Coexistence of competing stage-structured populations

This paper analyzes the stability of a coexistence equilibrium point of a model for competition between two stage-structured populations. In this model, for each population, competition for resources may affect any one of the following population parameters: reproduction, juvenile survival, maturation rate, or adult survival. The results show that the competitive strength of a population is affected by (1) the ratio of the population parameter influenced by competition under no resource limitation (maximum compensatory capacity) over the same parameter under a resource limitation due to competition (equilibrium rate) and (2) the ratio of interspecific competition over intraspecific competition; this ratio was previously shown to depend on resource-use overlap. The former ratio, which we define as fitness, can be equalized by adjusting organisms' life history strategies, thereby promoting coexistence. We conclude that in addition to niche differentiation among populations, the life history strategies of organisms play an important role in coexistence

Robust permanence for interacting structured populations

The dynamics of interacting structured populations can be modeled by $\frac{dx_i}{dt}= A_i (x)x_i$ where $x_i\in \R^{n_i}$, $x=(x_1,\dots,x_k)$, and $A_i(x)$ are matrices with non-negative off-diagonal entries. These models are permanent if there exists a positive global attractor and are robustly permanent if they remain permanent following perturbations of $A_i(x)$. Necessary and sufficient conditions for robust permanence are derived using dominant Lyapunov exponents $\lambda_i(\mu)$ of the $A_i(x)$ with respect to invariant measures $\mu$. The necessary condition requires $\max_i \lambda_i(\mu)>0$ for all ergodic measures with support in the boundary of the non-negative cone. The sufficient condition requires that the boundary admits a Morse decomposition such that $\max_i \lambda_i(\mu)>0$ for all invariant measures $\mu$ supported by a component of the Morse decomposition. When the Morse components are Axiom A, uniquely ergodic, or support all but one population, the necessary and sufficient conditions are equivalent. Applications to spatial ecology, epidemiology, and gene networks are given

Effects of stage structure on coexistence: mixed benefits

The properties of competition models where all individuals are identical are relatively well-understood; however, juveniles and adults can experience or generate competition differently. We study here less well-known structured competition models in discrete time that allow multiple life history parameters to depend on adult or juvenile population densities. A numerical study with Ricker density-dependence suggested that when competition coefficients acting on juvenile survival and fertility reflect opposite competitive hierarchies, stage structure could foster coexistence. We revisit and expand those results. First, through a Beverton-Holt two-species juvenile-adult model, we confirm that these findings do not depend on the specifics of density-dependence or life cycles, and obtain analytical expressions explaining how this coexistence emerging from stage structure can occur. Second, we show using a community-level sensitivity analysis that such emergent coexistence is robust to perturbations of parameter values. Finally, we ask whether these results extend from two to many species, using simulations. We show that they do not, as coexistence emerging from stage structure is only seen for very similar life-history parameters. Such emergent coexistence is therefore not likely to be a key mechanism of coexistence in very diverse ecosystems, although it may contribute to explaining coexistence of certain pairs of intensely competing species

Limiting Similarity Revisited

We reinvestigate the validity of the limiting similarity principle via numerical simulations of the Lotka-Volterra model. A Gaussian competition kernel is employed to describe decreasing competition with increasing difference in a one-dimensional phenotype variable. The simulations are initiated by a large number of species, evenly distributed along the phenotype axis. Exceptionally, the Gaussian carrying capacity supports coexistence of all species, initially present. In case of any other, distinctly different, carrying capacity functions, competition resulted in extinction of all, but a few species. A comprehensive study of classes of fractal-like carrying capacity functions with different fractal exponents was carried out. The average phenotype differences between surviving species were found to be roughly equal to the competition width. We conclude that, despite the existence of exceptional cases, the classical picture of limiting similarity and niche segregation is a good rule of thumb for practical purposes

Stochasticity and randomness in eco-evolutionary modelling

Evolution is an inherently stochastic process comprised of many randomly occurring events. The evolutionary fate of a population depends largely on its underlying ecological interactions, while ecological interactions can also be influenced by evolutionary change in turn. This phenomenon is known as an eco-evolutionary feedback loop. Ecological models tend to have a strong focus on how complex ecological features such as interaction structures influence the behaviour of ecosystems, rather than their consequences on long-term evolutionary fates. Evolutionary models on the other hand tend to overlook the complexities associated with their underlying ecological features. This is of particular importance since many evolutionary problems in nature, particularly those associated to the evolution of sexual reproduction, are underpinned by myriad ecological factors. The aim of this thesis is to develop mathematical models for ecological and evolutionary problems in biology, with particular focus on problems surrounding the evolution of sexual reproduction. We begin in chapter 2 by developing an analytical prediction for the stability of generalised Lotka-Volterra systems with biologically motivated interaction structures. In chapter 3, we develop an eco-evolutionary model for the evolution of gamete size and motility to study the evolution of male and female sexes. Chapter 4 repurposes the model of chapter 3 to look at how binary cell fusion can evolve in response to environmental stress. Chapter 5 investigates how genetic recombination evolves in response to environmental stress using an integrative mathematical model that incorporates aspects of population dynamics, population genetics and eco-evolutionary feedback. This allows us to explain analytically how recombination and hibernation evolved to occur together, as well as why they both occur shortly before the onset of environmental stress

Critical Review of the Literature on Marine Mammal Population Modelling

A comprehensive literature review and modeling effort have been conducted in order to determine which vital rates are most important to determining the growth and sustainability of marine mammal populations. Also addressed are the impacts of life-history, ecological, and genetic variation on vital rates and population sustainability and how much each vital parameter can change before a change in population trend would be expected. Additionally, the influence of ecological energetics and foraging strategies on vital rates and their limits of sustainable change are examined, and the nature of how an increase in sound in the marine environment might influence marine mammal behavior, and thus life functions, vital rates and population sustainability is explored. An analysis of the elasticity and sensitivity of marine mammal population models suggests that: 1) Most whale populations appear to be most sensitive to changes in adult female survival and least sensitive to calf survival. 2) Most whale populations appear to be secondarily sensitive to changes in juvenile survival and growth. 3) Most whale populations, with the exception of North Atlantic right whales (Eubalaena glacialis), appear to be insensitive to changes in fecundity at any age. 4) Adult female whales may be sensitive to changes in foraging success that limit their ability to acquire sufficient body stores of energy to sustain gestation, parturition, and lactation. 5) These results are similar to those arising from studies of non-mammalian marine predators as well as terrestrial vertebrates with similar life history characteristics. A risk assessment of the potential impacts of ocean noise on marine mammal populations based on modeling marine mammal populations suggests that: 1) Any increase in anthropogenic noise in the marine environment that reduces adult female survival, for whatever reason, is to be avoided, 2) It may be impossible to detect the impact of a change in a population vital rate on population growth because such a change may be less than the confidence interval around the estimates of the rate of growth of most marine mammal populations. 3) Sensitivity and elasticity analyses of marine mammal population models predict linear changes in marine mammal population growth rates caused by linear changes in vital rates, and do not indicate thresholds within which vital rates can change without altering population growth rates. Future research efforts should focus on the following: 1) The relationship between noise in the marine environment and adult female and juvenile survival. 2) To increase the precision and decrease the uncertainty of marine mammal population and vital rate estimates. 3) Improving the concept of potential biological removal (PBR) to reflect cumulative mortality impacts and to incorporate the effects of noise. 4) Increasing knowledge of marine mammal activity budgets seasonally and in different parts of their habitats. 5) To more fully elucidate the roles of marine mammals in their ecosystems, and their importance as sentinels of ecosystem health. 6) To exhaustively utilize existing data and models because of the cost and difficulty of gathering more data

The evolution of oscillatory behavior in age-structured species

A major challenge in ecology is to explain why so many species show oscillatory population dynamics and why the oscillations commonly occur with particular periods. The background environment, through noise or seasonality, is one possible driver of these oscillations, as are the components of the trophic web with which the species interacts. However, the oscillation may also be intrinsic, generated by density-dependent effects on the life history. Models of structured single-species systems indicate that a much broader range of oscillatory behavior than that seen in nature is theoretically possible. We test the hypothesis that it is selection that acts to constrain the range of periods. We analyze a nonlinear single-species matrix model with density dependence affecting reproduction and with trade-offs between reproduction and survival. We show that the evolutionarily stable state is oscillatory and has a period roughly twice the time to maturation, in line with observed patterns of periodicity. The robustness of this result to variations in trade-off function and density dependence is tested

Fitness

The fitness concept of evolutionary ecology differs from that of population genetics. The former is geared towards dealing with long term evolution through the repeated invasion of mutants for potentially complicated ecological scenarios, the latter with short term changes in relative frequencies of types for heavily simplified ecological scenarios. After a discussion of the conditions allowing for the definition of a general invasion fitness concept, among which that reproduction should be clonal, a framework is built within which the definition can be formalized. Recipes are given for calculating (proxies for) fitness in a large variety of instances. The main use of invasion fitness is in ESS calculations. Only under ecologically very special conditions ESSes can be calculated from optimization principles. These conditions are detailed, as well as the, even more special, conditions under which evolution maximizes r or Ro. The invasion fitness concept extends to any aggregates treatable as meta-individuals. Individual- and meta-individual-level invasion fitness coincide when the latter is larger than per capita within aggregate growth. Calculating invasion fitness through a meta-individual route often works beyond calculations based on inclusive fitness arguments, but provides less insight. Mendelian diploids are aggregates of clonally reproducing genes. Conditions are given for when predictions for virtual cloning diploids coincide with those from gene-based calculations