CAT. We also measured acetylcholinesterase to test the possible confounding effects of pesticides that might have occurred in fragmented landscapes with forests interspersed with agricultural areas. However, no difference in this enzyme activity was found among sampling populations. We argue that high levels of GST activity may be symptomatic of oxidative stress derived from inbreeding. An increased frequency of homozygous deleterious alleles due to inbreeding may cause homeostatic alterations and trigger the expression of GST for protection against hydrogen peroxide reactive oxygen species. We suggest using GST as a biomarker for environmental stressors with great caution and not to underestimate that the sources of stress deriving from habitat fragmentation could lead to an unbalance in the oxidative status, possibly increasing population susceptibility to infectious diseases and, potentially, spillover events and zoonoses.

An attractor domain model of seasonal and inter‐annual β diversity of stream macroinvertebrate communities

Abstract Ecological communities are dynamic systems that vary within and across years. In streams, disturbance by spates and the emergence of adult insects during the rainy summer contrast with more stable conditions in the dry winter and can potentially generate distinct and repeatable community states across years. However, demographic stochasticity and the legacies of previous spates may hamper the full attainment of characteristic community states associated with seasons. We developed an attractor domain model encapsulating these factors and hypothesised: (1) partially distinct rainy (summer) and dry (winter) communities. High benthic dynamism during the rainy period should cause higher inter‐annual variability, leading to (2) higher temporal β diversity among rainy periods than among dry periods. Historical effects (e.g., demographic stochasticity and disturbance by spates) should accumulate over the years and lead to (3) increased variation in community structures sampled further apart in time; furthermore, (4) this increase in variation should be higher among rainy than among dry communities. We used data of stream macroinvertebrates (mostly insects) in a subtropical basin in Brazil to evaluate inter‐annual variation using rank‐concordance statistics of the most common species and dissimilarity using all species. For each stream site, samples obtained in the two seasons tended to show distinct community structure using relative abundance data but were much less distinct using species composition (presence–absence). Temporal β diversity was higher among rainy than among dry seasons. The β diversity of both seasons increased with time, although this increase was 2–3 times greater during the rainy season. Our results support a model in which rainy (summer) communities are disrupted by the high dynamism caused by spates and the emergence of adult insects. The low intensity of these two factors during dry (winter) periods allows local environmental conditions to drive community structures toward a less variable, recurrent attractor state. However, the increase in β diversity with time indicates that the legacy effects of previous disturbances and demographic stochasticity preclude the full attainment of a definite stable state and that only a domain of states is approached.

Meter-scale variation within a single transect demands attention to taxon accumulation curves in riverine microbiome studies

Microbial communities inhabiting river ecosystems play crucial roles in global biogeochemical cycling and pollution attenuation. Spatial variations in local microbial assemblages are important for detailed understanding of community assembly and developing robust biodiversity sampling strategies. Here, we intensely analyzed twenty water samples collected from a one-meter spaced transect from the near-shore to the near-center in the Meramec River in eastern Missouri, USA and examined the microbial community composition with 16S rRNA gene amplicon sequencing. Riverine microbiomes across the transect exhibited extremely high similarity, with Pearson’s correlation coefficients above 0.9 for all pairwise community composition comparisons. However, despite the high similarity, PERMANOVA revealed significant spatial differences between near-shore and near-center communities (p = 0.001). Sloan’s neutral model simulations revealed that within-transect community composition variation was largely explained by demographic stochasticity (R2 = 0.89). Despite being primarily explained by neutral processes, LefSe analyses also revealed taxa from ten families of which relative abundances differed directionally from the bank to the river center, indicating an additional role of environmental filtering. Notably, the local variations within a river transect can have profound impacts on the documentation of alpha diversity. Taxon-accumulation curves indicated that even twenty samples did not fully saturate the sampling effort at the genus level, yet four, six and seven samples were able to capture 80% of the phylum-level, family-level, and genus-level diversity, respectively. This study for the first time reveals hyperlocal variations in riverine microbiomes and their assembly mechanisms, demanding attention to more robust sampling strategies for documenting microbial diversity in riverine systems.

A stochastic model for estimating sustainable limits to wildlife mortality in a changing world.

Human‐caused mortality of wildlife is a pervasive threat to biodiversity. Assessing the population‐level impact of fisheries bycatch and other human‐caused mortality of wildlife has typically relied upon deterministic methods. However, population declines are often accelerated by stochastic factors that are not accounted for in such conventional methods. Building on the widely applied potential biological removal (PBR) equation, we devised a new population modeling approach for estimating sustainable limits to human‐caused mortality and applied it in a case study of bottlenose dolphins affected by capture in an Australian demersal otter trawl fishery. Our approach, termed sustainable anthropogenic mortality in stochastic environments (SAMSE), incorporates environmental and demographic stochasticity, including the dependency of offspring on their mothers. The SAMSE limit is the maximum number of individuals that can be removed without causing negative stochastic population growth. We calculated a PBR of 16.2 dolphins per year based on the best abundance estimate available. In contrast, the SAMSE model indicated that only 2.3–8.0 dolphins could be removed annually without causing a population decline in a stochastic environment. These results suggest that reported bycatch rates are unsustainable in the long term, unless reproductive rates are consistently higher than average. The difference between the deterministic PBR calculation and the SAMSE limits showed that deterministic approaches may underestimate the true impact of human‐caused mortality of wildlife. This highlights the importance of integrating stochasticity when evaluating the impact of bycatch or other human‐caused mortality on wildlife, such as hunting, lethal control measures, and wind turbine collisions. Although population viability analysis (PVA) has been used to evaluate the impact of human‐caused mortality, SAMSE represents a novel PVA framework that incorporates stochasticity for estimating acceptable levels of human‐caused mortality. It offers a broadly applicable, stochastic addition to the demographic toolbox to evaluate the impact of human‐caused mortality on wildlife.

Allee Effects Plus Noise Induce Population Dynamics Resembling Binary Markov Highs and Lows.

We show that the combination of Allee effects and noise can produce a stochastic process with alternating sudden decline to a low population phase, followed, after a random time, by abrupt increase in population density. We introduce a new, flexible, deterministic model of attenuated Allee effects, which interpolates between the logistic and a usual Allee model. Into this model, we incorporate environmental and demographic noise. The solution of the resulting Kolmogorov forward equation shows a dichotomous distribution of residence times with heavy occupation of high, near saturation, and low population states. Investigation of simulated sample paths reveals that indeed attenuated Allee effects and noise, acting together, produce alternating, sustained, low and high population levels. We find that the transition times between the two types of states are approximately exponentially distributed, with different parameters, rendering the embedded hi-low process approximately Markov.

Trajectory to local extinction of an isolated dugong population near Okinawa Island, Japan

A small animal population becomes extinct owing to demographic and environmental stochasticity after declining below the minimum viable population (MVP). However, the actual process of extinction derived by stochastic factors after crossing MVP has not been recorded for long-lived marine mammals. Here, we reconstructed the declining history of a small, isolated population of dugongs in Okinawa over 125 years. The initial population size of approximately 280–420 in the nineteenth century declined to approximately < 100 in 1917 because of overfishing, < 70 in 1979, 11 in 1997, 3 after 2006, and all known individuals disappeared or died by 2019. After 1979, a decline in the natural growth rate has led to extinction. Long-lived animals may persist for a few decades after the population falls below the MVP, at which time active conservation measures, such as captive breeding, should be implemented.

Community variability in pond metacommunities: interactive effects of predators and isolation on stochastic community assembly

In the absence of environmental heterogeneity, spatial variation among local communities can be mostly attributed to random dispersal, demographic stochasticity and species interactions causing historical contingency in colonization (e.g. priority effects). The consequences of demographic stochasticity and random dispersal are highly dependent on community size, regional richness and local richness, which, along with historical contingency can be strongly affected by spatial isolation and the presence of predators. Here, we tested whether and how the presence of a generalist predatory fish and spatial isolation can change spatial community variability in artificial ponds by manipulating the presence/absence of fish (redbreast tilapia) at three different distances from a source wetland. We then used null models to compute how much the observed community variability within treatments deviates from the expected from randomly reassembled communities (i.e. beta‐deviation). We found that spatial isolation can have both negative and positive effects on community variability, and their importance may depend on the presence of predatory fish. Negative effects likely occurred because predatory insects cannot always successfully colonize highly isolated ponds, causing the abundance of herbivores and detritivores to increase, consequently increasing community size, which is known to decrease the importance of demographic stochasticity. However, when fish are absent, the more isolated communities exhibit more community variability than is expected from random community assembly. We believe that such an increase in variability is most likely due to an increase in the importance of historical contingency in colonization, generating more distinct communities in isolated ponds. Such effects were absent in the presence of generalist predatory fish, likely because fish prevented any early colonizing taxa from becoming too abundant. Our findings show that the presence of generalist predators can change how community variability responds to spatial isolation.

Temporal variation may have diverse impacts on range limits.

Environmental fluctuations are pervasive in nature, but the influence of non-directional temporal variation on range limits has received scant attention. We synthesize insights from the literature and use simple models to make conceptual points about the potentially wide range of ecological and evolutionary effects of temporal variation on range limits. Because organisms respond nonlinearly to environmental conditions, temporal variation can directionally alter long-term growth rates, either to shrink or to expand ranges. We illustrate this diversity of outcomes with a model of competition along a mortality gradient. Temporal variation can permit transitions between alternative states, potentially facilitating range expansion. We show this for variation in dispersal, using simple source–sink population models (with strong Allee effects, or with gene flow hampering local adaptation). Temporal variation enhances extinction risk owing to demographic stochasticity, rare events, and loss of genetic variation, all tending to shrink ranges. However, specific adaptations to exploit variation (including dispersal) may permit larger ranges than in similar but constant environments. Grappling with temporal variation is essential both to understand eco-evolutionary dynamics at range limits and to guide conservation and management strategies.This article is part of the theme issue ‘Species’ ranges in the face of changing environments (Part II)’.

Outbreak Size Distribution in Stochastic Epidemic Models.

Motivated by recent epidemic outbreaks, including those of COVID-19, we solve the canonical problem of calculating the dynamics and likelihood of extensive outbreaks in a population within a large class of stochastic epidemic models with demographic noise, including the susceptible-infected-recovered (SIR) model and its general extensions. In the limit of large populations, we compute the probability distribution for all extensive outbreaks, including those that entail unusually large or small (extreme) proportions of the population infected. Our approach reveals that, unlike other well-known examples of rare events occurring in discrete-state stochastic systems, the statistics of extreme outbreaks emanate from a full continuum of Hamiltonian paths, each satisfying unique boundary conditions with a conserved probability flux.

A Comparison of Deterministic and Stochastic Plant-Vector-Virus Models Based on Probability of Disease Extinction and Outbreak

In this investigation, we formulate and analyse a stochastic epidemic model using the continuous-time Markov chain model for the propagation of a vector-borne cassava mosaic disease in a single population. The stochastic model is based upon a pre-existing deterministic plant-vector-virus model. To see how demographic stochasticity affects the vector-borne cassava mosaic disease dynamics, we compare the disease dynamics of both deterministic and stochastic models through disease extinction process. The probability of disease extinction and therefore the major outbreak are estimated analytically using the multitype Galton-Watson branching process (GWbp) approximation. Also, we have found the approximate probabilities of disease extinction numerically based on 30000 sample paths, and it is shown to be good estimate with the calculated probabilities from GWbp approximation. In particular, it is observed that there is a very high probability of disease extinction when the disease is introduced via the infected vectors rather than through infected plants.

Similar species, different fates: Abundance dynamics in spatially structured populations of common and threatened frogs

AbstractAimUnderstanding which factors determine the variation in population size across space and time is crucial to plan sound conservation interventions. Amphibians are often characterized by large demographic changes, therefore a better understanding of factors driving these changes could help mitigate their global crisis. We investigated drivers of abundance dynamics of two similar frog species to understand why they met different fates in the same study area.LocationNorthern Italy.MethodsIn seven different years between 2004 and 2020, we performed repeated counts of egg masses of two similar frog species, the agile frog (Rana dalmatina) and the Italian agile frog (Rana latastei), in 31 wetlands, and used Bayesian models to estimate the relationships between frog abundance and candidate drivers acting at the scale of (i) site: wetland surface, shading percentage and the presence of the invasive red swamp crayfish (Procambarus clarkii); (ii) landscape: forest cover around wetlands; (iii) climate: yearly precipitation and (iv) spatially structured population (SSP): clutch incidence of the focal species and crayfish incidence in the surrounding landscape.ResultsThe two species showed sharp differences in population size and trends: R. dalmatina was abundant and showed a stable trend throughout the entire study period; R. latastei showed low abundance in the first years and then almost disappeared. The abundance of R. dalmatina was positively related to forest cover, shading, wetland area and precipitation, while negatively related to the occurrence of invasive crayfish at both local and SSP level. R. latastei abundance increased with wetland area and precipitation, while models were not able to detect relationships with other factors.Main conclusionsThe high sensitivity to drought and demographic stochasticity could have contributed to the quasi‐extinction of R. latastei in the study area, highlighting that similar species can meet different fates even under the same environmental conditions.

Genetic load and extinction in peripheral populations: the roles of migration, drift and demographic stochasticity

We analyse how migration from a large mainland influences genetic load and population numbers on an island, in a scenario where fitness-affecting variants are unconditionally deleterious, and where numbers decline with increasing load. Our analysis shows that migration can have qualitatively different effects, depending on the total mutation target and fitness effects of deleterious variants. In particular, we find that populations exhibit a genetic Allee effect across a wide range of parameter combinations, when variants are partially recessive, cycling between low-load (large-population) and high-load (sink) states. Increased migration reduces load in the sink state (by increasing heterozygosity) but further inflates load in the large-population state (by hindering purging). We identify various critical parameter thresholds at which one or other stable state collapses, and discuss how these thresholds are influenced by the genetic versus demographic effects of migration. Our analysis is based on a ‘semi-deterministic’ analysis, which accounts for genetic drift but neglects demographic stochasticity. We also compare against simulations which account for both demographic stochasticity and drift. Our results clarify the importance of gene flow as a key determinant of extinction risk in peripheral populations, even in the absence of ecological gradients.This article is part of the theme issue ‘Species’ ranges in the face of changing environments (part I)’.

Threats to Neglected Biodiversity: Conservation Success Requires More Than Charisma

Our planet is home to an incredible array of species; however, relatively few studies have compared how anthropogenic threats impact taxonomic groups over time. Our objective was to identify temporal trends in threats facing the four most speciose phyla protected by the United States Endangered Species Act: angiosperms, arthropods, chordates, and mollusks. We determined presence or absence of threats for each species in these phyla by reviewing Final Rule listing decisions. For each phylum, we evaluated whether there was a linear, quadratic, or pseudo-threshold association between year of listing and the presence of 24 anthropogenic threats. We identified temporal trends for 80% of the 96 threat-phylum combinations. We classified threats as topmost (probability of being included in a species' listing decision peaking at ≥ 0.81) and escalating (probability of being included in a listing decision increasing by ≥ 0.81 between a species' first and most recent years of listing). Angiosperms, arthropods, and mollusks each had more topmost and escalating threats than chordates. Percentages of topmost threats were 42.9% (N = 21) for mollusks, 36.4% (N = 22) for angiosperms, and 33.3% (N = 21) for arthropods. Percentages of escalating threats were 22.7% (N = 22) for angiosperms and 14.3% (N = 21) for arthropods and mollusks. In contrast, percentages of topmost and escalating threats were only 4.2% (N = 24) for chordates, this one threat being climate change. Our research suggests potential conservation successes; some overutilization and pollution threats showed only gradually increasing or declining trends for certain phyla. We identified authorized take impacting angiosperms as the sole threat-phylum combination for which the threat had been consistently decreasing since the phylum's first year of listing. Conversely, species interactions, environmental stochasticity, and demographic stochasticity threats have seen drastic increases across all phyla; we suggest conservation efforts focus on these areas of increasing concern. We also recommend that resources be allocated to phyla with numerous topmost and escalating threats, not just to chordates.

Estimating the population size and habitat quality of the Endangered fish Tlaloc hildebrandi in Mexico

The Chiapas killifish Tlaloc hildebrandi is an Endangered and endemic fish that inhabits wetlands, mountain streams, and rivers in Chiapas, Mexico. This species is considered vulnerable due to accelerated human population growth in its distribution range and the species’ low genetic diversity. To evaluate the conservation status of the species, we assessed habitat quality and estimated the population size of the remnant populations in the Amarillo River subbasin using the capture-mark-recapture technique. Our results showed substantial levels of habitat perturbation in the Amarillo River subbasin, including water pollution with a high presence of coliforms, the presence of exotic species, and modified habitat quality, which has resulted in a decrease in population sizes and the extirpation of certain populations. Our estimates of the population sizes of T. hildebrandi based on the Jolly-Seber model showed dramatically low population sizes, ranging from 93 to 208 fish across sites. Gross population sizes varied temporally, and the location of these populations in isolated sites may increase demographic stochasticity. To preserve some of these populations, urgent conservation and management activities must be implemented. We suggest the establishment of conservation areas for the species in the Fogótico River (which has the best water quality and habitat conditions) and habitat restoration in the protected areas of La Kisst and María Eugenia Mountain Wetlands, where populations of T. hildebrandi could be reintroduced. Finally, we propose the implementation of ex situ conservation programs to maintain genetic diversity and prevent local extinctions of the most vulnerable populations.

Individual-based and continuum models of phenotypically heterogeneous growing cell populations

&lt;abstract&gt; &lt;p&gt;Existing comparative studies between individual-based models of growing cell populations and their continuum counterparts have mainly been focused on homogeneous populations, in which all cells have the same phenotypic characteristics. However, significant intercellular phenotypic variability is commonly observed in cellular systems. In light of these considerations, we develop here an individual-based model for the growth of phenotypically heterogeneous cell populations. In this model, the phenotypic state of each cell is described by a structuring variable that captures intercellular variability in cell proliferation and migration rates. The model tracks the spatial evolutionary dynamics of single cells, which undergo pressure-dependent proliferation, heritable phenotypic changes and directional movement in response to pressure differentials. We formally show that the continuum limit of this model comprises a non-local partial differential equation for the cell population density function, which generalises earlier models of growing cell populations. We report on the results of numerical simulations of the individual-based model which illustrate how proliferation-migration tradeoffs shaping the evolutionary dynamics of single cells can lead to the formation, at the population level, of travelling waves whereby highly-mobile cells locally dominate at the invasive front, while more-proliferative cells are found at the rear. Moreover, we demonstrate that there is an excellent quantitative agreement between these results and the results of numerical simulations and formal travelling-wave analysis of the continuum model, when sufficiently large cell numbers are considered. We also provide numerical evidence of scenarios in which the predictions of the two models may differ due to demographic stochasticity, which cannot be captured by the continuum model. This indicates the importance of integrating individual-based and continuum approaches when modelling the growth of phenotypically heterogeneous cell populations.&lt;/p&gt; &lt;/abstract&gt;

Detecting patterns of correlational selection with sampling error: A simulation study.

The adoption of a multivariate perspective of selection implies the existence of multivariate adaptive peaks and pervasive correlational selection that promotes co-adaptation between traits. However, to test for the ubiquity of correlational selection in nature, we must first have a sense of how well can we estimate multivariate nonlinear selection (i.e., the γ-matrix) in the face of sampling error. To explore the sampling properties of estimated γ-matrices, we simulated inidividual traits and fitness under a wide range of sample sizes, using different strengths of correlational selection and of stabilizing selection, combined with different number of traits under selection, different amounts of residual variance in fitness, and distinct patterns of selection. We then ran nonlinear regressions with these simulated datasets to simulate γ-matrices after adding random error to individual fitness. To test how well could we detect the imposed pattern of correlational selection at different sample sizes, we measured the similarity between simulated and imposed γ-matrices. We show that detection of the pattern of correlational selection is highly dependent on the total strength of selection on traits and on the amount of residual variance in fitness. Minimum sample size needs to be at least 500 to precisely estimate the pattern of correlational selection. Furthermore, a pattern of selection in which different sets of traits contribute to different functions is the easiest to diagnose, even when using a large number of traits (10 traits), but with sample sizes in the order of 1000 individuals. Consequently, we recommend working with sets of traits from distinct functional complexes and fitness proxies less prone to effects of environmental and demographic stochasticity to test for correlational selection with lower sample sizes.