Effective size of density‐dependent populations in fluctuating environments

Reliable estimates of effective population size are of central importance in population genetics and evolutionary biology. For populations that fluctuate in size, harmonic mean population size is commonly used as a proxy for (multi‐) generational effective size. This assumes no effects of density dependence on the ratio between effective and actual population size, which limits its potential application. Here, we introduce density dependence on vital rates in a demographic model of variance effective size. We derive an expression for the ratio in a density‐regulated population in a fluctuating environment. We show by simulations that yearly genetic drift is accurately predicted by our model, and not proportional to as assumed by the harmonic mean model, where N is the total population size of mature individuals. We find a negative relationship between and N. For a given N, the ratio depends on variance in reproductive success and the degree of resource limitation acting on the population growth rate. Finally, our model indicate that environmental stochasticity may affect not only through fluctuations in N, but also for a given N at a given time. Our results show that estimates of effective population size must include effects of density dependence and environmental stochasticity.     

Facilitation can maintain clustered spatial pattern of plant populations during density‐dependent mortality: insights from a zone‐of‐influence model

Recent years have seen a growing body of evidence showing that plant competition and facilitation usually operate simultaneously to drive population dynamics, community structure and ecosystem functions. However, the potential role of facilitation in spatial patterning of plant populations has rarely been explicitly examined. We used a ‘zone‐of‐influence’ model to explore how facilitation interacts with competition and abiotic stress to determine the spatial patterning of populations during density‐dependent mortality. Model simulations revealed that started with the same clustered pattern, the final pattern of simulated populations depended strongly on the interaction among facilitation, stress level and size‐symmetry of competition. Asymmetric competition consistently led to immediate and non‐random mortality towards regularity, thus rapidly decayed the initially clustered pattern to final patterns of small‐scale regularity and large‐scale randomness. The role of symmetric competition in decaying the clustered pattern increased with abiotic stress because stress‐induced reductions in plants’ growth rates can make individuals in high‐density clusters more likely to die even from symmetric competition. Facilitation played a clear role in counteracting the effect of stress, thus tended to maintain the degree of clustering of the pattern during density‐dependent mortality. This is because the amelioration of harsh conditions by neighboring plants relieved the reductions in plant growth due to competition, thus slowed down and reduced the mortality inside clusters (relative to that outside clusters). Moreover, the effect of facilitation appeared to increase with abiotic stress. Our results indicate that facilitation among neighboring plants should partially be responsible for clustered population spatial patterns observed in stressful environments, even though its contribution relative to other factors (e.g. local dispersal and environmental heterogeneity) remains to be evaluated. In addition, the potential influence of facilitation on self‐thinning trajectory should be explicitly examined in future modeling and experimental studies considering its effects on density‐dependent mortality.     

Positive interactions can increase size inequality in plant populations

1.  Large variation in the size of individuals is a ubiquitous feature of natural plant populations. While the role of competition in generating this variation has been studied extensively, the potential effects of positive interactions among plants, which are common in high-stress environments, have not been investigated.
2.  Using an individual-based 'zone-of-influence' model, we investigate the effects of competition, abiotic stress and facilitation on size inequality in plant monocultures. In the model, stress reduces the growth rate of plants, and facilitation ameliorates the effects of stress. Both facilitation and competition occur in overlapping zones of influence. We tested some of the model's predictions with a field experiment using the clonal grass Elymus nutans in an alpine meadow.
3.  Facilitation increased the size inequality of model populations when there was no density-dependent mortality. This effect decreased with density as competition overwhelmed facilitation. The lowest size inequality was found at intermediate densities both with the model and in the field.
4.  When density-dependent mortality was included in the model, stress delayed its onset and reduced its rate by reducing growth rates, so the number of survivors at any point in time was higher under harsh than under more benign conditions. Facilitation increased size inequality during self-thinning.
5.   Synthesis . Our results demonstrate that facilitation interacts with abiotic stress and competition to influence the degree of size inequality in plant populations. Facilitation increased size inequality at low to intermediate densities and during self-thinning.     

Effective size of density‐dependent two‐sex populations: the effect of mating systems

Density dependence in vital rates is a key feature affecting temporal fluctuations of natural populations. This has important implications for the rate of random genetic drift. Mating systems also greatly affect effective population sizes, but knowledge of how mating system and density regulation interact to affect random genetic drift is poor. Using theoretical models and simulations, we compare N_e in short‐lived, density‐dependent animal populations with different mating systems. We study the impact of a fluctuating, density‐dependent sex ratio and consider both a stable and a fluctuating environment. We find a negative relationship between annual N_e/N and adult population size N due to density dependence, suggesting that loss of genetic variation is reduced at small densities. The magnitude of this decrease was affected by mating system and life history. A male‐biased, density‐dependent sex ratio reduces the rate of genetic drift compared to an equal, density‐independent sex ratio, but a stochastic change towards male bias reduces the N_e/N ratio. Environmental stochasticity amplifies temporal fluctuations in population size and is thus vital to consider in estimation of effective population sizes over longer time periods. Our results on the reduced loss of genetic variation at small densities, particularly in polygamous populations, indicate that density regulation may facilitate adaptive evolution at small population sizes.     

Facilitation among plants can accelerate density‐dependent mortality and steepen self‐thinning lines in stressful environments

The speed and slope of plant self‐thinning are all affected by plant–plant interactions across environmental gradients. Possible mechanisms driving the self‐thinning dynamics include the relative strength of root versus shoot competition, and the interplay between competition and facilitation. Although these mechanisms often act in concert, their relative importance has not yet been fully explored. We used both a one‐layer and a two‐layer zone‐of‐influence (ZOI) model to examine how competition and facilitation drive self‐thinning across stress gradients. As a development of the traditional ZOI model, the two‐layer version explicitly models shoot and root growth and neighbor interactions, and thus the overall size‐symmetry of competition is regulated by the relative strength of root versus shoot competition. One‐layer model simulations revealed that increasingly asymmetric competition accelerated thinning, and steepened (slope ranged from about –1 to –4/3) and lowered self‐thinning lines. Stress slowed down density‐dependent mortality considerably when competition was not completely symmetric. Stress significantly decreased the self‐thinning intercept, while facilitation simply counteracted stress effects. Both stress and facilitation showed little effect on the slope. In the two‐layer model, both stress and facilitation affected mortality in the same way as in the one‐layer version when competition was not completely symmetric. Different from the one‐layer model, the two‐layer version showed that the effects of stress and facilitation on the self‐thinning slope were mediated by the asymmetry of competition. As stress increased, the overall asymmetry of competition shifted from asymmetric to symmetric due to increased relative strength of root competition. High stress thus dramatically flattened self‐thinning lines, whereas the inclusion of facilitation counteracted stress and led to steeper self‐thinning lines. Our two‐layer model is based on the current knowledge of plant–plant interactions, and better represents ecological realities. It can help elaborate experiments for testing the role of competition and facilitation in driving plant population dynamics.     

Cascading effects of belowground predators on plant communities are density‐dependent

Soil food webs comprise a multitude of trophic interactions that can affect the composition and productivity of plant communities. Belowground predators feeding on microbial grazers like Collembola could decelerate nutrient mineralization by reducing microbial turnover in the soil, which in turn could negatively influence plant growth. However, empirical evidences for the ecological significance of belowground predators on nutrient cycling and plant communities are scarce. Here, we manipulated predator density (Hypoaspis aculeifer: predatory mite) with equal densities of three Collembola species as a prey in four functionally dissimilar plant communities in experimental microcosms: grass monoculture (Poa pratensis), herb monoculture (Rumex acetosa), legume monoculture (Trifolium pratense), and all three species as a mixed plant community. Density manipulation of predators allowed us to test for density‐mediated effects of belowground predators on Collembola and lower trophic groups. We hypothesized that predator density will reduce Collembola population causing a decrease in nutrient mineralization and hence detrimentally affect plant growth. First, we found a density‐dependent population change in predators, that is, an increase in low‐density treatments, but a decrease in high‐density treatments. Second, prey suppression was lower at high predator density, which caused a shift in the soil microbial community by increasing the fungal: bacterial biomass ratio, and an increase of nitrification rates, particularly in legume monocultures. Despite the increase in nutrient mineralization, legume monocultures performed worse at high predator density. Further, individual grass shoot biomass decreased in monocultures, while it increased in mixed plant communities with increasing predator density, which coincided with elevated soil N uptake by grasses. As a consequence, high predator density significantly increased plant complementarity effects indicating a decrease in interspecific plant competition. These results highlight that belowground predators can relax interspecific plant competition by increasing nutrient mineralization through their density‐dependent cascading effects on detritivore and soil microbial communities.     

Limited contributions of plant pathogens to density‐dependent seedling mortality of mast fruiting Bornean trees

Fungal pathogens are implicated in driving tropical plant diversity by facilitating strong, negative density‐dependent mortality of conspecific seedlings (C‐NDD). Assessment of the role of fungal pathogens in mediating coexistence derives from relatively few tree species and predominantly the Neotropics, limiting our understanding of their role in maintaining hyper‐diversity in many tropical forests. A key question is whether fungal pathogen‐mediated C‐NDD seedling mortality is ubiquitous across diverse plant communities. Using a manipulative shadehouse experiment, we tested the role of fungal pathogens in mediating C‐NDD seedling mortality of eight mast fruiting Bornean trees, typical of the species‐rich forests of South East Asia. We demonstrate species‐specific responses of seedlings to fungicide and density treatments, generating weak negative density‐dependent mortality. Overall seedling mortality was low and likely insufficient to promote overall community diversity. Although conducted in the same way as previous studies, we find little evidence that fungal pathogens play a substantial role in determining patterns of seedling mortality in a SE Asian mast fruiting forest, questioning our understanding of how Janzen‐Connell mechanisms structure the plant communities of this globally important forest type.     

Non‐additive effects of density‐dependent and density‐independent factors on brown trout vital rates

Interactions between density‐dependent and density‐independent processes can lead to variation in both growth and survival rates. Detecting such effects, however, will often require sampling on an individual level and at the appropriate spatial and temporal scale. This study documents substantial variation in survival and growth of stream‐dwelling brown trout Salmo trutta from a small Norwegian stream. The data is based on seasonal capture–recaptures of individually marked trout on fixed stations during eight years. The fish were small‐sized, rarely reaching sizes larger than 20 cm and ages older than seven years. Density varied between 0.2–0.8 fish m^?2. Variation in survival and recapture probabilities was analysed using program MARK. Apparent survival (the probability of being alive and present within the study area) generally decreased with increasing trout density and increasing drought level (measured as lowest observed water flow) during both winter and summer. Further, there was a significant interaction effect between density and water flow, indicating that density‐dependent effects on survival predominated when environmental conditions were benign (no drought), while density‐independent processes were most important under harsh environmental conditions (drought). Observed length‐at‐age during autumn indicated a more or less linear growth trajectory throughout life, and no effect of density, water flow or temperature was found. However, using the individual‐based capture–recapture data to estimated specific growth rate, significant positive effects of water flow and temperature and a negative effect of density were identified. Thus, the capture–recapture data suggest a strong potential for population regulation at the rather low densities found in this stream, and regulation may occur both through effects on survival and growth.     

Neural correlates to flight‐related density‐dependent phase characteristics in locusts

Locust phase polymorphism is an extreme example of behavioral plasticity; in response to changes in population density, locusts dramatically alter their behavior. These changes in behavior facilitate the appearance of various morphological and physiological phase characteristics. One of the principal behavioral changes is the more intense flight behavior and improved flight performance of gregarious locusts compared to solitary ones. Surprisingly, the neurophysiological basis of the behavioral phase characteristics has received little attention. Here we present density‐dependent differences in flight‐related sensory and central neural elements in the desert locust. Using techniques already established for gregarious locusts, we compared the response of locusts of both phases to controlled wind stimuli. Gregarious locusts demonstrated a lower threshold for wind‐induced flight initiation. Wind‐induced spiking activity in the locust tritocerebral commissure giants (TCG, a pair of identified interneurons that relay input from head hair receptors to thoracic motor centers) was found to be weaker in solitary locusts compared to gregarious ones. The solitary locusts' TCG also demonstrated much stronger spike frequency adaptation in response to wind stimuli. Although the number of forehead wind sensitive hairs was found to be larger in solitary locusts, the stimuli conveyed to their flight motor centers were weaker. The tritocerebral commissure dwarf (TCD) is an inhibitory flight‐related interneuron in the locust that responds to light stimuli. An increase in TCD spontaneous activity in dark conditions was significantly stronger in gregarious locusts than in solitary ones. Thus, phase‐dependent differences in the activity of flight‐related interneurons reflect behavioral phase characteristics. © 2003 Wiley Periodicals, Inc. J Neurobiol 57: 152–162, 2003     

Asymmetric competition in plant populations

Recently there has been much interest in the hypothesis that competition between individual plants is asymmetric or onesided: larger individuals obtain a disproportionate share of the resources (for their relative size) and suppress the growth of smaller individuals. This has important implications for population structure, for the analysis of competition between plants at the individual, population and community levels, and for our understanding of competition as a selective force in the evolution of plant populations.     

Spatial patterns of sapling mortality in a moist tropical forest: consistency with total density‐dependent effects

Density‐dependent mortality (DDM) is major driver of species coexistence in tropical forests. We assessed the occurrence and strength of this mechanism among saplings (i.e. trees with a diameter of 1–4 cm) in the moist tropical forest of Barro Colorado Island (BCI), Panama, over six inter‐census periods (26 years), by using spatial point pattern analysis. We considered conspecific density‐dependent mortality, but also total DDM (i.e. the effects of conspecific and heterospecific neighbours all together) upon saplings of all species (i.e. at the community level), and on saplings of light‐demanding and shade‐tolerant ones, separately (i.e. at the light‐guild level). We also analysed the effects of conspecific DDM at the community and light‐guild levels. Conspecific density‐dependent mortality affected a lower proportion of species than was to be expected. Its strength was not significantly related with species abundance, and it had relatively weak effects at the community and light guild levels. Conversely, we detected a significant spatial signature of total DDM among all saplings, and among saplings of the light‐demanding and shade‐tolerant species, but its strength showed pronounced temporal variation. Total DDM among light‐demanding saplings was stronger than among shade‐tolerant ones and its effects were particularly marked 10–15 years after the occurrence of unusually severe droughts associated with El Niño events. Our study indicates that conspecific DDM is relatively unimportant among saplings in comparison with total DDM at community and light‐guild levels. This finding contrasts strongly with the results for seedlings, where conspecific DDM was constituted the dominant process. The pronounced temporal variations observed in the occurrence and strength of total DDM among saplings indicate that time‐varying events associated with climatic disturbances such as canopy openings or episodes of high recruit emergence might be important drivers of this process. They also emphasize the importance of considering time frames longer than one decade to study density‐dependent effects among saplings in tropical forests.     

Adult trees cause density‐dependent mortality in conspecific seedlings by regulating the frequency of pathogenic soil fungi

Negative density‐dependent seedling mortality has been widely detected in tropical, subtropical and temperate forests, with soil pathogens as a major driver. Here we investigated how host density affects the composition of soil pathogen communities and consequently influences the strength of plant‐soil feedbacks. In field censuses of six 1‐ha permanent plots, we found that survival was much lower for newly germinated seedlings that were surrounded by more conspecific adults. The relative abundance of pathogenic fungi in soil increased with increasing conspecific tree density for five of nine tree species; more soil pathogens accumulated around roots where adult tree density was higher, and this greater pathogen frequency was associated with lower seedling survival. Our findings show how tree density influences populations of soil pathogens, which creates plant‐soil feedbacks that contribute to community‐level and population‐level compensatory trends in seedling survival.     

Evolution of density‐dependent movement during experimental range expansions

Range expansions and biological invasions are prime examples of transient processes that are likely impacted by rapid evolutionary changes. As a spatial process, range expansions are driven by dispersal and movement behaviour. Although it is widely accepted that dispersal and movement may be context‐dependent, for instance density‐dependent, and best represented by reaction norms, the evolution of density‐dependent movement during range expansions has received little experimental attention. We therefore tested current theory predicting the evolution of increased movement at low densities at range margins using highly replicated and controlled range expansion experiments across multiple genotypes of the protist model system Tetrahymena thermophila. Although rare, we found evolutionary changes during range expansions even in the absence of initial standing genetic variation. Range expansions led to the evolution of negatively density‐dependent movement at range margins. In addition, we report the evolution of increased intrastrain competitive ability and concurrently decreased population growth rates in range cores. Our findings highlight the importance of understanding movement and dispersal as evolving reaction norms and plastic life‐history traits of central relevance for range expansions, biological invasions and the dynamics of spatially structured systems in general.     

Pollination outcomes reveal negative density‐dependence coupled with interspecific facilitation among plants

Pollination is thought to be under positive density‐dependence, destabilising plant coexistence by conferring fitness disadvantages to rare species. Such disadvantage is exacerbated by interspecific competition but can be mitigated by facilitation and intraspecific competition. However, pollinator scarcity should enhance intraspecific plant competition and impose disadvantage on common over rare species (negative density‐dependence, NDD). We assessed pollination proxies (visitation rate, pollen receipt, pollen tubes) in a generalised plant community and related them to conspecific and heterospecific density, expecting NDD and interspecific facilitation due to the natural pollinator scarcity. Contrary to usual expectations, all proxies indicated strong intraspecific competition for common plants. Moreover interspecific facilitation prevailed and was stronger for rare than for common plants. Both NDD and interspecific facilitation were modulated by specialisation, floral display and pollinator group. The combination of intraspecific competition and interspecific facilitation fosters plant coexistence, suggesting that pollination can be a niche axis maintaining plant diversity.     

Spatio‐temporal dynamics of density‐dependent dispersal during a population colonisation

Predicting population colonisations requires understanding how spatio‐temporal changes in density affect dispersal. Density can inform on fitness prospects, acting as a cue for either habitat quality, or competition over resources. However, when escaping competition, high local density should only increase emigration if lower‐density patches are available elsewhere. Few empirical studies on dispersal have considered the effects of density at the local and landscape scale simultaneously. To explore this, we analyze 5 years of individual‐based data from an experimental introduction of wild guppies Poecilia reticulata. Natal dispersal showed a decrease in local density dependence as density at the landscape level increased. Landscape density did not affect dispersal among adults, but local density‐dependent dispersal switched from negative (conspecific attraction) to positive (conspecific avoidance), as the colonisation progressed. This study demonstrates that densities at various scales interact to determine dispersal, and suggests that dispersal trade‐offs differ across life stages.     

Density‐independent reproductive success of the hemiparasitic plant Striga hermonthica,despite positive and negative density‐dependent phases

The hemiparasite Striga hermonthica is a major constraint to smallholder farmer livelihoods and food security in sub‐Saharan Africa. A better understanding of its life‐cycle can help developing more effective management strategies. Here, we studied density dependence in S. hermonthica on Sorghum bicolor. We exposed two genotypes of S. bicolor that differed in the level of tolerance and resistance to S. hermonthica to a range of seed densities of the parasite. We evaluated multiple host and parasite performance parameters through periodic, destructive harvests and related these to the initial seed density using model selection. Initially, the probability for attachment was positively density‐dependent, suggesting facilitation of new infections. However, at host maturity, S. hermonthica infection probability showed strong negative density dependence, indicating severe competition, in particular in the early developmental stages. Although parasite shoot dry weight showed a strong negative density dependence at host maturity, flower production per parasite exhibited positive density dependence again, suggesting compensation. The two host genotypes had similar responses to increased parasite densities, indicating differences between the genotypes in tolerance but not resistance. Consequently, despite density dependence in life‐cycle components, the per capita reproductive output of S. hermonthica, R₀ (flowers seed^?1) was density‐independent. Apparently, management of the hemiparasite can neither benefit from a negatively density‐dependent bottleneck, nor from a positively density‐dependent Allee effect. The most promising suggestion to obtain S. hermonthica population decline (R₀ < 1) and long‐term control is to increase host shading by growing a vigorous, competitive crop.     

Is selection for territorial aggression in brown trout density‐dependent?

A comparison between a high-density (migratory) and a low-density (stream-resident) population of brown trout Salmo trutta , from the same stream, showed there was no support for the view that aggression was density-dependent.