The Math of Survival: How Population Models Can Guide African Elephant Conservation

Background

African Savanna elephants (Loxodonta africana) are not just the largest land mammals on Earth; they are also engineers of ecosystems and icons of Africa. Yet, they are endangered. 

African Savanna elephants (Loxodonta africana) are not just the largest land mammals alive today; they are ecosystem engineers and cultural symbols. Their movements carve pathways through forests, spread seeds, and open up landscapes that sustain countless other species. Yet despite their ecological and cultural importance, elephants face an uncertain future.

Since 1979, their range across sub-Saharan Africa has been cut in half, and their population has collapsed. Where there were once millions, today just approximately 40,000-50,000 individuals remain in the wild. The drivers of decline have shifted over time. In the 1970s and 80s, ivory poaching reduced national herds by more than 80%. Though international ivory bans and conservation efforts slowed this loss in some areas, new pressures have emerged: expanding farmland, rapid human population growth, and escalating human-elephant conflict.

Elephants are resilient, but their biology places limits on recovery. Females reproduce slowly, often giving birth only every four to six years after a 22-month pregnancy. Calf mortality is high, especially in the absence of their mothers. For this reason, conservation must be strategic. It is not enough to protect elephants reactively; we need predictive tools that can tell us which interventions will matter most.

Why Modelling Matters

Conservation is often presented as a matter of action on the ground: anti-poaching patrols, wildlife rangers, community programs, and habitat protection. These are vital, but they don’t always tell us what the future looks like. A national park may be secure today, but will it hold enough elephants in 20 years? A rescue centre may rear orphaned calves, but will those individuals change the trajectory of the species?

This is where modelling becomes powerful. Population models act like time machines. They allow us to take today's knowledge about survival and reproduction and project those numbers forward to see into the future. They help us visualise what the numbers actually mean; addressing not just the elephants alive now, but the generations yet to come.

For scientists, models provide a rigorous way to test scenarios without disturbing wild herds. For conservationists and policymakers, they highlight which life stages or threats matter most, ensuring that limited resources are spent where they will have the greatest impact. And for the public, models offer a way of turning abstract statistics into a clear story... if calves survive, elephants survive.

With this in mind, here I set out to use MATLAB modelling combined with ecological data to ask: what does the future look like for elephant populations, and how can we change it?

Building The Population Model

Data Sources

The foundation of the model came from the COMADRE Animal Matrix Database, a global repository of structured population data. For elephants, I drew on a study from Samburu and Buffalo Springs National Reserves in Kenya (1997–1999). These reserves, located in the arid north of the country, have been at the forefront of elephant research for decades, offering rare longitudinal insights into population dynamics.

Model Construction

I built a 26×26 population projection matrix (PPM) that separated individuals by sex and age class. This structure allowed me to incorporate elephants’ distinctive life history traits.

Elephants exhibit slow reproduction.

Female elephants do not reproduce until an average of 14 years of age, and pregnancies last nearly two years.

They have high calf mortality.

Only about 79% of male calves and 84% of female calves survive their first five years.

The model accounted for both survival probabilities (the likelihood of moving from one age class to the next) and fecundity values (the reproductive output of females).

Transition Rate Conversion & MATLAB Implementation

Because the COMADRE dataset was not in a directly usable form, I created a transition rate table mapping survival and reproduction across classes. With the function make.PPM_from_tr(n, tr), I converted this into a working PPM for MATLAB.

MATLAB’s matrix capabilities allowed me to simulate long-term population trajectories, calculate eigenvalues, and perform sensitivity analyses. The dominant eigenvalue (λ) provided the population’s growth rate under current conditions. For the Samburu dataset, λ ≈ 1.2, equivalent to ~20% growth per projection step.

Scenario Testing

I then tested “what if” scenarios, adjusting transition rates to explore the effect of different conservation strategies. The focus was on early survival, since calf mortality is a known limiting factor. My central question was: what changes would be needed to raise λ from 1.2 to 1.3, or from 20% to 30% growth?

Outcome Of The Model

The model produced three key insights.

First, Kenya’s elephants are recovering. While continental populations remain in crisis, Samburu’s elephants showed growth at ~20% per projection step. This reflects decades of investment in conservation, including anti-poaching enforcement, community engagement, and habitat management.

Kenya’s elephant population is set to keep growing. Growth is seen across all female age groups, from calves to older adults, showing how conservation success is reflected not just in overall numbers but in the survival of elephants throughout their lives.

There are clear differences between males and females. Both start out with similar numbers as calves, but over time the male population drops faster. This is partly because young males leave their family herds at around 12-15 years old and must survive on their own. Living alone makes them more vulnerable, and they are also more often targeted by poachers because of their larger tusks. Females, by contrast, remain in the safety of the herd, which helps them survive for longer. This highlights how behaviour and social structure shape survival, and why conservation needs to consider males and females separately.

Second, calves are the demographic bottleneck. Sensitivity analyses showed that calf survival had the greatest influence on long-term growth. To increase population growth from 20% to 30%, survival of elephants aged 0–10 would need to increase by 76%. While such a leap is biologically impossible, the result underscores where conservation matters most.

Finally, the model illustrated the contrast between local and continental trajectories. While Kenya provides a rare success story, elephants across Africa have declined by more than half in just three generations. Without broader adoption of conservation strategies, recovery will remain patchy.

Interpretation Of Results

So what does this mean? Protecting calves and their mothers could be the single most effective way to ensure population recovery. By contrast, attempts to boost reproduction rates are constrained by biology; elephants cannot be made to reproduce faster. This shifts conservation priorities squarely toward survival rather than fecundity.

For conservationists and policymakers, this means focusing resources on interventions that keep calves alive during their first vulnerable years. These might include:

• Strengthening anti-poaching patrols to protect breeding females.

• Expanding habitat connectivity to reduce conflict and allow herds to move freely.

• Supporting orphaned calves through sanctuaries until they can be reintroduced to the wild.

• Using tracking collars to identify hotspots of human-elephant conflict before they escalate.

Kenya’s experience demonstrates that these strategies can work. Since the devastating ivory crisis of the 1970s and 80s, Kenya has invested heavily in conservation, reducing poaching, expanding reserves, and involving local communities in wildlife management. As a result, elephant numbers have stabilised and begun to grow. My modelling projections suggest that if these strategies are maintained, Kenya’s elephant population will continue to increase.

For other African nations, Kenya’s recovery offers a blueprint for success. The precise balance of interventions may differ, but the principle remains the same: protect the youngest and most vulnerable elephants, and the population will have a chance to rebuild.

Conservation Beyond The Numbers

While the model is mathematical, its implications are deeply human. Supporting efforts like land use policies, enforcement of anti-poaching laws, and investment in communities are the choices that will allow the elephant populations to thrive.

As a conservation supporter, you should know elephants can recover, but only if we protect them where it matters most. Supporting organisations that work on the ground, reducing demand for ivory, and advocating for habitat preservation all play a role in shifting the numbers.

It is easy to think of conservation as a fight against decline, but Kenya shows that it can also be a story of resilience and recovery. Modelling gives us a way to see the future not just as hope, but as a realistic outcome if the right steps are taken.

Conclusion

Mathematical models are not abstract exercises; they are tools for making conservation precise. For African elephants, the model uncovered an important insight, if calves and their mothers survive, populations will recover.

By combining ecological data with predictive modelling, we can identify where conservation matters most and act accordingly. Extending strategies that have proven to work across Africa could transform elephants’ trajectory from decline to renewal.

This work shows that conservation is not just about the actions on the ground but also the maths supporting it. Bridging the two allows us to use data to guide action and track the success of conservation campaigns.

References