Mate Sampling Behavior Determines the Density Dependence of Sexual Selection.

AbstractTheory predicts that the strength of sexual selection (i.e., how well a trait predicts mating or fertilization success) should increase with population density, yet empirical support remains mixed. We explore how this discrepancy might reflect a disconnect between current theory and our understanding of the strategies individuals use to choose mates. We demonstrate that the density dependence of sexual selection predicted by previous theory arises from the assumption that individuals automatically sample more potential mates at higher densities. We provide an updated theoretical framework for the density dependence of sexual selection by (1) developing models that clarify the mechanisms through which density-dependent mate sampling strategies might be favored by selection and (2) using simulations to determine how sexual selection changes with population density when individuals use those strategies. We find that sexual selection may increase strongly with density if sampling strategies change adaptively in response to density-dependent sampling costs, whereas within-individual plasticity in sampling over time (e.g., due to adaptation to increasing sampling costs as the breeding season progresses) produces weaker density-dependent sexual selection. Our findings suggest that density dependence of sexual selection depends on the ecological context in which mate sampling has evolved.

Modeling the evolution of herbicide resistance in weed species with a complex life cycle.

A growing number of weed species have evolved resistance to herbicides in recent years, which causes an immense financial burden to farmers. An increasingly popular method of weed control is the adoption of crops that are resistant to specific herbicides, which allows farmers to apply the herbicide during the growing season without harming the crop. If such crops are planted in the presence of closely related weed species, it is possible that resistance genes could transfer from the crop species to feral populations of the wild species via gene flow and become stably introgressed under ongoing selective pressure by the herbicide. We use a density-dependent matrix model to evaluate the effect of planting such crops on the evolution of herbicide resistance under a range of management scenarios. Our model expands on previous simulation studies by considering weed species with a more complex life cycle (perennial, rhizomatous weed species), studying the effect of environmental variation in herbicide effectiveness, and evaluating the role of common simplifying genetic assumptions on resistance evolution. Our model predictions are qualitatively similar to previous modeling studies using species with a simpler life cycle, which is, crop rotation in combination with rotation of herbicide site of action effectively controls weed populations and slows the evolution of herbicide resistance. We find that ignoring the effect of environmental variation can lead to an over- or under-prediction of the speed of resistance evolution. The effect of environmental variation in herbicide effectiveness depends on the resistance allele frequency in the weed population at the beginning of the simulation. Finally, we find that degree of dominance and ploidy level have a much larger effect on the predicted speed of resistance evolution compared to the rate of gene flow.

Spectral properties of a non-compact operator in ecology.

Ecologists have recently used integral projection models (IPMs) to study fish and other animals which continue to grow throughout their lives. Such animals cannot shrink, since they have bony skeletons; a mathematical consequence of this is that the kernel of the integral projection operator T is unbounded, and the operator is not compact. To our knowledge, all theoretical work done on IPMs has assumed the operator is compact, and in particular has a bounded kernel. A priori, it is unclear whether these IPMs have an asymptotic growth rate [Formula: see text], or a stable-stage distribution [Formula: see text]. In the case of a compact operator, these quantities are its spectral radius and the associated eigenvector, respectively. Under biologically reasonable assumptions, we prove that the non-compact operators in these IPMs share some important traits with their compact counterparts: the operator T has a unique positive eigenvector [Formula: see text] corresponding to its spectral radius [Formula: see text], this [Formula: see text] is strictly greater than the supremum of the modulus of all other spectral values, and for any nonnegative initial population [Formula: see text], there is a [Formula: see text] such that [Formula: see text].

Does masting scale with plant size? High reproductive variability and low synchrony in small and unproductive individuals.

BACKGROUND AND AIMS: In a range of plant species, the distribution of individual mean fecundity is skewed and dominated by a few highly fecund individuals. Larger plants produce greater seed crops, but the exact nature of the relationship between size and reproductive patterns is poorly understood. This is especially clear in plants that reproduce by exhibiting synchronized quasi-periodic variation in fruit production, a process called masting. METHODS: We investigated covariation of plant size and fecundity with individual-plant-level masting patterns and seed predation in 12 mast-seeding species: Pinus pinea, Astragalus scaphoides, Sorbus aucuparia, Quercus ilex, Q. humilis, Q. rubra, Q. alba, Q. montana, Chionochloa pallens, C. macra, Celmisia lyallii and Phormium tenax. KEY RESULTS: Fecundity was non-linearly related to masting patterns. Small and unproductive plants frequently failed to produce any seeds, which elevated their annual variation and decreased synchrony. Above a low fecundity threshold, plants had similar variability and synchrony, regardless of their size and productivity. CONCLUSIONS: Our study shows that within-species variation in masting patterns is correlated with variation in fecundity, which in turn is related to plant size. Low synchrony of low-fertility plants shows that the failure years were idiosyncratic to each small plant, which in turn implies that the small plants fail to reproduce because of plant-specific factors (e.g. internal resource limits). Thus, the behaviour of these sub-producers is apparently the result of trade-offs in resource allocation and environmental limits with which the small plants cannot cope. Plant size and especially fecundity and propensity for mast failure years play a major role in determining the variability and synchrony of reproduction in plants.

Temporal Variation in Predation Risk May Explain Daily Rhythms of Foraging Behavior in an Orb-Weaving Spider.

Daily rhythms occur in numerous physiological and behavioral processes across an immense diversity of taxa, but there remain few cases in which mechanistic links between rhythms of trait expression and organismal fitness have been established. We construct a dynamic optimization model to determine whether risk allocation provides an adaptive explanation for the daily foraging rhythm observed in many species using the orb-weaving spider Cyclosa turbinata as a case study. Our model predicts that female C. turbinata should generally start foraging at lower levels of energy reserves (i.e., should be less bold) during midday when predators are most abundant. We also find that individuals' foraging efficacy determines whether daily rates of encounters with predators or prey more strongly influences boldness under high risk. The qualitative model predictions are robust to variation in our parameter estimates and likely apply to a wide range of taxa. The predictions are also consistent with observed patterns of foraging behavior under both laboratory and field conditions. We discuss the implications of our study for understanding the evolution of daily rhythms and the importance of model predictions for interpreting empirical studies and generating additional hypotheses regarding behavioral evolution.

Time-lagged effects of weather on plant demography: drought and Astragalus scaphoides.

Temperature and precipitation determine the conditions where plant species can occur. Despite their significance, to date, surprisingly few demographic field studies have considered the effects of abiotic drivers. This is problematic because anticipating the effect of global climate change on plant population viability requires understanding how weather variables affect population dynamics. One possible reason for omitting the effect of weather variables in demographic studies is the difficulty in detecting tight associations between vital rates and environmental drivers. In this paper, we applied Functional Linear Models (FLMs) to long-term demographic data of the perennial wildflower, Astragalus scaphoides, and explored sensitivity of the results to reduced amounts of data. We compared models of the effect of average temperature, total precipitation, or an integrated measure of drought intensity (standardized precipitation evapotranspiration index, SPEI), on plant vital rates. We found that transitions to flowering and recruitment in year t were highest if winter/spring of year t was wet (positive effect of SPEI). Counterintuitively, if the preceding spring of year t - 1 was wet, flowering probabilities were decreased (negative effect of SPEI). Survival of vegetative plants from t - 1 to t was also negatively affected by wet weather in the spring of year t - 1 and, for large plants, even wet weather in the spring of t - 2 had a negative effect. We assessed the integrated effect of all vital rates on life history performance by fitting FLMs to the asymptotic growth rate, log(λt). Log(λt) was highest if dry conditions in year t - 1 were followed by wet conditions in the year t. Overall, the positive effects of wet years exceeded their negative effects, suggesting that increasing frequency of drought conditions would reduce population viability of A. scaphoides. The drought signal weakened when reducing the number of monitoring years. Substituting space for time did not recover the weather signal, probably because the weather variables varied little between sites. We detected the SPEI signal when the analysis included data from two sites monitored over 20 yr (2 × 20 observations), but not when analyzing data from four sites monitored over 10 yr (4 × 10 observations).

Modeling effects of ecological factors on evolution of polygenic pesticide resistance.

Widespread use of pesticides has resulted in the evolution of resistance in many insect pests worldwide limiting their use in pest control. Effective pest and resistance management practices require understanding of the genetics of resistance and of the life history of the pest. Most models for pesticide resistance assume that resistance is monogenic, conferred by a single gene. However, resistance could evolve as a polygenic quantitative trait resulting from the action of several genes, especially when pesticide dose is low. Further, fitness of the pest could be density-dependent and might depend upon abiotic factors such as temperature. It is not known how these factors affect the evolution of polygenic resistance or pest population dynamics when resistance evolves. We use the western corn rootworm, Diabrotica virgifera virgifera, as a case study and use data on density-dependent survival, heritability and survival rates on the transgenic Cry3Bb1 toxin and corresponding LC50 values, to model polygenic resistance to Cry3Bb1. We found that LC50 increased rapidly even at doses that produced a mortality of less than 99.9%. However, survival reached 100% only when mortality was as high as 99.9%. Fast response to high selection pressure produced cyclical larval densities while lower selection pressures produced equilibrium densities. Interestingly we found that a relatively low density observed in a population may not be evidence for a low survival to the pesticide. As a consequence we found that larger refuges might not necessarily help in reducing pest densities especially when pesticide mortality is low. This effect, arising from the tradeoff between response to selection and density dependence, calls for careful assessment of the evolution of resistance based on change in survival as well as on pest densities. When selection pressure is low a lower initial density resulted in a larger response to selection. Finally, we showed that populations with shorter developmental times developed resistance faster initially irrespective of selection pressure. However, when selection pressure is low survival eventually became higher in populations with longer developmental times. Since developmental time depends on degree days spatio-temporal variation in temperature could be an important factor in polygenic resistance evolution.

Assessing the Influence of Temporal Autocorrelations on the Population Dynamics of a Disturbance Specialist Plant Population in a Random Environment.

Biological populations are strongly influenced by random variations in their environment, which are often autocorrelated in time. For disturbance specialist plant populations, the frequency and intensity of environmental stochasticity (via disturbances) can drive the qualitative nature of their population dynamics. In this article, we extended our earlier model to explore the effect of temporally autocorrelated disturbances on population persistence. In our earlier work, we only assumed disturbances were independent and identically distributed in time. We proved that the plant seed bank population converges in distribution, and we showed that the mean and variance in seed bank population size were both increasing functions of the autocorrelation coefficient for all parameter values considered, but the interplay between increasing population size and increasing variability caused interesting relationships between quasi-extinction probability and autocorrelation. For example, for populations with low seed survival, fecundity, and disturbance frequency, increasingly positive autocorrelated disturbances decreased quasi-extinction probability. Higher disturbance frequency coupled with low seed survival and fecundity caused a nonmontone relationship between autocorrelation and quasi-extinction, where increasingly positive autocorrelations eventually caused an increase in quasi-extinction probability. For higher seed survival, fecundity, and/or disturbance frequency, quasi-extinction probability was generally a monotonically increasing function of the autocorrelation coefficient.

Variation in the local population dynamics of the short-lived Opuntia macrorhiza (Cactaceae).

Spatiotemporal variation in demographic rates can have profound effects for population persistence, especially for dispersal-limited species living in fragmented landscapes. Long-term studies of plants in such habitats help with understanding the impacts of fragmentation on population persistence but such studies are rare. In this work, we reanalyzed demographic data from seven years of the short-lived cactus Opuntia macrorhiza var. macrorhiza at five plots in Boulder, Colorado. Previous work combining data from all years and all plots predicted a stable population (deterministic log lamda approximately 0). This approach assumed that all five plots were part of a single population. Since the plots were located in a suburban-agricultural interface separated by highways, grazing lands, and other barriers, and O. macrorhiza is likely dispersal limited, we analyzed the dynamics of each plot separately using stochastic matrix models assuming each plot represented a separate population. We found that the stochastic population growth rate log lamdaS varied widely between populations (log lamdaS = 0.1497, 0.0774, -0.0230, -0.2576, -0.4989). The three populations with the highest growth rates were located close together in space, while the two most isolated populations had the lowest growth rates suggesting that dispersal between populations is critical for the population viability of O. macrorhiza. With one exception, both our prospective (stochastic elasticity) and retrospective (stochastic life table response experiments) analysis suggested that means of stasis and growth, especially of smaller plants, were most important for population growth rate. This is surprising because recruitment is typically the most important vital rate in a short-lived species such as O. macrorhiza. We found that elasticity to the variance was mostly negligible, suggesting that O. macrorhiza populations are buffered against large temporal variation. Finally, single-year elasticities to means of transitions to the smallest stage (mostly due to reproduction) and growth differed considerably from their long-term elasticities. It is important to be aware of this difference when using models to predict the effect of manipulating plant vital rates within the time frame of typical plant demographic studies.

Integral control for population management.

We present a novel management methodology for restocking a declining population. The strategy uses integral control, a concept ubiquitous in control theory which has not been applied to population dynamics. Integral control is based on dynamic feedback-using measurements of the population to inform management strategies and is robust to model uncertainty, an important consideration for ecological models. We demonstrate from first principles why such an approach to population management is suitable via theory and examples.

Effects of virus on plant fecundity and population dynamics.

Microorganisms are ubiquitous and thought to regulate host populations. Although microorganisms can be pathogenic and affect components of fitness, few studies have examined their effects on wild plant populations. As individual traits might not contribute equally to changes in population growth rate, it is essential to examine the entire life cycle to determine how microorganisms affect host population dynamics. In this study, we used data from common garden experiments with plants from three Cucurbita pepo populations exposed to three virus treatments. These data were used to parameterize a deterministic matrix model, which allowed us to estimate the effect of virus on components of fitness and population growth rate. Virus did not reduce fruit number, but population growth rates varied among virus treatments and wild C. pepo populations. The effect of virus on population growth rate depended on virus species and wild C. pepo population. Contributions of life-history transitions and life-history traits to population growth rates varied among populations and virus treatments. However, this population-virus interaction was not evident when examining individual components of fitness. Thus, caution must be used when interpreting the effects of changes in individual traits, as single traits do not always predict population-level change accurately.

Frequency-dependent population dynamics: effect of sex ratio and mating system on the elasticity of population growth rate.

When vital rates depend on population structure (e.g., relative frequencies of males or females), an important question is how the long-term population growth rate λ responds to changes in rates. For instance, availability of mates may depend on the sex ratio of the population and hence reproductive rates could be frequency-dependent. In such cases change in any vital rate alters the structure, which in turn, affect frequency-dependent rates. We show that the elasticity of λ to a rate is the sum of (i) the effect of the linear change in the rate and (ii) the effect of nonlinear changes in frequency-dependent rates. The first component is always positive and is the classical elasticity in density-independent models obtained directly from the population projection matrix. The second component can be positive or negative and is absent in density-independent models. We explicitly express each component of the elasticity as a function of vital rates, eigenvalues and eigenvectors of the population projection matrix. We apply this result to a two-sex model, where male and female fertilities depend on adult sex ratio α (ratio of females to males) and the mating system (e.g., polygyny) through a harmonic mating function. We show that the nonlinear component of elasticity to a survival rate is negligible only when the average number of mates (per male) is close to α. In a strictly monogamous species, elasticity to female survival is larger than elasticity to male survival when α<1 (less females). In a polygynous species, elasticity to female survival can be larger than that of male survival even when sex ratio is female biased. Our results show how demography and mating system together determine the response to selection on sex-specific vital rates.

Native insect herbivory limits population growth rate of a non-native thistle.

The influence of native fauna on non-native plant population growth, size, and distribution is not well documented. Previous studies have shown that native insects associated with tall thistle (Cirsium altissimum) also feed on the leaves, stems, and flower heads of the Eurasian congener C. vulgare, thus limiting individual plant performance. In this study, we tested the effects of insect herbivores on the population growth rate of C. vulgare. We experimentally initiated invasions by adding seeds at four unoccupied grassland sites in eastern Nebraska, USA, and recorded plant establishment, survival, and reproduction. Cumulative foliage and floral herbivory reduced C. vulgare seedling density, and prevented almost any reproduction by C. vulgare in half the sites. The matrix model we constructed showed that this herbivory resulted in a reduction of the asymptotic population growth rate (λ), from an 88% annual increase to a 54% annual decline. These results provide strong support for the hypothesis that indigenous herbivores limit population invasion of this non-native plant species into otherwise suitable grassland habitat.

Modeling and analysis of a density-dependent stochastic integral projection model for a disturbance specialist plant and its seed bank.

In many plant species dormant seeds can persist in the soil for one to several years. The formation of these seed banks is especially important for disturbance specialist plants, as seeds of these species germinate only in disturbed soil. Seed movement caused by disturbances affects the survival and germination probability of seeds in the seed bank, which subsequently affect population dynamics. In this paper, we develop a stochastic integral projection model for a general disturbance specialist plant-seed bank population that takes into account both the frequency and intensity of random disturbances, as well as vertical seed movement and density-dependent seedling establishment. We show that the probability measures associated with the plant-seed bank population converge weakly to a unique measure, independent of initial population. We also show that the population either persists with probability one or goes extinct with probability one, and provides a sharp criteria for this dichotomy. We apply our results to an example motivated by wild sunflower (Helianthus annuus) populations, and explore how the presence or absence of a "storage effect" impacts how a population responds to different disturbance scenarios.

Global asymptotic stability of plant-seed bank models.

Many plant populations have persistent seed banks, which consist of viable seeds that remain dormant in the soil for many years. Seed banks are important for plant population dynamics because they buffer against environmental perturbations and reduce the probability of extinction. Viability of the seeds in the seed bank can depend on the seed's age, hence it is important to keep track of the age distribution of seeds in the seed bank. In this paper we construct a general density-dependent plant-seed bank model where the seed bank is age-structured. We consider density dependence in both seedling establishment and seed production, since previous work has highlighted that overcrowding can suppress both of these processes. Under certain assumptions on the density dependence, we prove that there is a globally stable equilibrium population vector which is independent of the initial state. We derive an analytical formula for the equilibrium population using methods from feedback control theory. We apply these results to a model for the plant species Cirsium palustre and its seed bank.

Comparison of the wing polyphenic response of pea aphids (Acyrthosiphon pisum) to crowding and predator cues.

1. Pea aphids (Acyrthosiphon pisum Harris; Hemiptera: Aphididae) exhibit transgenerational wing polyphenism, in which unwinged females produce genetically identical winged offspring in response to environmental cues such as overcrowding and predation risk that indicate poor habitat quality. 2. Laboratory experiments were carried out to explore the intensity of the wing polyphenic response of pea aphids exposed to cues from ladybird predators and crowding, and their response was compared to pea aphids that were not exposed to any cues (control). 3. The study used cues from two different ladybird species: Coccinella septempunctata L. (Coleoptera: Coccinellidae) and Hippodamia convergens Guérin-Méneville (Coleoptera: Coccinellidae) to investigate whether the wing polyphenic response of pea aphids to predator cues can be generalized 4. The intensity of the wing polyphenic response of pea aphids to crowding was found to be much stronger than their response to predator cues. There was no response to H. convergens cues and the response to C. septempunctata cues was mixed.

Disturbance frequency and vertical distribution of seeds affect long-term population dynamics: a mechanistic seed bank model.

Seed banks are critically important for disturbance specialist plants because seeds of these species germinate only in disturbed soil. Disturbance and seed depth affect the survival and germination probability of seeds in the seed bank, which in turn affect population dynamics. We develop a density-dependent stochastic integral projection model to evaluate the effect of stochastic soil disturbances on plant population dynamics with an emphasis on mimicking how disturbances vertically redistribute seeds within the seed bank. We perform a simulation analysis of the effect of the frequency and mean depth of disturbances on the population's quasi-extinction probability, as well as the long-term mean and variance of the total density of seeds in the seed bank. We show that increasing the frequency of disturbances increases the long-term viability of the population, but the relationship between the mean depth of disturbance and the long-term viability of the population are not necessarily monotonic for all parameter combinations. Specifically, an increase in the probability of disturbance increases the long-term viability of the total seed bank population. However, if the probability of disturbance is too low, a shallower mean depth of disturbance can increase long-term viability, a relationship that switches as the probability of disturbance increases. However, a shallow disturbance depth is beneficial only in scenarios with low survival in the seed bank.

Larval performance and kill rate of convergent ladybird beetles, Hippodamia convergens, on black bean aphids, Aphis fabae, and pea aphids, Acyrthosiphon pisum.

Generalist predator guilds play a prominent role in structuring insect communities and can contribute to limiting population sizes of insect pest species. A consequence of dietary breadth, particularly in predatory insects, is the inclusion of low-quality, or even toxic, prey items in the predator's diet. Consumption of low-quality prey items reduces growth, development, and survival of predator larvae, thereby reducing the population sizes of generalist predators. The objective of this paper was to examine the effect of a suspected low-quality aphid species, Aphis fabae (Scopoli) (Hemiptera: Aphididae), on the larval performance of an abundant North American predator, Hippodamia convergens (Guérin-Méneville) (Coleoptera: Coccinellidae). For comparison, H. convergens larvae were also reared on a known high-quality aphid species Acyrthosiphon pisum (Harris) (Hemiptera: Aphididae) and on a 50:50 mix of both aphid species. The proportion of H. convergens larvae surviving to the adult stage was dramatically lower (0.13) on the A. fabae diet than on the A. pisum diet (0.70); survival on the mixed diet was intermediate (0.45) to survival on the single-species diets. Similarly, surviving H. convergens larvae also developed more slowly and weighed less as adults on the A. fabae diet than on the A. pisum diet. Despite the relatively poor performance on the A. fabae diet, H. convergens larvae killed large numbers of A. fabae. Furthermore, H. convergens displayed a preference for A. fabae in the mixed diet treatment, most likely because A. fabae was easier to catch than A. pisum. The results suggest that increases in the distribution and abundance of A. fabae in North America may have negative effects on H. convergens population size.

Insect herbivory and propagule pressure influence Cirsium vulgare invasiveness across the landscape.

A current challenge in ecology is to better understand the magnitude, variation, and interaction in the factors that limit the invasiveness of exotic species. We conducted a factorial experiment involving herbivore manipulation (insecticide-in-water vs. water-only control) and seven densities of introduced nonnative Cirsium vulgare (bull thistle) seed. The experiment was repeated with two seed cohorts at eight grassland sites uninvaded by C. vulgare in the central Great Plains, USA. Herbivory by native insects significantly reduced thistle seedling density, causing the largest reductions in density at the highest propagule inputs. The magnitude of this herbivore effect varied widely among sites and between cohort years. The combination of herbivory and lower propagule pressure increased the rate at which new C. vulgare populations failed to establish during the initial stages of invasion. This experiment demonstrates that the interaction between biotic resistance by native insects, propagule pressure, and spatiotemporal variation in their effects were crucial to the initial invasion by this Eurasian plant in the western tallgrass prairie.

Global asymptotic stability of density dependent integral population projection models.

Many stage-structured density dependent populations with a continuum of stages can be naturally modeled using nonlinear integral projection models. In this paper, we study a trichotomy of global stability result for a class of density dependent systems which include a Platte thistle model. Specifically, we identify those systems parameters for which zero is globally asymptotically stable, parameters for which there is a positive asymptotically stable equilibrium, and parameters for which there is no asymptotically stable equilibrium.