[Journal of The Royal Society Interface, 25 October 2023]

Observations of male alternative reproductive tactics (ARTs) in a variety of species have stimulated the development of mathematical models that can account for the evolution and stable coexistence of multiple male phenotypes. However, little attention has been given to the population dynamic consequences of ARTs. We present a population model that takes account of the existence of two male ARTs (guarders and sneakers), assuming that tactic frequencies are environmentally determined and tactic reproductive success depends on the densities of both types. The presence of sneakers typically increases overall population density. However, if sneakers comprise a sufficiently large proportion of the population—or, equivalently, if guarders are sufficiently rare—then it is possible for the total population to crash to extinction (in this extreme regime, there is also an Allee effect, i.e. a threshold density below which the population will go extinct). We apply the model to the example of the invasive round goby (Neogobius melanostomus). We argue that ARTs can dramatically influence population dynamics and suggest that considering such phenotypic plasticity in population models is potentially important, especially for species of conservation or commercial importance.

[Ecological Modelling, 31 July 2023]

Populations of wild insect pollinators such as bumble bees are threatened worldwide, which compromises pollinator-dependent crop yields. Intentionally planting wildflower patches in agricultural landscapes can support these populations and increase the pollination of nearby crops via the “spillover effect” (i.e., the exporter hypothesis), but may also distract bees from the crops and reduce their pollination via the “Circe principle” (i.e., the aggregation hypothesis). Considering the potentially high costs of these management strategies and the necessity to support wild insect pollinators in the Anthropocene, there is a pressing need to provide simulation tools that can inform best practices for wildflower plantings in agro-ecosystems. We developed a spatially implicit ordinary differential equations (ODEs) model specifically designed to determine the optimal wildflower-to-crop ratio as a function of wildflower patch (i) attractiveness, (ii) nutritional benefits, and (iii) blooming period relative to the crop. The model represents the population dynamics of a bumble bee colony and floral resources (crop and wildflower) in the landscape and nest during one harvesting season. We conduct a full factorial simulation experiment to identify the optimal characteristics of the wildflower patch (i.e., blooming period, attractiveness, relative abundance) that maximise crop yield via the enhancement of the number of bees pollinating crop flowers in a fictional blueberry farm. Our results suggest that providing highly attractive and nutritive wildflower resources before and not during the crop blooming season is the most beneficial strategy. When both flower types are in competition, pollination services can decrease, either when wildflowers are too attractive, or if they provide less benefits to the bees than the crop due to a trade-off between resources quality versus quantity.

Empirical observations and mathematical models show that climate warming can lead to the northern (or, more generally, poleward) spread of host species ranges and their corresponding diseases. Here, we consider an unexpected possibility whereby climate warming facilitates disease spread in the opposite direction to the directional shift in the host species range. To explore this possibility, we consider two host species, both susceptible to a disease, but spatially isolated due to distinct thermal niches, and where prior to climate warming the disease is endemic in the northern species only. Previous theoretical results show that species distributions can lag behind species thermal niches when climate warming occurs. As such, we hypothesize that climate warming may increase the overlap between northern and southern host species ranges, due to the northern species lagging behind its thermal tolerance limit. To test our hypothesis, we simulate climate warming as a reaction-diffusion equation model with a Susceptible-Infected (SI) epidemiological structure, for two competing species with distinct temperature-dependent niches. We show that climate warming, by shifting both species niches northwards, can facilitate the southward spread of disease, due to increased range overlap between the two populations. As our model is general, our findings may apply to viral, bacterial, and prion diseases that do not have thermal tolerance limits and are inextricably linked to their hosts distributions, such as the spread of rabies from arctic to red foxes.

[Mathematical Biosciences and Engineering, 16 May 2023]

Much of the focus of applied dynamical systems is on asymptotic dynamics such as equilibria and periodic solutions. However, in many systems there are transient phenomena, such as temporary population collapses and the honeymoon period after the start of mass vaccination, that can last for a very long time and play an important role in ecological and epidemiological applications. In previous work we defined transient centers which are points in state space that give rise to arbitrarily long and arbitrarily slow transient dynamics. Here we present the mathematical properties of transient centers and provide further insight into these special points. We show that under certain conditions, the entire forward and backward trajectory of a transient center, as well as all its limit points must also be transient centers. We also derive conditions that can be used to verify which points are transient centers and whether those are reachable transient centers. Finally we present examples to demonstrate the utility of the theory, including applications to predatory-prey systems and disease transmission models, and show that the long transience noted in these models are generated by transient centers.

[Diversity and Distributions, 19 December 2022]

Aim: Many freshwater fishes are migrating poleward to more thermally suitable habitats in response to warming climates. In this study, we aimed to identify which freshwater fishes are most sensitive to climatic changes and asked: (i) how fast are lakes warming? (ii) how fast are fishes moving? and (iii) are freshwater fishes tracking climate?

Location: Ontario, Canada.

Methods: We assembled a database containing time series data on climate and species occurrence data from 10,732 lakes between 1986 and 2017. We calculated the rate of lake warming and climate velocity for these lakes. Climate velocities were compared with biotic velocities, specifically the rate at which the northernmost extent of each species shifted north.

Results: Lakes in Ontario warmed by 0.2°C decade−1 on average, at a climate velocity of 9.4 km decade−1 between 1986 and 2017. In response, some freshwater fishes have shifted their northern range boundaries with considerable interspecific variation ranging from species moving southwards at a rate of −58.9 km decade−1 to species ranges moving northwards at a rate of 83.6 km decade−1 over the same time period. More freshwater fish species are moving into northern lakes in Ontario than those being lost. Generally, predators are moving their range edges northwards, whereas prey fishes are being lost from northern lakes.

Main Conclusions: The concurrent loss of cooler refugia, combined with antagonistic competitive and predatory interactions with the range expanding species, has resulted in many commercially important predators moving their range edges northwards, whereas prey species have contracted their northern range edge boundaries. Trophic partitioning of range shifts highlights a previously undocumented observation of the loss of freshwater fishes from lower trophic levels in response to climate-driven migrations.

[Journal of Mathematical Biology, 2 February 2024]

The evolution of mutualism between host and symbiont communities plays an essential role in maintaining ecosystem function and should therefore have a profound effect on their range expansion dynamics. In particular, the presence of mutualistic symbionts at the leading edge of a host-symbiont community should enhance its propagation in space. We develop a theoretical framework that captures the eco-evolutionary dynamics of host-symbiont communities, to investigate how the evolution of resource exchange may shape community structure during range expansion. We consider a community with symbionts that are mutualistic or parasitic to various degrees, where parasitic symbionts receive the same amount of resource from the host as mutualistic symbionts, but at a lower cost. The selective advantage of parasitic symbionts over mutualistic ones is increased with resource availability (i.e. with host density), promoting mutualism at the range edges, where host density is low, and parasitism at the population core, where host density is higher. This spatial selection also influences the speed of spread. We find that the host growth rate (which depends on the average benefit provided by the symbionts) is maximal at the range edges, where symbionts are more mutualistic, and that host-symbiont communities with high symbiont density at their core (e.g. resulting from more mutualistic hosts) spread faster into new territories. These results indicate that the expansion of host-symbiont communities is pulled by the hosts but pushed by the symbionts, in a unique push-pull dynamic where both the host and symbionts are active and tightly-linked players.