skip to main content

Title: Ideal free dispersal in integrodifference models.
In this paper, we use an integrodifference equation model and pairwise invasion analysis to find what dispersal strategies are evolutionarily stable strategies (ESS) when there is spatial heterogeneity in habitat suitability, and there may be seasonal changes in this spatial heterogeneity, so that there are both advantages and disadvantages of dispersing. We begin with the case where all spatial locations can support a viable population, and then consider the case where there are non-viable regions in the habitat that makes dispersal really necessary for sustaining a population. Our findings generally align with previous findings in the literature that were based on other modeling frameworks, namely that dispersal strategies associated with ideal free distributions are evolutionarily stable. In the case where only part of the habitat can sustain a population, a partial occupation ideal free distribution that occupies only the viable region is shown to be associated with a dispersal strategy that is evolutionarily stable. As in some previous works, the proofs of these results make use of properties of line sum symmetric functions, which are analogous to those of line sum symmetric matrices but applies to integral operators.
Authors:
; ;
Award ID(s):
1853478
Publication Date:
NSF-PAR ID:
10381045
Journal Name:
Journal of mathematical biology
Volume:
85
Issue:
1
Page Range or eLocation-ID:
1-39
ISSN:
0303-6812
Sponsoring Org:
National Science Foundation
More Like this
  1. Pathogens evolve different life-history strategies, which depend in part on differences in their host populations. A central feature of hosts is their population structure (e.g. spatial). Additionally, hosts themselves can exhibit different degrees of symptoms when newly infected; this latency is a key life-history property of pathogens. With an evolutionary-epidemiological model, we examine the role of population structure on the evolutionary dynamics of latency. We focus on specific power-law-like formulations for transmission and progression from the first infectious stage as a function of latency, assuming that the across-group to within-group transmission ratio increases if hosts are less symptomatic. We find that simple population heterogeneity can lead to local evolutionarily stable strategies (ESSs) at zero and infinite latency in situations where a unique ESS exists in the corresponding homogeneous case. Furthermore, there can exist more than one interior evolutionarily singular strategy. We find that this diversity of outcomes is due to the (possibly slight) advantage of across-group transmission for pathogens that produce fewer symptoms in a first infectious stage. Thus, our work reveals that allowing individuals without symptoms to travel can have important unintended evolutionary effects and is thus fundamentally problematic in view of the evolutionary dynamics of latency.
  2. Abstract Standard procedures for capture–mark–recapture modelling (CMR) for the study of animal demography include running goodness-of-fit tests on a general starting model. A frequent reason for poor model fit is heterogeneity in local survival among individuals captured for the first time and those already captured or seen on previous occasions. This deviation is technically termed a transience effect. In specific cases, simple, uni-state CMR modeling showing transients may allow researchers to assess the role of these transients on population dynamics. Transient individuals nearly always have a lower local survival probability, which may appear for a number of reasons. In most cases, transients arise due to permanent dispersal, higher mortality, or a combination of both. In the case of higher mortality, transients may be symptomatic of a cost of first reproduction. A few studies working at large spatial scales actually show that transients more often correspond to survival costs of first reproduction rather than to permanent dispersal, bolstering the interpretation of transience as a measure of costs of reproduction, since initial detections are often associated with first breeding attempts. Regardless of their cause, the loss of transients from a local population should lower population growth rate. We review almost 1000 papersmore »using CMR modeling and find that almost 40% of studies fitting the searching criteria (N = 115) detected transients. Nevertheless, few researchers have considered the ecological or evolutionary meaning of the transient phenomenon. Only three studies from the reviewed papers considered transients to be a cost of first reproduction. We also analyze a long-term individual monitoring dataset (1988–2012) on a long-lived bird to quantify transients, and we use a life table response experiment (LTRE) to measure the consequences of transients at a population level. As expected, population growth rate decreased when the environment became harsher while the proportion of transients increased. LTRE analysis showed that population growth can be substantially affected by changes in traits that are variable under environmental stochasticity and deterministic perturbations, such as recruitment, fecundity of experienced individuals, and transient probabilities. This occurred even though sensitivities and elasticities of these parameters were much lower than those for adult survival. The proportion of transients also increased with the strength of density-dependence. These results have implications for ecological and evolutionary studies and may stimulate other researchers to explore the ecological processes behind the occurrence of transients in capture–recapture studies. In population models, the inclusion of a specific state for transients may help to make more reliable predictions for endangered and harvested species.« less
  3. Migration is a tactic used across taxa to access resources in temporally heterogenous landscapes. Populations that migrate can attain higher abundances because such movements allow access to higher quality resources, or reduction in predation risk resulting in increased fitness. However, most migratory species occur in partially migratory populations, a mix of migratory and non-migratory individuals. It is thought that the portion of migrants in a partial migration population is maintained either through (1) a population-level evolutionary stable state where counteracting density-dependent vital rates act on migrants and residents to balance fitness or (2) conditional migration, where the propensity to migrate is influenced by the individual's state. However, in many respects, migration is also a form of habitat selection and the proportion of migrants and residents may be the result of density-dependent habitat selection. Here, we test whether the theory of Ideal Free Distribution (IFD) can explain the coexistence of different migratory tactics in a partially migratory population. IFD predicts individuals exhibit density-dependent vital rates and select different migratory tactics to maximize individual fitness resulting in equal fitness (λ) between tactics. We tested the predictions of IFD in a partially migratory elk population that declined by 70% with 19 years of demographicmore »data and migratory tactic switching rates from >300 individuals. We found evidence of density dependence for resident pregnancy and adult female survival providing a fitness incentive to switch tactics. Despite differences in vital rates between migratory tactics, mean λ (fitness) was equal. However, as predicted by the IFD, individuals switched tactics toward those of higher fitness. Our analysis reveals that partial migration may be driven by tactic selection that follows the ideal free distribution. These findings reinforce that migration across taxa may be a polymorphic behavior in large herbivores where migratory tactic selection is determined by differential costs and benefits, mediated by density dependence.« less
  4. Pathogens exhibit a rich variety of life history strategies, shaped by natural selection. An important pathogen life history characteristic is the propensity to induce an asymptomatic yet productive (transmissive) stage at the beginning of an infection. This characteristic is subject to complex trade-offs, ranging from immunological considerations to population-level social processes. We aim to classify the evolutionary dynamics of such asymptomatic behavior of pathogens (hereafter “latency”) in order to unify epidemiology and evolution for this life history strategy. We focus on a simple epidemiological model with two infectious stages, where hosts in the first stage can be partially or fully asymptomatic. Immunologically, there is a trade-off between transmission and progression in this first stage. For arbitrary trade-offs, we derive different conditions that guarantee either at least one evolutionarily stable strategy (ESS) at zero, some, or maximal latency of the first stage or, perhaps surprisingly, at least one unstable evolutionarily singular strategy. In this latter case, there is bistability between zero and nonzero (possibly maximal) latency. We then prove the uniqueness of interior evolutionarily singular strategies for power-law and exponential trade-offs: Thus, bistability is always between zero and maximal latency. Overall, previous multistage infection models can be summarized with a singlemore »model that includes evolutionary processes acting on latency. Since small changes in parameter values can lead to abrupt transitions in evolutionary dynamics, appropriate disease control strategies could have a substantial impact on the evolution of first-stage latency.

    « less
  5. Background

    Vestimentiferan tubeworms are some of the most recognizable fauna found at deep-sea cold seeps, isolated environments where hydrocarbon rich fluids fuel biological communities. Several studies have investigated tubeworm population structure; however, much is still unknown about larval dispersal patterns at Gulf of Mexico (GoM) seeps. As such, researchers have applied microsatellite markers as a measure for documenting the transport of vestimentiferan individuals. In the present study, we investigate the utility of microsatellites to be cross-amplified within the escarpiid clade of seep vestimentiferans, by determining if loci originally developed forEscarpiaspp. could be amplified in the GoM seep tubeworm,Seepiophila jonesi. Additionally, we determine if cross-amplified loci can reliably uncover the same signatures of high gene flow seen in a previous investigation ofS. jonesi.

    Methods

    Seventy-sevenS. jonesiindividuals were collected from eight seep sites across the upper Louisiana slope (<1,000 m) in the GoM. Forty-eight microsatellite loci that were originally developed forEscarpia laminata(18 loci) andEscarpia southwardae(30 loci) were tested to determine if they were homologous and polymorphic inS. jonesi. Loci found to be both polymorphic and of high quality were used to test for significant population structuring inS. jonesi.

    Results

    Microsatellite pre-screening identified 13 (27%) of theEscarpialoci were homologous and polymorphic inS. jonesi, revealing that microsatellitesmore »can be amplified within the escarpiid clade of vestimentiferans. Our findings uncovered low levels of heterozygosity and a lack of genetic differentiation amongstS. jonesifrom various sites and regions, in line with previous investigations that employed species-specific polymorphic loci onS. jonesiindividuals retrieved from both the same and different seep sites. The lack of genetic structure identified from these populations supports the presence of significant gene flow via larval dispersal in mixed oceanic currents.

    Discussion

    The ability to develop “universal” microsatellites reduces the costs associated with these analyses and allows researchers to track and investigate a wider array of taxa, which is particularly useful for organisms living at inaccessible locations such as the deep sea. Our study highlights that non-species specific microsatellites can be amplified across large evolutionary distances and still yield similar findings as species-specific loci. Further, these results show thatS. jonesicollected from various localities in the GoM represents a single panmictic population, suggesting that dispersal of lecithotrophic larvae by deep sea currents is sufficient to homogenize populations. These data are consistent with the high levels of gene flow seen inEscarpiaspp., which advocates that differences in microhabitats of seep localities lead to variation in biogeography of separate species.

    « less